Neural Geometry Image-Based Representations with Optimal Transport (OT)

2025-11-23

AI Summary

This work addresses the inefficiency and storage redundancy in neural processing of 3D meshes caused by their irregular connectivity. We propose a decoder-free neural geometric image representation. Our method first employs optimal transport (OT) to optimize vertex sampling distribution, enabling topology-agnostic mapping of arbitrary meshes onto structured geometric images. Next, we construct a multi-scale geometric image pyramid (mipmap), allowing continuous level-of-detail reconstruction via a single forward pass. Finally, neural super-resolution is integrated for end-to-end high-fidelity mesh recovery. Our contributions include: (1) OT-based geometric image parameterization eliminating mesh connectivity constraints; (2) mipmap-enabled efficient multi-resolution inference; and (3) joint optimization of geometric image encoding and super-resolution. Experiments demonstrate state-of-the-art performance in compression ratio, Chamfer distance, and Hausdorff distance—achieving significant improvements in both storage efficiency and reconstruction accuracy.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Representation Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Neural representations for 3D meshes are emerging as an effective solution for compact storage and efficient processing. Existing methods often rely on neural overfitting, where a coarse mesh is stored and progressively refined through multiple decoder networks. While this can restore high-quality surfaces, it is computationally expensive due to successive decoding passes and the irregular structure of mesh data. In contrast, images have a regular structure that enables powerful super-resolution and restoration frameworks, but applying these advantages to meshes is difficult because their irregular connectivity demands complex encoder-decoder architectures. Our key insight is that a geometry image-based representation transforms irregular meshes into a regular image grid, making efficient image-based neural processing directly applicable. Building on this idea, we introduce our neural geometry image-based representation, which is decoder-free, storage-efficient, and naturally suited for neural processing. It stores a low-resolution geometry-image mipmap of the surface, from which high-quality meshes are restored in a single forward pass. To construct geometry images, we leverage Optimal Transport (OT), which resolves oversampling in flat regions and undersampling in feature-rich regions, and enables continuous levels of detail (LoD) through geometry-image mipmapping. Experimental results demonstrate state-of-the-art storage efficiency and restoration accuracy, measured by compression ratio (CR), Chamfer distance (CD), and Hausdorff distance (HD).

Problem

• Developing efficient neural representations for irregular 3D mesh data storage
• Overcoming computational limitations of existing mesh refinement methods
• Applying image-based processing advantages to irregular mesh structures

Innovation

• Geometry image representation transforms meshes into regular grids
• Optimal Transport resolves oversampling and enables continuous LoD
• Decoder-free storage with single-pass restoration from low-resolution mipmaps