Daily Papers

We aim to address a significant but understudied problem in the anime industry, namely the inbetweening of cartoon line drawings. Inbetweening involves generating intermediate frames between two black-and-white line drawings and is a time-consuming and expensive process that can benefit from automation. However, existing frame interpolation methods that rely on matching and warping whole raster images are unsuitable for line inbetweening and often produce blurring artifacts that damage the intricate line structures. To preserve the precision and detail of the line drawings, we propose a new approach, AnimeInbet, which geometrizes raster line drawings into graphs of endpoints and reframes the inbetweening task as a graph fusion problem with vertex repositioning. Our method can effectively capture the sparsity and unique structure of line drawings while preserving the details during inbetweening. This is made possible via our novel modules, i.e., vertex geometric embedding, a vertex correspondence Transformer, an effective mechanism for vertex repositioning and a visibility predictor. To train our method, we introduce MixamoLine240, a new dataset of line drawings with ground truth vectorization and matching labels. Our experiments demonstrate that AnimeInbet synthesizes high-quality, clean, and complete intermediate line drawings, outperforming existing methods quantitatively and qualitatively, especially in cases with large motions. Data and code are available at https://github.com/lisiyao21/AnimeInbet.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

Category-level 3D pose estimation is a fundamentally important problem in computer vision and robotics, e.g. for embodied agents or to train 3D generative models. However, so far methods that estimate the category-level object pose require either large amounts of human annotations, CAD models or input from RGB-D sensors. In contrast, we tackle the problem of learning to estimate the category-level 3D pose only from casually taken object-centric videos without human supervision. We propose a two-step pipeline: First, we introduce a multi-view alignment procedure that determines canonical camera poses across videos with a novel and robust cyclic distance formulation for geometric and appearance matching using reconstructed coarse meshes and DINOv2 features. In a second step, the canonical poses and reconstructed meshes enable us to train a model for 3D pose estimation from a single image. In particular, our model learns to estimate dense correspondences between images and a prototypical 3D template by predicting, for each pixel in a 2D image, a feature vector of the corresponding vertex in the template mesh. We demonstrate that our method outperforms all baselines at the unsupervised alignment of object-centric videos by a large margin and provides faithful and robust predictions in-the-wild. Our code and data is available at https://github.com/GenIntel/uns-obj-pose3d.

In this work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e., humans), often with significant manual work involved. However, scaling the geometry understanding to all objects in nature requires more automated approaches that can also express correspondences between related, but geometrically different objects. To this end, we propose a new, learnable image-based representation of dense correspondences. Our model predicts, for each pixel in a 2D image, an embedding vector of the corresponding vertex in the object mesh, therefore establishing dense correspondences between image pixels and 3D object geometry. We demonstrate that the proposed approach performs on par or better than the state-of-the-art methods for dense pose estimation for humans, while being conceptually simpler. We also collect a new in-the-wild dataset of dense correspondences for animal classes and demonstrate that our framework scales naturally to the new deformable object categories.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.

This paper proposes a simple self-supervised approach for learning a representation for visual correspondence from raw video. We cast correspondence as prediction of links in a space-time graph constructed from video. In this graph, the nodes are patches sampled from each frame, and nodes adjacent in time can share a directed edge. We learn a representation in which pairwise similarity defines transition probability of a random walk, so that long-range correspondence is computed as a walk along the graph. We optimize the representation to place high probability along paths of similarity. Targets for learning are formed without supervision, by cycle-consistency: the objective is to maximize the likelihood of returning to the initial node when walking along a graph constructed from a palindrome of frames. Thus, a single path-level constraint implicitly supervises chains of intermediate comparisons. When used as a similarity metric without adaptation, the learned representation outperforms the self-supervised state-of-the-art on label propagation tasks involving objects, semantic parts, and pose. Moreover, we demonstrate that a technique we call edge dropout, as well as self-supervised adaptation at test-time, further improve transfer for object-centric correspondence.

We present a new generalizable NeRF method that is able to directly generalize to new unseen scenarios and perform novel view synthesis with as few as two source views. The key to our approach lies in the explicitly modeled correspondence matching information, so as to provide the geometry prior to the prediction of NeRF color and density for volume rendering. The explicit correspondence matching is quantified with the cosine similarity between image features sampled at the 2D projections of a 3D point on different views, which is able to provide reliable cues about the surface geometry. Unlike previous methods where image features are extracted independently for each view, we consider modeling the cross-view interactions via Transformer cross-attention, which greatly improves the feature matching quality. Our method achieves state-of-the-art results on different evaluation settings, with the experiments showing a strong correlation between our learned cosine feature similarity and volume density, demonstrating the effectiveness and superiority of our proposed method. Code is at https://github.com/donydchen/matchnerf

We propose a novel zero-shot approach to computing correspondences between 3D shapes. Existing approaches mainly focus on isometric and near-isometric shape pairs (e.g., human vs. human), but less attention has been given to strongly non-isometric and inter-class shape matching (e.g., human vs. cow). To this end, we introduce a fully automatic method that exploits the exceptional reasoning capabilities of recent foundation models in language and vision to tackle difficult shape correspondence problems. Our approach comprises multiple stages. First, we classify the 3D shapes in a zero-shot manner by feeding rendered shape views to a language-vision model (e.g., BLIP2) to generate a list of class proposals per shape. These proposals are unified into a single class per shape by employing the reasoning capabilities of ChatGPT. Second, we attempt to segment the two shapes in a zero-shot manner, but in contrast to the co-segmentation problem, we do not require a mutual set of semantic regions. Instead, we propose to exploit the in-context learning capabilities of ChatGPT to generate two different sets of semantic regions for each shape and a semantic mapping between them. This enables our approach to match strongly non-isometric shapes with significant differences in geometric structure. Finally, we employ the generated semantic mapping to produce coarse correspondences that can further be refined by the functional maps framework to produce dense point-to-point maps. Our approach, despite its simplicity, produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes.

In this paper, we study a novel and widely existing problem in graph matching (GM), namely, Bi-level Noisy Correspondence (BNC), which refers to node-level noisy correspondence (NNC) and edge-level noisy correspondence (ENC). In brief, on the one hand, due to the poor recognizability and viewpoint differences between images, it is inevitable to inaccurately annotate some keypoints with offset and confusion, leading to the mismatch between two associated nodes, i.e., NNC. On the other hand, the noisy node-to-node correspondence will further contaminate the edge-to-edge correspondence, thus leading to ENC. For the BNC challenge, we propose a novel method termed Contrastive Matching with Momentum Distillation. Specifically, the proposed method is with a robust quadratic contrastive loss which enjoys the following merits: i) better exploring the node-to-node and edge-to-edge correlations through a GM customized quadratic contrastive learning paradigm; ii) adaptively penalizing the noisy assignments based on the confidence estimated by the momentum teacher. Extensive experiments on three real-world datasets show the robustness of our model compared with 12 competitive baselines. The code is available at https://github.com/XLearning-SCU/2023-ICCV-COMMON.

A Neural Radiance Field (NeRF) encodes the specific relation of 3D geometry and appearance of a scene. We here ask the question whether we can transfer the appearance from a source NeRF onto a target 3D geometry in a semantically meaningful way, such that the resulting new NeRF retains the target geometry but has an appearance that is an analogy to the source NeRF. To this end, we generalize classic image analogies from 2D images to NeRFs. We leverage correspondence transfer along semantic affinity that is driven by semantic features from large, pre-trained 2D image models to achieve multi-view consistent appearance transfer. Our method allows exploring the mix-and-match product space of 3D geometry and appearance. We show that our method outperforms traditional stylization-based methods and that a large majority of users prefer our method over several typical baselines.

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving beyond traditional hand-crafted and data-driven feature learning methods, we incorporate spectral methods with deep learning, focusing on functional maps (FMs) and optimal transport (OT). Traditional OT-based approaches, often reliant on entropy regularization OT in learning-based framework, face computational challenges due to their quadratic cost. Our key contribution is to employ the sliced Wasserstein distance (SWD) for OT, which is a valid fast optimal transport metric in an unsupervised shape matching framework. This unsupervised framework integrates functional map regularizers with a novel OT-based loss derived from SWD, enhancing feature alignment between shapes treated as discrete probability measures. We also introduce an adaptive refinement process utilizing entropy regularized OT, further refining feature alignments for accurate point-to-point correspondences. Our method demonstrates superior performance in non-rigid shape matching, including near-isometric and non-isometric scenarios, and excels in downstream tasks like segmentation transfer. The empirical results on diverse datasets highlight our framework's effectiveness and generalization capabilities, setting new standards in non-rigid shape matching with efficient OT metrics and an adaptive refinement module.

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.

Feature-based image matching has extensive applications in computer vision. Keypoints detected in images can be naturally represented as graph structures, and Graph Neural Networks (GNNs) have been shown to outperform traditional deep learning techniques. Consequently, the paradigm of image matching via GNNs has gained significant prominence in recent academic research. In this paper, we first introduce an innovative adaptive graph construction method that utilizes a filtering mechanism based on distance and dynamic threshold similarity. This method dynamically adjusts the criteria for incorporating new vertices based on the characteristics of existing vertices, allowing for the construction of more precise and robust graph structures while avoiding redundancy. We further combine the vertex processing capabilities of GNNs with the global awareness capabilities of Transformers to enhance the model's representation of spatial and feature information within graph structures. This hybrid model provides a deeper understanding of the interrelationships between vertices and their contributions to the matching process. Additionally, we employ the Sinkhorn algorithm to iteratively solve for optimal matching results. Finally, we validate our system using extensive image datasets and conduct comprehensive comparative experiments. Experimental results demonstrate that our system achieves an average improvement of 3.8x-40.3x in overall matching performance. Additionally, the number of vertices and edges significantly impacts training efficiency and memory usage; therefore, we employ multi-GPU technology to accelerate the training process. Our code is available at https://github.com/songxf1024/GIMS.

