Hierarchical Neural Surfaces for 3D Mesh Compression

2025-12-17

AI Summary

Triangle meshes—the dominant 3D representation in industry—suffer from low compression efficiency, while existing implicit neural representations (INRs) are primarily designed for signed distance functions (SDFs) and other conventional implicit fields, making them ill-suited for direct mesh encoding. Method: We propose a hierarchical implicit neural surface method tailored to genus-zero manifolds. Our approach spherical parameterizes the mesh surface onto the unit sphere, models a continuous displacement field over this domain, and employs a coarse-to-fine hierarchical neural encoding scheme. Contribution/Results: This is the first INR framework enabling both efficient compression and real-time decoding of triangle meshes. It achieves a superior trade-off between compression ratio and geometric fidelity, attains state-of-the-art performance in reconstruction quality versus bit-rate, supports arbitrary-resolution output, enables millisecond-level real-time decoding, and preserves topological consistency.

Technology Category

Machine Learning: Learning with ManifoldsCognitive Modeling & Cognitive Systems: Neural Spike CodingComputer Vision: 3D Computer Vision

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Efficiency and scalability of Web search enginesUser Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Compresses 3D triangle meshes using compact implicit neural representations
• Enables real-time decoding of arbitrary resolution meshes from compressed form
• Achieves optimal balance between reconstruction quality and compression size

Innovation

• Uses spherical parameterization for mesh compression
• Encodes displacement vector field with hierarchical INRs
• Enables real-time decoding of arbitrary resolution meshes