Differentiable Voxelization of Surface Representations

• URL: http://arxiv.org/abs/2608.15934v1
• Date: Sun, 16 Aug 2026 21:15:05 GMT
• Title: Differentiable Voxelization of Surface Representations
• Abstract summary: We derive a gradient for winding numbers and show that it can be efficiently computed for values sampled on a regular grid.<n>We demonstrate the practical use of this approach at the examples of deforming meshes to resolve intersections, being manufacturable by cutting with representations from three directions.
• Score: 14.232644012462378
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Different shape representations facilitate different computations. Surface representations, in particular meshes, are often used for modeling, whereas volume representations are useful for spatial queries such as intersection or containment. Optimizing a surface representation based on a volumetric properties by gradient descent requires the derivatives of the volume relative to its bounding surface. We derive this gradient for winding numbers and show that it can be efficiently computed for volumetric values sampled on a regular grid (voxel representation) and surface parameters based on vertex sets (triangle meshes). This enables an efficient solution for a variety of optimization problems. We demonstrate the practical use of this approach at the examples of deforming meshes to resolve intersections, being manufacturable by cutting with a bandsaw from three directions, and creating shapes that are close to tiling 3D space.

Related papers

• MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction [38.02000636240954]
  We present MILo, a novel framework that bridges the gap between volumetric and surface representations by differentiably extracting a mesh from the 3D Gaussians.<n>Our approach can reconstruct complete scenes, including backgrounds, with state-of-the-art quality while requiring an order of magnitude fewer mesh vertices than previous methods.
  arXiv  Detail & Related papers  (2025-06-30T17:48:54Z)
• Surf-D: Generating High-Quality Surfaces of Arbitrary Topologies Using Diffusion Models [83.35835521670955]
  Surf-D is a novel method for generating high-quality 3D shapes as Surfaces with arbitrary topologies. We use the Unsigned Distance Field (UDF) as our surface representation to accommodate arbitrary topologies. We also propose a new pipeline that employs a point-based AutoEncoder to learn a compact and continuous latent space for accurately encoding UDF.
  arXiv  Detail & Related papers  (2023-11-28T18:56:01Z)
• Flexible Isosurface Extraction for Gradient-Based Mesh Optimization [65.76362454554754]
  This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives.
  arXiv  Detail & Related papers  (2023-08-10T06:40:19Z)
• MeshDiffusion: Score-based Generative 3D Mesh Modeling [68.40770889259143]
  We consider the task of generating realistic 3D shapes for automatic scene generation and physical simulation. We take advantage of the graph structure of meshes and use a simple yet very effective generative modeling method to generate 3D meshes. Specifically, we represent meshes with deformable tetrahedral grids, and then train a diffusion model on this direct parametrization.
  arXiv  Detail & Related papers  (2023-03-14T17:59:01Z)
• Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulation [54.09274684734721]
  We present a new approach for 3D shape generation, inversion, and manipulation, through a direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose a compact wavelet representation with a pair of coarse and detail coefficient volumes to implicitly represent 3D shapes via truncated signed distance functions and multi-scale biorthogonal wavelets. We may jointly train an encoder network to learn a latent space for inverting shapes, allowing us to enable a rich variety of whole-shape and region-aware shape manipulations.
  arXiv  Detail & Related papers  (2023-02-01T02:47:53Z)
• NeuralMeshing: Differentiable Meshing of Implicit Neural Representations [63.18340058854517]
  We propose a novel differentiable meshing algorithm for extracting surface meshes from neural implicit representations. Our method produces meshes with regular tessellation patterns and fewer triangle faces compared to existing methods.
  arXiv  Detail & Related papers  (2022-10-05T16:52:25Z)
• Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework [11.523323270411959]
  This paper introduces a set of numerical methods for shape analysis of 3D surfaces. We address the computation of geodesics and geodesic distances between parametrized or unparametrized surfaces represented as 3D meshes.
  arXiv  Detail & Related papers  (2022-04-08T18:19:05Z)
• Differentiable Surface Triangulation [40.13834693745158]
  We present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably weighted Delaunay triangulation. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints.
  arXiv  Detail & Related papers  (2021-09-22T12:42:43Z)
• Differentiable Surface Rendering via Non-Differentiable Sampling [19.606523934811577]
  We present a method for differentiable rendering of 3D surfaces that supports both explicit and implicit representations. We show for the first time efficient, differentiable rendering of an iso extracted from a neural radiance field (NeRF), and demonstrate surface-based, rather than volume-based, rendering of a NeRF.
  arXiv  Detail & Related papers  (2021-08-10T19:25:06Z)
• DeepMesh: Differentiable Iso-Surface Extraction [53.77622255726208]
  We introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples. We exploit this to define DeepMesh -- end-to-end differentiable mesh representation that can vary its topology.
  arXiv  Detail & Related papers  (2021-06-20T20:12:41Z)
• Deep Implicit Surface Point Prediction Networks [49.286550880464866]
  Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models. This paper presents a novel approach that models such surfaces using a new class of implicit representations called the closest surface-point (CSP) representation.
  arXiv  Detail & Related papers  (2021-06-10T14:31:54Z)
• MeshSDF: Differentiable Iso-Surface Extraction [45.769838982991736]
  We introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples. We exploit this to define MeshSDF, an end-to-end differentiable mesh representation which can vary its topology.
  arXiv  Detail & Related papers  (2020-06-06T23:44:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.