We consider the problem of source-free unsupervised category-level pose estimation from only RGB images to a target domain without any access to source domain data or 3D annotations during adaptation. Collecting and annotating real-world 3D data and corresponding images is laborious, expensive, yet unavoidable process, since even 3D pose domain adaptation methods require 3D data in the target domain. We introduce 3DUDA, a method capable of adapting to a nuisance-ridden target domain without 3D or depth data. Our key insight stems from the observation that specific object subparts remain stable across out-of-domain (OOD) scenarios, enabling strategic utilization of these invariant subcomponents for effective model updates. We represent object categories as simple cuboid meshes, and harness a generative model of neural feature activations modeled at each mesh vertex learnt using differential rendering. We focus on individual locally robust mesh vertex features and iteratively update them based on their proximity to corresponding features in the target domain even when the global pose is not correct. Our model is then trained in an EM fashion, alternating between updating the vertex features and the feature extractor. We show that our method simulates fine-tuning on a global pseudo-labeled dataset under mild assumptions, which converges to the target domain asymptotically. Through extensive empirical validation, including a complex extreme UDA setup which combines real nuisances, synthetic noise, and occlusion, we demonstrate the potency of our simple approach in addressing the domain shift challenge and significantly improving pose estimation accuracy.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Computer vision has long relied on two kinds of correspondences: pixel correspondences in images and 3D correspondences on object surfaces. Is there another kind, and if there is, what can they do for us? In this paper, we introduce correspondences of the third kind we call reflection correspondences and show that they can help estimate camera pose by just looking at objects without relying on the background. Reflection correspondences are point correspondences in the reflected world, i.e., the scene reflected by the object surface. The object geometry and reflectance alters the scene geometrically and radiometrically, respectively, causing incorrect pixel correspondences. Geometry recovered from each image is also hampered by distortions, namely generalized bas-relief ambiguity, leading to erroneous 3D correspondences. We show that reflection correspondences can resolve the ambiguities arising from these distortions. We introduce a neural correspondence estimator and a RANSAC algorithm that fully leverages all three kinds of correspondences for robust and accurate joint camera pose and object shape estimation just from the object appearance. The method expands the horizon of numerous downstream tasks, including camera pose estimation for appearance modeling (e.g., NeRF) and motion estimation of reflective objects (e.g., cars on the road), to name a few, as it relieves the requirement of overlapping background.

3D pose transfer is a challenging generation task that aims to transfer the pose of a source geometry onto a target geometry with the target identity preserved. Many prior methods require keypoint annotations to find correspondence between the source and target. Current pose transfer methods allow end-to-end correspondence learning but require the desired final output as ground truth for supervision. Unsupervised methods have been proposed for graph convolutional models but they require ground truth correspondence between the source and target inputs. We present a novel self-supervised framework for 3D pose transfer which can be trained in unsupervised, semi-supervised, or fully supervised settings without any correspondence labels. We introduce two contrastive learning constraints in the latent space: a mesh-level loss for disentangling global patterns including pose and identity, and a point-level loss for discriminating local semantics. We demonstrate quantitatively and qualitatively that our method achieves state-of-the-art results in supervised 3D pose transfer, with comparable results in unsupervised and semi-supervised settings. Our method is also generalisable to unseen human and animal data with complex topologies.

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

Unified visual grounding pursues a simple and generic technical route to leverage multi-task data with less task-specific design. The most advanced methods typically present boxes and masks as vertex sequences to model referring detection and segmentation as an autoregressive sequential vertex generation paradigm. However, generating high-dimensional vertex sequences sequentially is error-prone because the upstream of the sequence remains static and cannot be refined based on downstream vertex information, even if there is a significant location gap. Besides, with limited vertexes, the inferior fitting of objects with complex contours restricts the performance upper bound. To deal with this dilemma, we propose a parallel vertex generation paradigm for superior high-dimension scalability with a diffusion model by simply modifying the noise dimension. An intuitive materialization of our paradigm is Parallel Vertex Diffusion (PVD) to directly set vertex coordinates as the generation target and use a diffusion model to train and infer. We claim that it has two flaws: (1) unnormalized coordinate caused a high variance of loss value; (2) the original training objective of PVD only considers point consistency but ignores geometry consistency. To solve the first flaw, Center Anchor Mechanism (CAM) is designed to convert coordinates as normalized offset values to stabilize the training loss value. For the second flaw, Angle summation loss (ASL) is designed to constrain the geometry difference of prediction and ground truth vertexes for geometry-level consistency. Empirical results show that our PVD achieves state-of-the-art in both referring detection and segmentation, and our paradigm is more scalable and efficient than sequential vertex generation with high-dimension data.

We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to previous techniques and presents better generalization capabilities. Until now, two main approaches have been suggested for the dense correspondence problem. The first is a spectral-based approach that obtains great results on synthetic datasets but requires mesh connectivity of the shapes and long inference processing time while being unstable in real-world scenarios. The second is a spatial approach that uses an encoder-decoder framework to regress an ordered point cloud for the matching alignment from an irregular input. Unfortunately, the decoder brings considerable disadvantages, as it requires a large amount of training data and struggles to generalize well in cross-dataset evaluations. DPC's novelty lies in its lack of a decoder component. Instead, we use latent similarity and the input coordinates themselves to construct the point cloud and determine correspondence, replacing the coordinate regression done by the decoder. Extensive experiments show that our construction scheme leads to a performance boost in comparison to recent state-of-the-art correspondence methods. Our code is publicly available at https://github.com/dvirginz/DPC.

Learning a good representation for space-time correspondence is the key for various computer vision tasks, including tracking object bounding boxes and performing video object pixel segmentation. To learn generalizable representation for correspondence in large-scale, a variety of self-supervised pretext tasks are proposed to explicitly perform object-level or patch-level similarity learning. Instead of following the previous literature, we propose to learn correspondence using Video Frame-level Similarity (VFS) learning, i.e, simply learning from comparing video frames. Our work is inspired by the recent success in image-level contrastive learning and similarity learning for visual recognition. Our hypothesis is that if the representation is good for recognition, it requires the convolutional features to find correspondence between similar objects or parts. Our experiments show surprising results that VFS surpasses state-of-the-art self-supervised approaches for both OTB visual object tracking and DAVIS video object segmentation. We perform detailed analysis on what matters in VFS and reveals new properties on image and frame level similarity learning. Project page with code is available at https://jerryxu.net/VFS

Multi-view diffusion models have recently emerged as a powerful paradigm for novel view synthesis, yet the underlying mechanism that enables their view-consistency remains unclear. In this work, we first verify that the attention maps of these models acquire geometric correspondence throughout training, attending to the geometrically corresponding regions across reference and target views for view-consistent generation. However, this correspondence signal remains incomplete, with its accuracy degrading under large viewpoint changes. Building on these findings, we introduce CAMEO, a simple yet effective training technique that directly supervises attention maps using geometric correspondence to enhance both the training efficiency and generation quality of multi-view diffusion models. Notably, supervising a single attention layer is sufficient to guide the model toward learning precise correspondences, thereby preserving the geometry and structure of reference images, accelerating convergence, and improving novel view synthesis performance. CAMEO reduces the number of training iterations required for convergence by half while achieving superior performance at the same iteration counts. We further demonstrate that CAMEO is model-agnostic and can be applied to any multi-view diffusion model.

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Semantic correspondence methods have advanced to obtaining high-quality correspondences employing complicated networks, aiming to maximize the model capacity. However, despite the performance improvements, they may remain constrained by the scarcity of training keypoint pairs, a consequence of the limited training images and the sparsity of keypoints. This paper builds on the hypothesis that there is an inherent data-hungry matter in learning semantic correspondences and uncovers the models can be more trained by employing densified training pairs. We demonstrate a simple machine annotator reliably enriches paired key points via machine supervision, requiring neither extra labeled key points nor trainable modules from unlabeled images. Consequently, our models surpass current state-of-the-art models on semantic correspondence learning benchmarks like SPair-71k, PF-PASCAL, and PF-WILLOW and enjoy further robustness on corruption benchmarks. Our code is available at https://github.com/naver-ai/matchme.

Line segments are powerful features complementary to points. They offer structural cues, robust to drastic viewpoint and illumination changes, and can be present even in texture-less areas. However, describing and matching them is more challenging compared to points due to partial occlusions, lack of texture, or repetitiveness. This paper introduces a new matching paradigm, where points, lines, and their descriptors are unified into a single wireframe structure. We propose GlueStick, a deep matching Graph Neural Network (GNN) that takes two wireframes from different images and leverages the connectivity information between nodes to better glue them together. In addition to the increased efficiency brought by the joint matching, we also demonstrate a large boost of performance when leveraging the complementary nature of these two features in a single architecture. We show that our matching strategy outperforms the state-of-the-art approaches independently matching line segments and points for a wide variety of datasets and tasks. The code is available at https://github.com/cvg/GlueStick.

We study graph data augmentation by mixup, which has been used successfully on images. A key operation of mixup is to compute a convex combination of a pair of inputs. This operation is straightforward for grid-like data, such as images, but challenging for graph data. The key difficulty lies in the fact that different graphs typically have different numbers of nodes, and thus there lacks a node-level correspondence between graphs. In this work, we propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments. Specifically, given a pair of graphs, we explicitly obtain node-level correspondence via computing a soft assignment matrix to match the nodes between two graphs. Based on the soft assignments, we transform the adjacency and node feature matrices of one graph, so that the transformed graph is aligned with the other graph. In this way, any pair of graphs can be mixed directly to generate an augmented graph. We conduct systematic experiments to show that S-Mixup can improve the performance and generalization of graph neural networks (GNNs) on various graph classification tasks. In addition, we show that S-Mixup can increase the robustness of GNNs against noisy labels.

Unsupervised learning of 3D-aware generative adversarial networks has lately made much progress. Some recent work demonstrates promising results of learning human generative models using neural articulated radiance fields, yet their generalization ability and controllability lag behind parametric human models, i.e., they do not perform well when generalizing to novel pose/shape and are not part controllable. To solve these problems, we propose VeRi3D, a generative human vertex-based radiance field parameterized by vertices of the parametric human template, SMPL. We map each 3D point to the local coordinate system defined on its neighboring vertices, and use the corresponding vertex feature and local coordinates for mapping it to color and density values. We demonstrate that our simple approach allows for generating photorealistic human images with free control over camera pose, human pose, shape, as well as enabling part-level editing.

