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We introduce a novel learning-based method for encoding and manipulating 3D surface meshes. Our method is specifically designed to create an interpretable embedding space for deformable shape collections. Unlike previous 3D mesh…

We formulate object segmentation in video as a graph partitioning problem in space and time, in which nodes are pixels and their relations form local neighborhoods. We claim that the strongest cluster in this pixel-level graph represents…

Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

Along with increasingly popular virtual reality applications, the three-dimensional (3D) point cloud has become a fundamental data structure to characterize 3D objects and surroundings. To process 3D point clouds efficiently, a suitable…

With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…

Permutation synchronization is an important problem in computer science that constitutes the key step of many computer vision tasks. The goal is to recover $n$ latent permutations from their noisy and incomplete pairwise measurements. In…

We propose an approach to reconstruct dense three-dimensional (3D) model of tissue surface from stereo optical videos in real-time, the basic idea of which is to first extract 3D information from video frames by using stereo matching, and…

Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…

We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…

We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows…

With the advancement of computer vision, dynamic 3D reconstruction techniques have seen significant progress and found applications in various fields. However, these techniques generate large amounts of 3D data sequences, necessitating…

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…

Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…

Diffusion Probabilistic Models (DPMs) have achieved great success in image generation but suffer from high inference latency due to their iterative denoising nature. Motivated by the evolving feature dynamics across the denoising…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…

Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match…

Hyperspectral image analysis often requires selecting the most informative bands instead of processing the whole data without losing the key information. Existing band reduction (BR) methods have the capability to reveal the nonlinear…

With the rapid development of high-resolution 3D vision applications, the traditional way of manipulating surface detail requires considerable memory and computing time. To address these problems, we introduce an efficient surface detail…