Neural Surface Maps

• URL: http://arxiv.org/abs/2103.16942v1
• Date: Wed, 31 Mar 2021 09:48:26 GMT
• Title: Neural Surface Maps
• Authors: Luca Morreale, Noam Aigerman, Vladimir Kim, Niloy J. Mitra
• Abstract summary: We advocate considering neural networks as encoding surface maps. We show it is easy to use them to define surfaces via atlases, compose them for surface-to-surface mappings, and optimize differentiable objectives relating to them, such as any notion of distortion, in a trivial manner.
• Score: 38.172396047006266
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as paramterization, shape analysis, remeshing, and deformation. Unfortunately, most computational representations of surface maps do not lend themselves to manipulation and optimization, usually entailing hard, discrete problems. While algorithms exist to solve these problems, they are problem-specific, and a general framework for surface maps is still in need. In this paper, we advocate considering neural networks as encoding surface maps. Since neural networks can be composed on one another and are differentiable, we show it is easy to use them to define surfaces via atlases, compose them for surface-to-surface mappings, and optimize differentiable objectives relating to them, such as any notion of distortion, in a trivial manner. In our experiments, we represent surfaces by generating a neural map that approximates a UV parameterization of a 3D model. Then, we compose this map with other neural maps which we optimize with respect to distortion measures. We show that our formulation enables trivial optimization of rather elusive mapping tasks, such as maps between a collection of surfaces.

Related papers

• Geometry Distributions [51.4061133324376]
  We propose a novel geometric data representation that models geometry as distributions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity.
  arXiv  Detail & Related papers  (2024-11-25T04:06:48Z)
• Neural Geometry Processing via Spherical Neural Surfaces [29.30952578277242]
  We show how to compute core geometric operators directly on a neural surface representation. These operators, in turn, enable us to create geometry processing tools that act directly on the neural representations. We demonstrate illustrative applications in (neural) spectral analysis, heat flow and mean curvature flow.
  arXiv  Detail & Related papers  (2024-07-10T15:28:02Z)
• Neural Semantic Surface Maps [52.61017226479506]
  We present an automated technique for computing a map between two genus-zero shapes, which matches semantically corresponding regions to one another. Our approach can generate semantic surface-to-surface maps, eliminating manual annotations or any 3D training data requirement.
  arXiv  Detail & Related papers  (2023-09-09T16:21:56Z)
• Learning Neural Implicit Representations with Surface Signal Parameterizations [14.835882967340968]
  We present a neural network architecture that implicitly encodes the underlying surface parameterization suitable for appearance data. Our model remains compatible with existing mesh-based digital content with appearance data.
  arXiv  Detail & Related papers  (2022-11-01T15:10:58Z)
• Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion [71.52576837870166]
  We present Minimal Neural Atlas, a novel atlas-based explicit neural surface representation. At its core is a fully learnable parametric domain, given by an implicit probabilistic occupancy field defined on an open square of the parametric space. Our reconstructions are more accurate in terms of the overall geometry, due to the separation of concerns on topology and geometry.
  arXiv  Detail & Related papers  (2022-07-29T16:55:06Z)
• Neural Convolutional Surfaces [59.172308741945336]
  This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. We show that this approach achieves better neural shape compression than the state of the art, as well as enabling manipulation and transfer of shape details.
  arXiv  Detail & Related papers  (2022-04-05T15:40:11Z)
• A shallow physics-informed neural network for solving partial differential equations on surfaces [0.0]
  We introduce a mesh-free physics-informed neural network for solving partial differential equations on surfaces. With the aid of level set function, the surface geometrical quantities, such as the normal and mean curvature of the surface, can be computed directly and used in our surface differential expressions. With just a few hundred trainable parameters, our network model is able to achieve high predictive accuracy.
  arXiv  Detail & Related papers  (2022-03-03T09:18:21Z)
• 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)
• 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.