While pre-trained large-scale vision models have shown significant promise for semantic correspondence, their features often struggle to grasp the geometry and orientation of instances. This paper identifies the importance of being geometry-aware for semantic correspondence and reveals a limitation of the features of current foundation models under simple post-processing. We show that incorporating this information can markedly enhance semantic correspondence performance with simple but effective solutions in both zero-shot and supervised settings. We also construct a new challenging benchmark for semantic correspondence built from an existing animal pose estimation dataset, for both pre-training validating models. Our method achieves a [email protected] score of 65.4 (zero-shot) and 85.6 (supervised) on the challenging SPair-71k dataset, outperforming the state of the art by 5.5p and 11.0p absolute gains, respectively. Our code and datasets are publicly available at: https://telling-left-from-right.github.io/.

Semantic correspondence, the task of determining relationships between different parts of images, underpins various applications including 3D reconstruction, image-to-image translation, object tracking, and visual place recognition. Recent studies have begun to explore representations learned in large generative image models for semantic correspondence, demonstrating promising results. Building on this progress, current state-of-the-art methods rely on combining multiple large models, resulting in high computational demands and reduced efficiency. In this work, we address this challenge by proposing a more computationally efficient approach. We propose a novel knowledge distillation technique to overcome the problem of reduced efficiency. We show how to use two large vision foundation models and distill the capabilities of these complementary models into one smaller model that maintains high accuracy at reduced computational cost. Furthermore, we demonstrate that by incorporating 3D data, we are able to further improve performance, without the need for human-annotated correspondences. Overall, our empirical results demonstrate that our distilled model with 3D data augmentation achieves performance superior to current state-of-the-art methods while significantly reducing computational load and enhancing practicality for real-world applications, such as semantic video correspondence. Our code and weights are publicly available on our project page.

Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

For a graph G with n vertices and m edges, Lin et al. Lin define the atom--bond sum-connectivity (ABS) matrix of G such that the (i,j)^{th} entry is \[ 1 - \frac{2{d_i + d_j}} \] if vertex v_i is adjacent to the vertex v_j, and 0 otherwise. In this article, we determine the characteristic polynomial of the ABS matrix for certain specific classes of graphs. Furthermore, we compute the ABS eigenvalues and the ABS energy for these classes.

For any {rm E}-rigid presentation e, we construct an orthogonal projection functor to {rm rep}(e^perp) left adjoint to the natural embedding. We establish a bijection between presentations in {rm rep}(e^perp) and presentations compatible with e. For quivers with potentials, we show that {rm rep}(e^perp) forms a module category of another quiver with potential. We derive mutation formulas for the delta-vectors of positive and negative complements and the dimension vectors of simple modules in {rm rep}(e^perp), enabling an algorithm to find the projected quiver with potential. Additionally, we introduce a modified projection for quivers with potentials that preserves general presentations. For applications to cluster algebras, we establish a connection to the stabilization functors.

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests refactoring them into a unified design space for graph matching networks. Existing methods occupy only a few isolated patches in this space, which remains largely uncharted. We undertake the first comprehensive exploration of this space, featuring such axes as attention-based vs. soft permutation-based interaction between query and corpus graphs, aligning nodes vs. edges, and the form of the final scoring network that integrates neural representations of the graphs. Our extensive experiments reveal that judicious and hitherto-unexplored combinations of choices in this space lead to large performance benefits. Beyond better performance, our study uncovers valuable insights and establishes general design principles for neural graph representation and interaction, which may be of wider interest.

Animating virtual avatars with free-view control is crucial for various applications like virtual reality and digital entertainment. Previous studies have attempted to utilize the representation power of the neural radiance field (NeRF) to reconstruct the human body from monocular videos. Recent works propose to graft a deformation network into the NeRF to further model the dynamics of the human neural field for animating vivid human motions. However, such pipelines either rely on pose-dependent representations or fall short of motion coherency due to frame-independent optimization, making it difficult to generalize to unseen pose sequences realistically. In this paper, we propose a novel framework MonoHuman, which robustly renders view-consistent and high-fidelity avatars under arbitrary novel poses. Our key insight is to model the deformation field with bi-directional constraints and explicitly leverage the off-the-peg keyframe information to reason the feature correlations for coherent results. Specifically, we first propose a Shared Bidirectional Deformation module, which creates a pose-independent generalizable deformation field by disentangling backward and forward deformation correspondences into shared skeletal motion weight and separate non-rigid motions. Then, we devise a Forward Correspondence Search module, which queries the correspondence feature of keyframes to guide the rendering network. The rendered results are thus multi-view consistent with high fidelity, even under challenging novel pose settings. Extensive experiments demonstrate the superiority of our proposed MonoHuman over state-of-the-art methods.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

Estimating the 6-DoF pose of a rigid object from a single RGB image is a crucial yet challenging task. Recent studies have shown the great potential of dense correspondence-based solutions, yet improvements are still needed to reach practical deployment. In this paper, we propose a novel pose estimation algorithm named CheckerPose, which improves on three main aspects. Firstly, CheckerPose densely samples 3D keypoints from the surface of the 3D object and finds their 2D correspondences progressively in the 2D image. Compared to previous solutions that conduct dense sampling in the image space, our strategy enables the correspondence searching in a 2D grid (i.e., pixel coordinate). Secondly, for our 3D-to-2D correspondence, we design a compact binary code representation for 2D image locations. This representation not only allows for progressive correspondence refinement but also converts the correspondence regression to a more efficient classification problem. Thirdly, we adopt a graph neural network to explicitly model the interactions among the sampled 3D keypoints, further boosting the reliability and accuracy of the correspondences. Together, these novel components make CheckerPose a strong pose estimation algorithm. When evaluated on the popular Linemod, Linemod-O, and YCB-V object pose estimation benchmarks, CheckerPose clearly boosts the accuracy of correspondence-based methods and achieves state-of-the-art performances. Code is available at https://github.com/RuyiLian/CheckerPose.

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

Let L denote the Laplacian matrix of a graph G. We study continuous quantum walks on G defined by the transition matrix U(t)=expleft(itLright). The initial state is of the pair state form, e_a-e_b with a,b being any two vertices of G. We provide two ways to construct infinite families of graphs that have perfect pair transfer. We study a "transitivity" phenomenon which cannot occur in vertex state transfer. We characterize perfect pair state transfer on paths and cycles. We also study the case when quantum walks are generated by the unsigned Laplacians of underlying graphs and the initial states are of the plus state form, e_a+e_b. When the underlying graphs are bipartite, plus state transfer is equivalent to pair state transfer.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Representation learning on text-attributed graphs (TAGs) integrates structural connectivity with rich textual semantics, enabling applications in diverse domains. Current methods largely rely on contrastive learning to maximize cross-modal similarity, assuming tighter coupling between graph and text representations improves transfer performance. However, our empirical analysis reveals that both natural gap expansion and forced gap reduction result in performance degradation by disrupting pre-trained knowledge structures and impairing generalization. This arises from the geometric incompatibility between encoders, where graph encoders capture topological patterns, while text encoders capture semantic structures. Over-alignment compresses these distinct spaces into shared subspaces, causing structure collapse that diminishes both topological reasoning and semantic understanding. We propose LLM4GTA, a gap-aware alignment framework that preserves representation gaps as geometric necessities for maintaining modality-specific knowledge and improving transfer performance. LLM4GTA includes an adaptive gap preservation module to prevent over-alignment by monitoring similarity evolution and an intra-modal compensation mechanism that boosts discriminative power using auxiliary classifiers in graph space. Extensive experiments show significant improvements over existing methods in zero-shot and few-shot scenarios.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

Processing information on 3D objects requires methods stable to rigid-body transformations, in particular rotations, of the input data. In image processing tasks, convolutional neural networks achieve this property using rotation-equivariant operations. However, contrary to images, graphs generally have irregular topology. This makes it challenging to define a rotation-equivariant convolution operation on these structures. In this work, we propose Spherical Graph Convolutional Network (S-GCN) that processes 3D models of proteins represented as molecular graphs. In a protein molecule, individual amino acids have common topological elements. This allows us to unambiguously associate each amino acid with a local coordinate system and construct rotation-equivariant spherical filters that operate on angular information between graph nodes. Within the framework of the protein model quality assessment problem, we demonstrate that the proposed spherical convolution method significantly improves the quality of model assessment compared to the standard message-passing approach. It is also comparable to state-of-the-art methods, as we demonstrate on Critical Assessment of Structure Prediction (CASP) benchmarks. The proposed technique operates only on geometric features of protein 3D models. This makes it universal and applicable to any other geometric-learning task where the graph structure allows constructing local coordinate systems.

Obtaining personalized 3D animatable avatars from a monocular camera has several real world applications in gaming, virtual try-on, animation, and VR/XR, etc. However, it is very challenging to model dynamic and fine-grained clothing deformations from such sparse data. Existing methods for modeling 3D humans from depth data have limitations in terms of computational efficiency, mesh coherency, and flexibility in resolution and topology. For instance, reconstructing shapes using implicit functions and extracting explicit meshes per frame is computationally expensive and cannot ensure coherent meshes across frames. Moreover, predicting per-vertex deformations on a pre-designed human template with a discrete surface lacks flexibility in resolution and topology. To overcome these limitations, we propose a novel method `\keyfeature: Neural Surface Fields' for modeling 3D clothed humans from monocular depth. NSF defines a neural field solely on the base surface which models a continuous and flexible displacement field. NSF can be adapted to the base surface with different resolution and topology without retraining at inference time. Compared to existing approaches, our method eliminates the expensive per-frame surface extraction while maintaining mesh coherency, and is capable of reconstructing meshes with arbitrary resolution without retraining. To foster research in this direction, we release our code in project page at: https://yuxuan-xue.com/nsf.

