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Hierarchical Neural Surfaces for 3D Mesh Compression

Sai Karthikey Pentapati, Gregoire Phillips, Alan Bovik

TL;DR

This work tackles 3D mesh compression by learning hierarchical implicit neural representations anchored on a spherical parameterization of zero-genus meshes. It decomposes the encoding into a coarse INR for the sphere-to-coarse-surface mapping and a fine INR for a displacement field that adds fine geometry, enabling high-quality reconstructions at multiple bitrates with real-time decoding. The approach avoids topological artifacts common in SDF-based methods and supports encoding of surface attributes. Experiments on Thingi10K demonstrate state-of-the-art rate-accuracy trade-offs at high compression, albeit with slower per-instance encoding.

Abstract

Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts of traditional implicit representations of 3D geometries, such as signed distance functions. However, the triangle mesh-based representation of geometry remains the most widely used representation in the industry, while building INRs capable of generating them has been sparsely studied. In this paper, we present a method for building compact INRs of zero-genus 3D manifolds. Our method relies on creating a spherical parameterization of a given 3D mesh - mapping the surface of a mesh to that of a unit sphere - then constructing an INR that encodes the displacement vector field defined continuously on its surface that regenerates the original shape. The compactness of our representation can be attributed to its hierarchical structure, wherein it first recovers the coarse structure of the encoded surface before adding high-frequency details to it. Once the INR is computed, 3D meshes of arbitrary resolution/connectivity can be decoded from it. The decoding can be performed in real time while achieving a state-of-the-art trade-off between reconstruction quality and the size of the compressed representations.

Hierarchical Neural Surfaces for 3D Mesh Compression

TL;DR

This work tackles 3D mesh compression by learning hierarchical implicit neural representations anchored on a spherical parameterization of zero-genus meshes. It decomposes the encoding into a coarse INR for the sphere-to-coarse-surface mapping and a fine INR for a displacement field that adds fine geometry, enabling high-quality reconstructions at multiple bitrates with real-time decoding. The approach avoids topological artifacts common in SDF-based methods and supports encoding of surface attributes. Experiments on Thingi10K demonstrate state-of-the-art rate-accuracy trade-offs at high compression, albeit with slower per-instance encoding.

Abstract

Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts of traditional implicit representations of 3D geometries, such as signed distance functions. However, the triangle mesh-based representation of geometry remains the most widely used representation in the industry, while building INRs capable of generating them has been sparsely studied. In this paper, we present a method for building compact INRs of zero-genus 3D manifolds. Our method relies on creating a spherical parameterization of a given 3D mesh - mapping the surface of a mesh to that of a unit sphere - then constructing an INR that encodes the displacement vector field defined continuously on its surface that regenerates the original shape. The compactness of our representation can be attributed to its hierarchical structure, wherein it first recovers the coarse structure of the encoded surface before adding high-frequency details to it. Once the INR is computed, 3D meshes of arbitrary resolution/connectivity can be decoded from it. The decoding can be performed in real time while achieving a state-of-the-art trade-off between reconstruction quality and the size of the compressed representations.

Paper Structure

This paper contains 10 sections, 1 equation, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Overview
  4. Coarse INR Training
  5. Fine INR Training
  6. Model Architecture
  7. Experiments
  8. Training Details
  9. Additional Experiments
  10. Conclusion

Figures (3)

  • Figure 1: Overview of our method for mesh compression: A given surface is is represented as the inverse function of its spherical parameterization which is then modeled by a hierarchical INR. The methods yields high quality reconstructions even at high compression ratios.
  • Figure 2: Our method accurately reconstructs the originals over a broad range of bitrates. QNDF has visible quantization artifacts, SNS suffers warping artifacts, while QS-DRC produces very low resolution meshes
  • Figure 3: Our method can be successfully extended for compressing surface maps like textures.