Neural Marching Cubes

• URL: http://arxiv.org/abs/2106.11272v1
• Date: Mon, 21 Jun 2021 17:18:52 GMT
• Title: Neural Marching Cubes
• Authors: Zhiqin Chen, Hao Zhang
• Abstract summary: We introduce Neural Marching Cubes (NMC), a data-driven approach for extracting a triangle mesh from a discretized implicit field. We show that our network learns local features with limited fields, hence it generalizes well to new shapes and new datasets.
• Score: 14.314650721573743
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce Neural Marching Cubes (NMC), a data-driven approach for extracting a triangle mesh from a discretized implicit field. Classical MC is defined by coarse tessellation templates isolated to individual cubes. While more refined tessellations have been proposed, they all make heuristic assumptions, such as trilinearity, when determining the vertex positions and local mesh topologies in each cube. In principle, none of these approaches can reconstruct geometric features that reveal coherence or dependencies between nearby cubes (e.g., a sharp edge), as such information is unaccounted for, resulting in poor estimates of the true underlying implicit field. To tackle these challenges, we re-cast MC from a deep learning perspective, by designing tessellation templates more apt at preserving geometric features, and learning the vertex positions and mesh topologies from training meshes, to account for contextual information from nearby cubes. We develop a compact per-cube parameterization to represent the output triangle mesh, while being compatible with neural processing, so that a simple 3D convolutional network can be employed for the training. We show that all topological cases in each cube that are applicable to our design can be easily derived using our representation, and the resulting tessellations can also be obtained naturally and efficiently by following a few design guidelines. In addition, our network learns local features with limited receptive fields, hence it generalizes well to new shapes and new datasets. We evaluate our neural MC approach by quantitative and qualitative comparisons to all well-known MC variants. In particular, we demonstrate the ability of our network to recover sharp features such as edges and corners, a long-standing issue of MC and its variants. Our network also reconstructs local mesh topologies more accurately than previous approaches.

Related papers

• SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes [61.110517195874074]
  We present a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh, which implies the discrete mesh. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.
  arXiv  Detail & Related papers  (2024-09-30T17:59:03Z)
• PoNQ: a Neural QEM-based Mesh Representation [33.81124790808585]
  We introduce a learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids.
  arXiv  Detail & Related papers  (2024-03-19T16:15:08Z)
• From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity [54.01594785269913]
  We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. The training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset.
  arXiv  Detail & Related papers  (2023-09-28T15:19:30Z)
• 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)
• Differential Geometry in Neural Implicits [0.6198237241838558]
  We introduce a neural implicit framework that bridges discrete differential geometry of triangle meshes and continuous differential geometry of neural implicit surfaces. It exploits the differentiable properties of neural networks and the discrete geometry of triangle meshes to approximate them as the zero-level sets of neural implicit functions.
  arXiv  Detail & Related papers  (2022-01-23T13:40:45Z)
• Learning Deformable Tetrahedral Meshes for 3D Reconstruction [78.0514377738632]
  3D shape representations that accommodate learning-based 3D reconstruction are an open problem in machine learning and computer graphics. Previous work on neural 3D reconstruction demonstrated benefits, but also limitations, of point cloud, voxel, surface mesh, and implicit function representations. We introduce Deformable Tetrahedral Meshes (DefTet) as a particular parameterization that utilizes volumetric tetrahedral meshes for the reconstruction problem.
  arXiv  Detail & Related papers  (2020-11-03T02:57:01Z)
• Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
  We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them. We provide theoretical insights of our approach using tools from the mesh-simplification literature.
  arXiv  Detail & Related papers  (2020-10-23T14:49:02Z)
• Neural Subdivision [58.97214948753937]
  This paper introduces Neural Subdivision, a novel framework for data-driven coarseto-fine geometry modeling. We optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. We demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.
  arXiv  Detail & Related papers  (2020-05-04T20:03:21Z)

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.