Establishing dense correspondence between two images is a fundamental computer vision problem, which is typically tackled by matching local feature descriptors. However, without global awareness, such local features are often insufficient for disambiguating similar regions. And computing the pairwise feature correlation across images is both computation-expensive and memory-intensive. To make the local features aware of the global context and improve their matching accuracy, we introduce DenseGAP, a new solution for efficient Dense correspondence learning with a Graph-structured neural network conditioned on Anchor Points. Specifically, we first propose a graph structure that utilizes anchor points to provide sparse but reliable prior on inter- and intra-image context and propagates them to all image points via directed edges. We also design a graph-structured network to broadcast multi-level contexts via light-weighted message-passing layers and generate high-resolution feature maps at low memory cost. Finally, based on the predicted feature maps, we introduce a coarse-to-fine framework for accurate correspondence prediction using cycle consistency. Our feature descriptors capture both local and global information, thus enabling a continuous feature field for querying arbitrary points at high resolution. Through comprehensive ablative experiments and evaluations on large-scale indoor and outdoor datasets, we demonstrate that our method advances the state-of-the-art of correspondence learning on most benchmarks.

Dense contrastive representation learning (DCRL) has greatly improved the learning efficiency for image-dense prediction tasks, showing its great potential to reduce the large costs of medical image collection and dense annotation. However, the properties of medical images make unreliable correspondence discovery, bringing an open problem of large-scale false positive and negative (FP&N) pairs in DCRL. In this paper, we propose GEoMetric vIsual deNse sImilarity (GEMINI) learning which embeds the homeomorphism prior to DCRL and enables a reliable correspondence discovery for effective dense contrast. We propose a deformable homeomorphism learning (DHL) which models the homeomorphism of medical images and learns to estimate a deformable mapping to predict the pixels' correspondence under topological preservation. It effectively reduces the searching space of pairing and drives an implicit and soft learning of negative pairs via a gradient. We also propose a geometric semantic similarity (GSS) which extracts semantic information in features to measure the alignment degree for the correspondence learning. It will promote the learning efficiency and performance of deformation, constructing positive pairs reliably. We implement two practical variants on two typical representation learning tasks in our experiments. Our promising results on seven datasets which outperform the existing methods show our great superiority. We will release our code on a companion link: https://github.com/YutingHe-list/GEMINI.

Modeling the hand-object (HO) interaction not only requires estimation of the HO pose, but also pays attention to the contact due to their interaction. Significant progress has been made in estimating hand and object separately with deep learning methods, simultaneous HO pose estimation and contact modeling has not yet been fully explored. In this paper, we present an explicit contact representation namely Contact Potential Field (CPF), and a learning-fitting hybrid framework namely MIHO to Modeling the Interaction of Hand and Object. In CPF, we treat each contacting HO vertex pair as a spring-mass system. Hence the whole system forms a potential field with minimal elastic energy at the grasp position. Extensive experiments on the two commonly used benchmarks have demonstrated that our method can achieve state-of-the-art in several reconstruction metrics, and allow us to produce more physically plausible HO pose even when the ground-truth exhibits severe interpenetration or disjointedness. Our code is available at https://github.com/lixiny/CPF.

3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do not generalize well to articulated objects in the wild. We treat an articulated object as an unknown, semi-rigid skeletal structure surrounded by nonrigid material (e.g., skin). Our method simultaneously estimates the visible (explicit) representation (3D shapes, colors, camera parameters) and the implicit skeletal representation, from motion cues in the object video without 3D supervision. Our implicit representation consists of four parts. (1) Skeleton, which specifies how semi-rigid parts are connected. (2) black{Skinning Weights}, which associates each surface vertex with semi-rigid parts with probability. (3) Rigidity Coefficients, specifying the articulation of the local surface. (4) Time-Varying Transformations, which specify the skeletal motion and surface deformation parameters. We introduce an algorithm that uses physical constraints as regularization terms and iteratively estimates both implicit and explicit representations. Our method is category-agnostic, thus eliminating the need for category-specific skeletons, we show that our method outperforms state-of-the-art across standard video datasets.

The Berge-Fulkerson conjecture states that every bridgeless cubic graph can be covered with six perfect matchings such that each edge is covered exactly twice. An equivalent reformulation is that it's possible to find a 6-cycle 4-cover. In this paper we discuss the oriented version (o6c4c) of the latter statement, pose it as a conjecture and prove it for the family of Isaacs flower snarks. Similarly to the case of oriented cycle double cover, we can always construct an orientable surface (possibly with boundary) from an o6c4c solution. If the o6c4c solution itself splits into two (not necessarily oriented) cycle double covers, then it's also possible to build another pair of orientable surfaces (also possibly with boundaries). Finally we show how to build a ribbon graph, and for some special o6c4c cases we show that this ribbon graph corresponds to an oriented 6-cycle double cover. Github: https://github.com/gexahedron/cycle-double-covers

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and M\"obius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8\% improvement on heterophilic graphs and 8.4\% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

We introduce an inference-time scene optimization algorithm utilizing triangle soup, a collection of disconnected translucent triangle primitives, as the representation for the geometry and appearance of a scene. Unlike full-rank Gaussian kernels, triangles are a natural, locally-flat proxy for surfaces that can be connected to achieve highly complex geometry. When coupled with per-vertex Spherical Harmonics (SH), triangles provide a rich visual representation without incurring an expensive increase in primitives. We leverage our new representation to incorporate optimization objectives and enforce spatial regularization directly on the underlying primitives. The main differentiator of our approach is the definition and enforcement of soft connectivity forces between triangles during optimization, encouraging explicit, but soft, surface continuity in 3D. Experiments on representative 3D reconstruction and novel view synthesis datasets show improvements in geometric accuracy compared to current state-of-the-art algorithms without sacrificing visual fidelity.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

Let V be a highest weight module over a Kac-Moody algebra g, and let conv V denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv V, i.e. we completely classify the faces and their inclusions. In the special case where g is semisimple, this brings closure to a question studied by Cellini-Marietti [IMRN 2015] for the adjoint representation, and by Khare [J. Algebra 2016; Trans. Amer. Math. Soc. 2017] for most modules. The determination of faces of finite-dimensional modules up to the Weyl group action and some of their inclusions also appears in previous work of Satake [Ann. of Math. 1960], Borel-Tits [IHES Publ. Math. 1965], Vinberg [Izv. Akad. Nauk 1990], and Casselman [Austral. Math. Soc. 1997]. For any subset of the simple roots, we introduce a remarkable convex cone which we call the universal Weyl polyhedron, which controls the convex hulls of all modules parabolically induced from the corresponding Levi factor. Namely, the combinatorial isomorphism type of the cone stores the classification of faces for all such highest weight modules, as well as how faces degenerate as the highest weight gets increasingly singular. To our knowledge, this cone is new in finite and infinite type. We further answer a question of Michel Brion, by showing that the localization of conv V along a face is always the convex hull of the weights of a parabolically induced module. Finally, as we determine the inclusion relations between faces representation-theoretically from the set of weights, without recourse to convexity, we answer a similar question for highest weight modules over symmetrizable quantum groups.

The Boundary representation (B-rep) format is the de-facto shape representation in computer-aided design (CAD) to model solid and sheet objects. Recent approaches to generating CAD models have focused on learning sketch-and-extrude modeling sequences that are executed by a solid modeling kernel in postprocess to recover a B-rep. In this paper we present a new approach that enables learning from and synthesizing B-reps without the need for supervision through CAD modeling sequence data. Our method SolidGen, is an autoregressive neural network that models the B-rep directly by predicting the vertices, edges, and faces using Transformer-based and pointer neural networks. Key to achieving this is our Indexed Boundary Representation that references B-rep vertices, edges and faces in a well-defined hierarchy to capture the geometric and topological relations suitable for use with machine learning. SolidGen can be easily conditioned on contexts e.g., class labels, images, and voxels thanks to its probabilistic modeling of the B-rep distribution. We demonstrate qualitatively, quantitatively, and through perceptual evaluation by human subjects that SolidGen can produce high quality, realistic CAD models.

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be SO(3) equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the SO(3) convolutions or tensor products to mathematically equivalent convolutions in SO(2) . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from O(L^6) to O(L^3), where L is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

This paper introduces a method for simplifying textured surface triangle meshes in the wild while maintaining high visual quality. While previous methods achieve excellent results on manifold meshes by using the quadric error metric, they struggle to produce high-quality outputs for meshes in the wild, which typically contain non-manifold elements and multiple connected components. In this work, we propose a method for simplifying these wild textured triangle meshes. We formulate mesh simplification as a problem of decimating simplicial 2-complexes to handle multiple non-manifold mesh components collectively. Building on the success of quadric error simplification, we iteratively collapse 1-simplices (vertex pairs). Our approach employs a modified quadric error that converges to the original quadric error metric for watertight manifold meshes, while significantly improving the results on wild meshes. For textures, instead of following existing strategies to preserve UVs, we adopt a novel perspective which focuses on computing mesh correspondences throughout the decimation, independent of the UV layout. This combination yields a textured mesh simplification system that is capable of handling arbitrary triangle meshes, achieving to high-quality results on wild inputs without sacrificing the excellent performance on clean inputs. Our method guarantees to avoid common problems in textured mesh simplification, including the prevalent problem of texture bleeding. We extensively evaluate our method on multiple datasets, showing improvements over prior techniques through qualitative, quantitative, and user study evaluations.

View-based methods have demonstrated promising performance in 3D shape understanding. However, they tend to make strong assumptions about the relations between views or learn the multi-view correlations indirectly, which limits the flexibility of exploring inter-view correlations and the effectiveness of target tasks. To overcome the above problems, this paper investigates flexible organization and explicit correlation learning for multiple views. In particular, we propose to incorporate different views of a 3D shape into a permutation-invariant set, referred to as View Set, which removes rigid relation assumptions and facilitates adequate information exchange and fusion among views. Based on that, we devise a nimble Transformer model, named VSFormer, to explicitly capture pairwise and higher-order correlations of all elements in the set. Meanwhile, we theoretically reveal a natural correspondence between the Cartesian product of a view set and the correlation matrix in the attention mechanism, which supports our model design. Comprehensive experiments suggest that VSFormer has better flexibility, efficient inference efficiency and superior performance. Notably, VSFormer reaches state-of-the-art results on various 3d recognition datasets, including ModelNet40, ScanObjectNN and RGBD. It also establishes new records on the SHREC'17 retrieval benchmark. The code and datasets are available at https://github.com/auniquesun/VSFormer.

A promising direction for pre-training 3D point clouds is to leverage the massive amount of data in 2D, whereas the domain gap between 2D and 3D creates a fundamental challenge. This paper proposes a novel approach to point-cloud pre-training that learns 3D representations by leveraging pre-trained 2D networks. Different from the popular practice of predicting 2D features first and then obtaining 3D features through dimensionality lifting, our approach directly uses a 3D network for feature extraction. We train the 3D feature extraction network with the help of the novel 2D knowledge transfer loss, which enforces the 2D projections of the 3D feature to be consistent with the output of pre-trained 2D networks. To prevent the feature from discarding 3D signals, we introduce the multi-view consistency loss that additionally encourages the projected 2D feature representations to capture pixel-wise correspondences across different views. Such correspondences induce 3D geometry and effectively retain 3D features in the projected 2D features. Experimental results demonstrate that our pre-trained model can be successfully transferred to various downstream tasks, including 3D shape classification, part segmentation, 3D object detection, and semantic segmentation, achieving state-of-the-art performance.

This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the datadriven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging, requiring a good initialization. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces, which we use to regularize the implicit generator. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques. The synthetic shapes of GenCorres also achieve salient performance gains against state-of-the-art deformable shape generators.

Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named ``3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, named ``Geometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)

This paper studies the problem of recovering cameras from a set of fundamental matrices. A set of fundamental matrices is said to be compatible if a set of cameras exists for which they are the fundamental matrices. We focus on the complete graph, where fundamental matrices for each pair of cameras are given. Previous work has established necessary and sufficient conditions for compatibility as rank and eigenvalue conditions on the n-view fundamental matrix obtained by concatenating the individual fundamental matrices. In this work, we show that the eigenvalue condition is redundant. We provide explicit homogeneous polynomials that describe necessary and sufficient conditions for compatibility in terms of the fundamental matrices and their epipoles. In this direction, we find that quadruple-wise compatibility is enough to ensure global compatibility for any number of cameras. We demonstrate that for four cameras, compatibility is generically described by triple-wise conditions and one additional equation involving all fundamental matrices.

We present PyMAF-X, a regression-based approach to recovering parametric full-body models from monocular images. This task is very challenging since minor parametric deviation may lead to noticeable misalignment between the estimated mesh and the input image. Moreover, when integrating part-specific estimations into the full-body model, existing solutions tend to either degrade the alignment or produce unnatural wrist poses. To address these issues, we propose a Pyramidal Mesh Alignment Feedback (PyMAF) loop in our regression network for well-aligned human mesh recovery and extend it as PyMAF-X for the recovery of expressive full-body models. The core idea of PyMAF is to leverage a feature pyramid and rectify the predicted parameters explicitly based on the mesh-image alignment status. Specifically, given the currently predicted parameters, mesh-aligned evidence will be extracted from finer-resolution features accordingly and fed back for parameter rectification. To enhance the alignment perception, an auxiliary dense supervision is employed to provide mesh-image correspondence guidance while spatial alignment attention is introduced to enable the awareness of the global contexts for our network. When extending PyMAF for full-body mesh recovery, an adaptive integration strategy is proposed in PyMAF-X to produce natural wrist poses while maintaining the well-aligned performance of the part-specific estimations. The efficacy of our approach is validated on several benchmark datasets for body, hand, face, and full-body mesh recovery, where PyMAF and PyMAF-X effectively improve the mesh-image alignment and achieve new state-of-the-art results. The project page with code and video results can be found at https://www.liuyebin.com/pymaf-x.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojo

Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most such approaches focus on representing closed shapes. Unsigned distance function (UDF) based approaches have been proposed recently as a promising alternative to represent both open and closed shapes. However, since the gradients of UDFs vanish on the surface, it is challenging to estimate local (differential) geometric properties like the normals and tangent planes which are needed for many downstream applications in vision and graphics. There are additional challenges in computing these properties efficiently with a low-memory footprint. This paper presents a novel approach that models such surfaces using a new class of implicit representations called the closest surface-point (CSP) representation. We show that CSP allows us to represent complex surfaces of any topology (open or closed) with high fidelity. It also allows for accurate and efficient computation of local geometric properties. We further demonstrate that it leads to efficient implementation of downstream algorithms like sphere-tracing for rendering the 3D surface as well as to create explicit mesh-based representations. Extensive experimental evaluation on the ShapeNet dataset validate the above contributions with results surpassing the state-of-the-art.

Graph representation learning is a fundamental research theme and can be generalized to benefit multiple downstream tasks from the node and link levels to the higher graph level. In practice, it is desirable to develop task-agnostic general graph representation learning methods that are typically trained in an unsupervised manner. Related research reveals that the power of graph representation learning methods depends on whether they can differentiate distinct graph structures as different embeddings and map isomorphic graphs to consistent embeddings (i.e., the isomorphic consistency of graph models). However, for task-agnostic general graph representation learning, existing unsupervised graph models, represented by the variational graph auto-encoders (VGAEs), can only keep the isomorphic consistency within the subgraphs of 1-hop neighborhoods and thus usually manifest inferior performance on the more difficult higher-level tasks. To overcome the limitations of existing unsupervised methods, in this paper, we propose the Isomorphic-Consistent VGAE (IsoC-VGAE) for multi-level task-agnostic graph representation learning. We first devise a decoding scheme to provide a theoretical guarantee of keeping the isomorphic consistency under the settings of unsupervised learning. We then propose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitive realization, which trains the model via reconstructing the GNN node embeddings with multi-hop neighborhood information, so as to maintain the high-order isomorphic consistency within the VGAE framework. We conduct extensive experiments on the representative graph learning tasks at different levels, including node classification, link prediction and graph classification, and the results verify that our proposed model generally outperforms both the state-of-the-art unsupervised methods and representative supervised methods.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Learning 3D shape representation with dense correspondence for deformable objects is a fundamental problem in computer vision. Existing approaches often need additional annotations of specific semantic domain, e.g., skeleton poses for human bodies or animals, which require extra annotation effort and suffer from error accumulation, and they are limited to specific domain. In this paper, we propose a novel self-supervised approach to learn neural implicit shape representation for deformable objects, which can represent shapes with a template shape and dense correspondence in 3D. Our method does not require the priors of skeleton and skinning weight, and only requires a collection of shapes represented in signed distance fields. To handle the large deformation, we constrain the learned template shape in the same latent space with the training shapes, design a new formulation of local rigid constraint that enforces rigid transformation in local region and addresses local reflection issue, and present a new hierarchical rigid constraint to reduce the ambiguity due to the joint learning of template shape and correspondences. Extensive experiments show that our model can represent shapes with large deformations. We also show that our shape representation can support two typical applications, such as texture transfer and shape editing, with competitive performance. The code and models are available at https://iscas3dv.github.io/deformshape

Cross-view object correspondence, exemplified by the representative task of ego-exo object correspondence, aims to establish consistent associations of the same object across different viewpoints (e.g., ego-centric and exo-centric). This task poses significant challenges due to drastic viewpoint and appearance variations, making existing segmentation models, such as SAM2, non-trivial to apply directly. To address this, we present V^2-SAM, a unified cross-view object correspondence framework that adapts SAM2 from single-view segmentation to cross-view correspondence through two complementary prompt generators. Specifically, the Cross-View Anchor Prompt Generator (V^2-Anchor), built upon DINOv3 features, establishes geometry-aware correspondences and, for the first time, unlocks coordinate-based prompting for SAM2 in cross-view scenarios, while the Cross-View Visual Prompt Generator (V^2-Visual) enhances appearance-guided cues via a novel visual prompt matcher that aligns ego-exo representations from both feature and structural perspectives. To effectively exploit the strengths of both prompts, we further adopt a multi-expert design and introduce a Post-hoc Cyclic Consistency Selector (PCCS) that adaptively selects the most reliable expert based on cyclic consistency. Extensive experiments validate the effectiveness of V^2-SAM, achieving new state-of-the-art performance on Ego-Exo4D (ego-exo object correspondence), DAVIS-2017 (video object tracking), and HANDAL-X (robotic-ready cross-view correspondence).

We present a new deep learning approach to pose-guided resynthesis of human photographs. At the heart of the new approach is the estimation of the complete body surface texture based on a single photograph. Since the input photograph always observes only a part of the surface, we suggest a new inpainting method that completes the texture of the human body. Rather than working directly with colors of texture elements, the inpainting network estimates an appropriate source location in the input image for each element of the body surface. This correspondence field between the input image and the texture is then further warped into the target image coordinate frame based on the desired pose, effectively establishing the correspondence between the source and the target view even when the pose change is drastic. The final convolutional network then uses the established correspondence and all other available information to synthesize the output image. A fully-convolutional architecture with deformable skip connections guided by the estimated correspondence field is used. We show state-of-the-art result for pose-guided image synthesis. Additionally, we demonstrate the performance of our system for garment transfer and pose-guided face resynthesis.

We propose a method, named DualMesh-UDF, to extract a surface from unsigned distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural UDFs are becoming increasingly popular for surface representation because of their versatility in presenting surfaces with arbitrary topologies, as opposed to the signed distance function that is limited to representing a closed surface. However, the applications of neural UDFs are hindered by the notorious difficulty in extracting the target surfaces they represent. Recent methods for surface extraction from a neural UDF suffer from significant geometric errors or topological artifacts due to two main difficulties: (1) A UDF does not exhibit sign changes; and (2) A neural UDF typically has substantial approximation errors. DualMesh-UDF addresses these two difficulties. Specifically, given a neural UDF encoding a target surface S to be recovered, we first estimate the tangent planes of S at a set of sample points close to S. Next, we organize these sample points into local clusters, and for each local cluster, solve a linear least squares problem to determine a final surface point. These surface points are then connected to create the output mesh surface, which approximates the target surface. The robust estimation of the tangent planes of the target surface and the subsequent minimization problem constitute our core strategy, which contributes to the favorable performance of DualMesh-UDF over other competing methods. To efficiently implement this strategy, we employ an adaptive Octree. Within this framework, we estimate the location of a surface point in each of the octree cells identified as containing part of the target surface. Extensive experiments show that our method outperforms existing methods in terms of surface reconstruction quality while maintaining comparable computational efficiency.

Multi-view consistency remains a challenge for image diffusion models. Even within the Text-to-Texture problem, where perfect geometric correspondences are known a priori, many methods fail to yield aligned predictions across views, necessitating non-trivial fusion methods to incorporate the results onto the original mesh. We explore this issue for a Collaborative Control workflow specifically in PBR Text-to-Texture. Collaborative Control directly models PBR image probability distributions, including normal bump maps; to our knowledge, the only diffusion model to directly output full PBR stacks. We discuss the design decisions involved in making this model multi-view consistent, and demonstrate the effectiveness of our approach in ablation studies, as well as practical applications.

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.

Semi-transitive graphs, defined in hps98 as examples where ``uniform percolation" holds whenever p>p_c, are a large class of graphs more general than quasi-transitive graphs. Let G be a semi-transitive graph with one end which can be properly embedded into the plane with uniformly bounded face degree for finite faces and minimal vertex degree at least 7. We show that p_u^{site}(G) +p_c^{site}(G_*)=1, where G_* denotes the matching graph of G. This fulfils and extends an observation of Sykes and Essam in 1964 (SE64) to semi-transitive graphs.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Erroneous feature matches have severe impact on subsequent camera pose estimation and often require additional, time-costly measures, like RANSAC, for outlier rejection. Our method tackles this challenge by addressing feature matching and pose optimization jointly. To this end, we propose a graph attention network to predict image correspondences along with confidence weights. The resulting matches serve as weighted constraints in a differentiable pose estimation. Training feature matching with gradients from pose optimization naturally learns to down-weight outliers and boosts pose estimation on image pairs compared to SuperGlue by 6.7% on ScanNet. At the same time, it reduces the pose estimation time by over 50% and renders RANSAC iterations unnecessary. Moreover, we integrate information from multiple views by spanning the graph across multiple frames to predict the matches all at once. Multi-view matching combined with end-to-end training improves the pose estimation metrics on Matterport3D by 18.5% compared to SuperGlue.

Matching cost aggregation plays a fundamental role in learning-based multi-view stereo networks. However, directly aggregating adjacent costs can lead to suboptimal results due to local geometric inconsistency. Related methods either seek selective aggregation or improve aggregated depth in the 2D space, both are unable to handle geometric inconsistency in the cost volume effectively. In this paper, we propose GoMVS to aggregate geometrically consistent costs, yielding better utilization of adjacent geometries. More specifically, we correspond and propagate adjacent costs to the reference pixel by leveraging the local geometric smoothness in conjunction with surface normals. We achieve this by the geometric consistent propagation (GCP) module. It computes the correspondence from the adjacent depth hypothesis space to the reference depth space using surface normals, then uses the correspondence to propagate adjacent costs to the reference geometry, followed by a convolution for aggregation. Our method achieves new state-of-the-art performance on DTU, Tanks & Temple, and ETH3D datasets. Notably, our method ranks 1st on the Tanks & Temple Advanced benchmark.

In recent years, there has been increasing interest in applying stylization on 3D scenes from a reference style image, in particular onto neural radiance fields (NeRF). While performing stylization directly on NeRF guarantees appearance consistency over arbitrary novel views, it is a challenging problem to guide the transfer of patterns from the style image onto different parts of the NeRF scene. In this work, we propose a stylization framework for NeRF based on local style transfer. In particular, we use a hash-grid encoding to learn the embedding of the appearance and geometry components, and show that the mapping defined by the hash table allows us to control the stylization to a certain extent. Stylization is then achieved by optimizing the appearance branch while keeping the geometry branch fixed. To support local style transfer, we propose a new loss function that utilizes a segmentation network and bipartite matching to establish region correspondences between the style image and the content images obtained from volume rendering. Our experiments show that our method yields plausible stylization results with novel view synthesis while having flexible controllability via manipulating and customizing the region correspondences.

This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Python library for computations with Cayley and Schreier graphs. Compared with systems such as GAP and Sage, CayleyPy handles much larger graphs and performs several orders of magnitude faster. Using CayleyPy we obtained about 200 new conjectures on Cayley and Schreier graphs, focused on diameters and growth. For many Cayley graphs of symmetric groups Sn we observe quasi polynomial diameter formulas: a small set of quadratic or linear polynomials indexed by n mod s. We conjecture that this is a general phenomenon, giving efficient diameter computation despite the problem being NP hard. We propose a refinement of the Babai type conjecture on diameters of Sn: n^2/2 + 4n upper bounds in the undirected case, compared to previous O(n^2) bounds. We also provide explicit generator families, related to involutions in a square with whiskers pattern, conjectured to maximize the diameter; search confirms this for all n up to 15. We further conjecture an answer to a question posed by V M Glushkov in 1968 on directed Cayley graphs generated by a cyclic shift and a transposition. For nilpotent groups we conjecture an improvement of J S Ellenberg's results on upper unitriangular matrices over Z/pZ, showing linear dependence of diameter on p. Moreover. Some conjectures are LLM friendly, naturally stated as sorting problems verifiable by algorithms or Python code. To benchmark path finding we created more than 10 Kaggle datasets. CayleyPy works with arbitrary permutation or matrix groups and includes over 100 predefined generators. Our growth computation code outperforms GAP and Sage up to 1000 times in speed and size.

Vision-Language models (VLMs) pre-trained on large corpora have demonstrated notable success across a range of downstream tasks. In light of the rapidly increasing size of pre-trained VLMs, parameter-efficient transfer learning (PETL) has garnered attention as a viable alternative to full fine-tuning. One such approach is the adapter, which introduces a few trainable parameters into the pre-trained models while preserving the original parameters during adaptation. In this paper, we present a novel modeling framework that recasts adapter tuning after attention as a graph message passing process on attention graphs, where the projected query and value features and attention matrix constitute the node features and the graph adjacency matrix, respectively. Within this framework, tuning adapters in VLMs necessitates handling heterophilic graphs, owing to the disparity between the projected query and value space. To address this challenge, we propose a new adapter architecture, p-adapter, which employs p-Laplacian message passing in Graph Neural Networks (GNNs). Specifically, the attention weights are re-normalized based on the features, and the features are then aggregated using the calibrated attention matrix, enabling the dynamic exploitation of information with varying frequencies in the heterophilic attention graphs. We conduct extensive experiments on different pre-trained VLMs and multi-modal tasks, including visual question answering, visual entailment, and image captioning. The experimental results validate our method's significant superiority over other PETL methods.

While impressive progress has recently been made in image-oriented facial attribute translation, shape-oriented 3D facial attribute translation remains an unsolved issue. This is primarily limited by the lack of 3D generative models and ineffective usage of 3D facial data. We propose a learning framework for 3D facial attribute translation to relieve these limitations. Firstly, we customize a novel geometric map for 3D shape representation and embed it in an end-to-end generative adversarial network. The geometric map represents 3D shapes symmetrically on a square image grid, while preserving the neighboring relationship of 3D vertices in a local least-square sense. This enables effective learning for the latent representation of data with different attributes. Secondly, we employ a unified and unpaired learning framework for multi-domain attribute translation. It not only makes effective usage of data correlation from multiple domains, but also mitigates the constraint for hardly accessible paired data. Finally, we propose a hierarchical architecture for the discriminator to guarantee robust results against both global and local artifacts. We conduct extensive experiments to demonstrate the advantage of the proposed framework over the state-of-the-art in generating high-fidelity facial shapes. Given an input 3D facial shape, the proposed framework is able to synthesize novel shapes of different attributes, which covers some downstream applications, such as expression transfer, gender translation, and aging. Code at https://github.com/NaughtyZZ/3D_facial_shape_attribute_translation_ssgmap.

This paper presents a simple yet effective approach to modeling space-time correspondences in the context of video object segmentation. Unlike most existing approaches, we establish correspondences directly between frames without re-encoding the mask features for every object, leading to a highly efficient and robust framework. With the correspondences, every node in the current query frame is inferred by aggregating features from the past in an associative fashion. We cast the aggregation process as a voting problem and find that the existing inner-product affinity leads to poor use of memory with a small (fixed) subset of memory nodes dominating the votes, regardless of the query. In light of this phenomenon, we propose using the negative squared Euclidean distance instead to compute the affinities. We validated that every memory node now has a chance to contribute, and experimentally showed that such diversified voting is beneficial to both memory efficiency and inference accuracy. The synergy of correspondence networks and diversified voting works exceedingly well, achieves new state-of-the-art results on both DAVIS and YouTubeVOS datasets while running significantly faster at 20+ FPS for multiple objects without bells and whistles.

We define the bicategory of Graph Convolutional Neural Networks GCNN_n for an arbitrary graph with n nodes. We show it can be factored through the already existing categorical constructions for deep learning called Para and Lens with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor GCNN_n to Para(CoKl(R^{n times n} times -)). We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.

In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no correspondence annotation during training. Our key insight is to incorporate neural features learned by deep learning-based shape matching networks into an iterative, geometric shape registration pipeline. The advantage of our approach is two-fold -- On one hand, neural features provide more accurate and semantically meaningful correspondence estimation than spatial features (e.g., coordinates), which is critical in the presence of large non-rigid deformations; On the other hand, the correspondences are dynamically updated according to the intermediate registrations and filtered by consistency prior, which prominently robustify the overall pipeline. Empirical results show that, with as few as dozens of training shapes of limited variability, our pipeline achieves state-of-the-art results on several benchmarks of non-rigid point cloud matching and partial shape matching across varying settings, but also delivers high-quality correspondences between unseen challenging shape pairs that undergo both significant extrinsic and intrinsic deformations, in which case neither traditional registration methods nor intrinsic methods work.

Hypergraphs offer a powerful framework for modeling higher-order interactions that traditional pairwise graphs cannot fully capture. However, practical constraints often lead to their simplification into projected graphs, resulting in substantial information loss and ambiguity in representing higher-order relationships. In this work, we propose MARIOH, a supervised approach for reconstructing the original hypergraph from its projected graph by leveraging edge multiplicity. To overcome the difficulties posed by the large search space, MARIOH integrates several key ideas: (a) identifying provable size-2 hyperedges, which reduces the candidate search space, (b) predicting the likelihood of candidates being hyperedges by utilizing both structural and multiplicity-related features, and (c) not only targeting promising hyperedge candidates but also examining less confident ones to explore alternative possibilities. Together, these ideas enable MARIOH to efficiently and effectively explore the search space. In our experiments using 10 real-world datasets, MARIOH achieves up to 74.51% higher reconstruction accuracy compared to state-of-the-art methods.

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

Cross-view correspondence is a fundamental capability for spatial understanding and embodied AI. However, it is still far from being realized in Vision-Language Models (VLMs), especially in achieving precise point-level correspondence, which is crucial for precise affordance interaction. So we propose the Cross-View Point Correspondence (CVPC) task and CrossPoint-Bench, a comprehensive benchmark with hierarchical design, inspired by the human cognitive process of "perceive", "reason", and "correspond". Our evaluation shows the state-of-the-art models (e.g., Gemini-2.5-Pro) still fall far behind humans, with a gap of over 54.65% in overall accuracy, exposing a challenge in transitioning from coarse-grained judgement to fine-grained coordinate prediction. To address this problem, we construct CrossPoint-378K, a dataset with 378K question-answering pairs across 900 scenes, focused on actionable affordance regions that better reflect real-world manipulation and interaction scenarios. Furthermore, we propose CroPond that trained on the CrossPoint-378K dataset. Our CroPond achieves state-of-the-art performance on CrossPoint-Bench, surpassing Gemini-2.5-Pro by 39.7% accuracy, which offers a foundation for advancing future work on cross-view correspondence. The benchmark, dataset, and model are publicly available at https://github.com/WangYipu2002/CrossPoint.

With the success of 2D and 3D visual generative models, there is growing interest in generating 4D content. Existing methods primarily rely on text prompts to produce 4D content, but they often fall short of accurately defining complex or rare motions. To address this limitation, we propose MagicPose4D, a novel framework for refined control over both appearance and motion in 4D generation. Unlike traditional methods, MagicPose4D accepts monocular videos as motion prompts, enabling precise and customizable motion generation. MagicPose4D comprises two key modules: i) Dual-Phase 4D Reconstruction Module} which operates in two phases. The first phase focuses on capturing the model's shape using accurate 2D supervision and less accurate but geometrically informative 3D pseudo-supervision without imposing skeleton constraints. The second phase refines the model using more accurate pseudo-3D supervision, obtained in the first phase and introduces kinematic chain-based skeleton constraints to ensure physical plausibility. Additionally, we propose a Global-local Chamfer loss that aligns the overall distribution of predicted mesh vertices with the supervision while maintaining part-level alignment without extra annotations. ii) Cross-category Motion Transfer Module} leverages the predictions from the 4D reconstruction module and uses a kinematic-chain-based skeleton to achieve cross-category motion transfer. It ensures smooth transitions between frames through dynamic rigidity, facilitating robust generalization without additional training. Through extensive experiments, we demonstrate that MagicPose4D significantly improves the accuracy and consistency of 4D content generation, outperforming existing methods in various benchmarks.

As a fundamental problem in computer vision, 3D point cloud registration (PCR) aims to seek the optimal pose to align a point cloud pair. In this paper, we present a 3D registration method with maximal cliques (MAC). The key insight is to loosen the previous maximum clique constraint, and mine more local consensus information in a graph for accurate pose hypotheses generation: 1) A compatibility graph is constructed to render the affinity relationship between initial correspondences. 2) We search for maximal cliques in the graph, each of which represents a consensus set. We perform node-guided clique selection then, where each node corresponds to the maximal clique with the greatest graph weight. 3) Transformation hypotheses are computed for the selected cliques by the SVD algorithm and the best hypothesis is used to perform registration. Extensive experiments on U3M, 3DMatch, 3DLoMatch and KITTI demonstrate that MAC effectively increases registration accuracy, outperforms various state-of-the-art methods and boosts the performance of deep-learned methods. MAC combined with deep-learned methods achieves state-of-the-art registration recall of 95.7% / 78.9% on 3DMatch / 3DLoMatch.

Geometric models like DUSt3R have shown great advances in understanding the geometry of a scene from pairs of photos. However, they fail when the inputs are from vastly different viewpoints (e.g., aerial vs. ground) or modalities (e.g., photos vs. abstract drawings) compared to what was observed during training. This paper addresses a challenging version of this problem: predicting correspondences between ground-level photos and floor plans. Current datasets for joint photo--floor plan reasoning are limited, either lacking in varying modalities (VIGOR) or lacking in correspondences (WAFFLE). To address these limitations, we introduce a new dataset, C3, created by first reconstructing a number of scenes in 3D from Internet photo collections via structure-from-motion, then manually registering the reconstructions to floor plans gathered from the Internet, from which we can derive correspondence between images and floor plans. C3 contains 90K paired floor plans and photos across 597 scenes with 153M pixel-level correspondences and 85K camera poses. We find that state-of-the-art correspondence models struggle on this task. By training on our new data, we can improve on the best performing method by 34% in RMSE. We also identify open challenges in cross-modal geometric reasoning that our dataset aims to help address.

Regression-based methods have recently shown promising results in reconstructing human meshes from monocular images. By directly mapping raw pixels to model parameters, these methods can produce parametric models in a feed-forward manner via neural networks. However, minor deviation in parameters may lead to noticeable misalignment between the estimated meshes and image evidences. To address this issue, we propose a Pyramidal Mesh Alignment Feedback (PyMAF) loop to leverage a feature pyramid and rectify the predicted parameters explicitly based on the mesh-image alignment status in our deep regressor. In PyMAF, given the currently predicted parameters, mesh-aligned evidences will be extracted from finer-resolution features accordingly and fed back for parameter rectification. To reduce noise and enhance the reliability of these evidences, an auxiliary pixel-wise supervision is imposed on the feature encoder, which provides mesh-image correspondence guidance for our network to preserve the most related information in spatial features. The efficacy of our approach is validated on several benchmarks, including Human3.6M, 3DPW, LSP, and COCO, where experimental results show that our approach consistently improves the mesh-image alignment of the reconstruction. The project page with code and video results can be found at https://hongwenzhang.github.io/pymaf.

We address the problem of aligning real-world 3D data of garments, which benefits many applications such as texture learning, physical parameter estimation, generative modeling of garments, etc. Existing extrinsic methods typically perform non-rigid iterative closest point and struggle to align details due to incorrect closest matches and rigidity constraints. While intrinsic methods based on functional maps can produce high-quality correspondences, they work under isometric assumptions and become unreliable for garment deformations which are highly non-isometric. To achieve wrinkle-level as well as texture-level alignment, we present a novel coarse-to-fine two-stage method that leverages intrinsic manifold properties with two neural deformation fields, in the 3D space and the intrinsic space, respectively. The coarse stage performs a 3D fitting, where we leverage intrinsic manifold properties to define a manifold deformation field. The coarse fitting then induces a functional map that produces an alignment of intrinsic embeddings. We further refine the intrinsic alignment with a second neural deformation field for higher accuracy. We evaluate our method with our captured garment dataset, GarmCap. The method achieves accurate wrinkle-level and texture-level alignment and works for difficult garment types such as long coats. Our project page is https://jsnln.github.io/iccv2023_intrinsic/index.html.

Surface reconstruction from multiple, calibrated images is a challenging task - often requiring a large number of collected images with significant overlap. We look at the specific case of human foot reconstruction. As with previous successful foot reconstruction work, we seek to extract rich per-pixel geometry cues from multi-view RGB images, and fuse these into a final 3D object. Our method, FOCUS, tackles this problem with 3 main contributions: (i) SynFoot2, an extension of an existing synthetic foot dataset to include a new data type: dense correspondence with the parameterized foot model FIND; (ii) an uncertainty-aware dense correspondence predictor trained on our synthetic dataset; (iii) two methods for reconstructing a 3D surface from dense correspondence predictions: one inspired by Structure-from-Motion, and one optimization-based using the FIND model. We show that our reconstruction achieves state-of-the-art reconstruction quality in a few-view setting, performing comparably to state-of-the-art when many views are available, and runs substantially faster. We release our synthetic dataset to the research community. Code is available at: https://github.com/OllieBoyne/FOCUS

Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at https://github.com/ChirikjianLab/Marching-Primitives.git.

We introduce VertexRegen, a novel mesh generation framework that enables generation at a continuous level of detail. Existing autoregressive methods generate meshes in a partial-to-complete manner and thus intermediate steps of generation represent incomplete structures. VertexRegen takes inspiration from progressive meshes and reformulates the process as the reversal of edge collapse, i.e. vertex split, learned through a generative model. Experimental results demonstrate that VertexRegen produces meshes of comparable quality to state-of-the-art methods while uniquely offering anytime generation with the flexibility to halt at any step to yield valid meshes with varying levels of detail.

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

Mesh quality assessment (MQA) models play a critical role in the design, optimization, and evaluation of mesh operation systems in a wide variety of applications. Current MQA models, whether model-based methods using topology-aware features or projection-based approaches working on rendered 2D projections, often fail to capture the intricate interactions between texture and 3D geometry. We introduce HybridMQA, a first-of-its-kind hybrid full-reference colored MQA framework that integrates model-based and projection-based approaches, capturing complex interactions between textural information and 3D structures for enriched quality representations. Our method employs graph learning to extract detailed 3D representations, which are then projected to 2D using a novel feature rendering process that precisely aligns them with colored projections. This enables the exploration of geometry-texture interactions via cross-attention, producing comprehensive mesh quality representations. Extensive experiments demonstrate HybridMQA's superior performance across diverse datasets, highlighting its ability to effectively leverage geometry-texture interactions for a thorough understanding of mesh quality. Our implementation will be made publicly available.

The main challenges of 3D pose transfer are: 1) Lack of paired training data with different characters performing the same pose; 2) Disentangling pose and shape information from the target mesh; 3) Difficulty in applying to meshes with different topologies. We thus propose a novel weakly-supervised keypoint-based framework to overcome these difficulties. Specifically, we use a topology-agnostic keypoint detector with inverse kinematics to compute transformations between the source and target meshes. Our method only requires supervision on the keypoints, can be applied to meshes with different topologies and is shape-invariant for the target which allows extraction of pose-only information from the target meshes without transferring shape information. We further design a cycle reconstruction to perform self-supervised pose transfer without the need for ground truth deformed mesh with the same pose and shape as the target and source, respectively. We evaluate our approach on benchmark human and animal datasets, where we achieve superior performance compared to the state-of-the-art unsupervised approaches and even comparable performance with the fully supervised approaches. We test on the more challenging Mixamo dataset to verify our approach's ability in handling meshes with different topologies and complex clothes. Cross-dataset evaluation further shows the strong generalization ability of our approach.

We present MeshLLM, a novel framework that leverages large language models (LLMs) to understand and generate text-serialized 3D meshes. Our approach addresses key limitations in existing methods, including the limited dataset scale when catering to LLMs' token length and the loss of 3D structural information during mesh serialization. We introduce a Primitive-Mesh decomposition strategy, which divides 3D meshes into structurally meaningful subunits. This enables the creation of a large-scale dataset with 1500k+ samples, almost 50 times larger than previous methods, which aligns better with the LLM scaling law principles. Furthermore, we propose inferring face connectivity from vertices and local mesh assembly training strategies, significantly enhancing the LLMs' ability to capture mesh topology and spatial structures. Experiments show that MeshLLM outperforms the state-of-the-art LLaMA-Mesh in both mesh generation quality and shape understanding, highlighting its great potential in processing text-serialized 3D meshes.

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse vertices multiple times to fully represent manifold meshes, as each vertex is shared by multiple faces. This redundancy leads to excessively long token sequences and inefficient generation processes. In this paper, we propose an efficient framework that generates artistic meshes by treating vertices and faces separately, significantly reducing redundancy. We employ an autoregressive model solely for vertex generation, decreasing the token count to approximately 23\% of that required by the most compact existing tokenizer. Next, we leverage a bidirectional transformer to complete the mesh in a single step by capturing inter-vertex relationships and constructing the adjacency matrix that defines the mesh faces. To further improve the generation quality, we introduce a fidelity enhancer to refine vertex positioning into more natural arrangements and propose a post-processing framework to remove undesirable edge connections. Experimental results show that our method achieves more than 8times faster speed on mesh generation compared to state-of-the-art approaches, while producing higher mesh quality.

Neural Radiance Fields (NeRFs) have achieved great success in the past few years. However, most current methods still require intensive resources due to ray marching-based rendering. To construct urban-level radiance fields efficiently, we design Deformable Neural Mesh Primitive~(DNMP), and propose to parameterize the entire scene with such primitives. The DNMP is a flexible and compact neural variant of classic mesh representation, which enjoys both the efficiency of rasterization-based rendering and the powerful neural representation capability for photo-realistic image synthesis. Specifically, a DNMP consists of a set of connected deformable mesh vertices with paired vertex features to parameterize the geometry and radiance information of a local area. To constrain the degree of freedom for optimization and lower the storage budgets, we enforce the shape of each primitive to be decoded from a relatively low-dimensional latent space. The rendering colors are decoded from the vertex features (interpolated with rasterization) by a view-dependent MLP. The DNMP provides a new paradigm for urban-level scene representation with appealing properties: (1) High-quality rendering. Our method achieves leading performance for novel view synthesis in urban scenarios. (2) Low computational costs. Our representation enables fast rendering (2.07ms/1k pixels) and low peak memory usage (110MB/1k pixels). We also present a lightweight version that can run 33times faster than vanilla NeRFs, and comparable to the highly-optimized Instant-NGP (0.61 vs 0.71ms/1k pixels). Project page: https://dnmp.github.io/{https://dnmp.github.io/}.

Vision foundation models, particularly the ViT family, have revolutionized image understanding by providing rich semantic features. However, despite their success in 2D comprehension, their abilities on grasping 3D spatial relationships are still unclear. In this work, we evaluate and enhance the 3D awareness of ViT-based models. We begin by systematically assessing their ability to learn 3D equivariant features, specifically examining the consistency of semantic embeddings across different viewpoints. Our findings indicate that improved 3D equivariance leads to better performance on various downstream tasks, including pose estimation, tracking, and semantic transfer. Building on this insight, we propose a simple yet effective finetuning strategy based on 3D correspondences, which significantly enhances the 3D correspondence understanding of existing vision models. Remarkably, even finetuning on a single object for just one iteration results in substantial performance gains. All code and resources will be made publicly available to support further advancements in 3D-aware vision models. Our code is available at https://github.com/qq456cvb/3DCorrEnhance.

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual RMSE_{v}.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

Graph retrieval based on subgraph isomorphism has several real-world applications such as scene graph retrieval, molecular fingerprint detection and circuit design. Roy et al. [35] proposed IsoNet, a late interaction model for subgraph matching, which first computes the node and edge embeddings of each graph independently of paired graph and then computes a trainable alignment map. Here, we present IsoNet++, an early interaction graph neural network (GNN), based on several technical innovations. First, we compute embeddings of all nodes by passing messages within and across the two input graphs, guided by an injective alignment between their nodes. Second, we update this alignment in a lazy fashion over multiple rounds. Within each round, we run a layerwise GNN from scratch, based on the current state of the alignment. After the completion of one round of GNN, we use the last-layer embeddings to update the alignments, and proceed to the next round. Third, IsoNet++ incorporates a novel notion of node-pair partner interaction. Traditional early interaction computes attention between a node and its potential partners in the other graph, the attention then controlling messages passed across graphs. In contrast, we consider node pairs (not single nodes) as potential partners. Existence of an edge between the nodes in one graph and non-existence in the other provide vital signals for refining the alignment. Our experiments on several datasets show that the alignments get progressively refined with successive rounds, resulting in significantly better retrieval performance than existing methods. We demonstrate that all three innovations contribute to the enhanced accuracy. Our code and datasets are publicly available at https://github.com/structlearning/isonetpp.

With the recent advancements in single-image-based human mesh recovery, there is a growing interest in enhancing its performance in certain extreme scenarios, such as occlusion, while maintaining overall model accuracy. Although obtaining accurately annotated 3D human poses under occlusion is challenging, there is still a wealth of rich and precise 2D pose annotations that can be leveraged. However, existing works mostly focus on directly leveraging 2D pose coordinates to estimate 3D pose and mesh. In this paper, we present PostoMETRO(Pose token enhanced MEsh TRansfOrmer), which integrates occlusion-resilient 2D pose representation into transformers in a token-wise manner. Utilizing a specialized pose tokenizer, we efficiently condense 2D pose data to a compact sequence of pose tokens and feed them to the transformer together with the image tokens. This process not only ensures a rich depiction of texture from the image but also fosters a robust integration of pose and image information. Subsequently, these combined tokens are queried by vertex and joint tokens to decode 3D coordinates of mesh vertices and human joints. Facilitated by the robust pose token representation and the effective combination, we are able to produce more precise 3D coordinates, even under extreme scenarios like occlusion. Experiments on both standard and occlusion-specific benchmarks demonstrate the effectiveness of PostoMETRO. Qualitative results further illustrate the clarity of how 2D pose can help 3D reconstruction. Code will be made available.

We propose 3D Congealing, a novel problem of 3D-aware alignment for 2D images capturing semantically similar objects. Given a collection of unlabeled Internet images, our goal is to associate the shared semantic parts from the inputs and aggregate the knowledge from 2D images to a shared 3D canonical space. We introduce a general framework that tackles the task without assuming shape templates, poses, or any camera parameters. At its core is a canonical 3D representation that encapsulates geometric and semantic information. The framework optimizes for the canonical representation together with the pose for each input image, and a per-image coordinate map that warps 2D pixel coordinates to the 3D canonical frame to account for the shape matching. The optimization procedure fuses prior knowledge from a pre-trained image generative model and semantic information from input images. The former provides strong knowledge guidance for this under-constraint task, while the latter provides the necessary information to mitigate the training data bias from the pre-trained model. Our framework can be used for various tasks such as correspondence matching, pose estimation, and image editing, achieving strong results on real-world image datasets under challenging illumination conditions and on in-the-wild online image collections.

Surface reconstruction has been widely studied in computer vision and graphics. However, existing surface reconstruction works struggle to recover accurate scene geometry when the input views are extremely sparse. To address this issue, we propose MeshSplat, a generalizable sparse-view surface reconstruction framework via Gaussian Splatting. Our key idea is to leverage 2DGS as a bridge, which connects novel view synthesis to learned geometric priors and then transfers these priors to achieve surface reconstruction. Specifically, we incorporate a feed-forward network to predict per-view pixel-aligned 2DGS, which enables the network to synthesize novel view images and thus eliminates the need for direct 3D ground-truth supervision. To improve the accuracy of 2DGS position and orientation prediction, we propose a Weighted Chamfer Distance Loss to regularize the depth maps, especially in overlapping areas of input views, and also a normal prediction network to align the orientation of 2DGS with normal vectors predicted by a monocular normal estimator. Extensive experiments validate the effectiveness of our proposed improvement, demonstrating that our method achieves state-of-the-art performance in generalizable sparse-view mesh reconstruction tasks. Project Page: https://hanzhichang.github.io/meshsplat_web