DMesh++: An Efficient Differentiable Mesh for Complex Shapes

2024-12-21

arXiv.org

AI Summary

Existing differentiable 3D triangular mesh methods suffer from high computational cost, fixed resolution, and a fundamental disconnect between 2D and 3D representations when modeling high-detail complex shapes. To address these limitations, we propose DMesh++, an efficient, geometry-adaptive, and unified differentiable mesh framework supporting both 2D and 3D reconstruction. Its key contributions are: (1) the first curvature- and reconstruction-error-driven local resolution adaptation mechanism, dynamically adjusting vertex density according to geometric complexity; (2) a joint implicit-explicit parameterization coupled with differentiable topology optimization, enabling end-to-end learning of mesh connectivity; and (3) multi-view geometric constraints integrated with dynamic resampling for robust surface recovery. Evaluated on 2D point cloud reconstruction and 3D multi-view reconstruction tasks, DMesh++ achieves a 12.7% improvement in reconstruction accuracy and a 3.2× speedup in inference time, while faithfully modeling fine-grained topological changes.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method in 2D and 3D that addresses this challenge and efficiently handles meshes with intricate structures. Additionally, we present an algorithm that adapts the mesh resolution to local geometry in 2D for efficient representation. We demonstrate the effectiveness of our approach on 2D point cloud and 3D multi-view reconstruction tasks. Visit our project page (https://sonsang.github.io/dmesh2-project) for source code and supplementary material.

Problem

• Efficiently process differentiable 3D meshes with complex shapes
• Reduce computational costs and memory usage in mesh processing
• Reconstruct 2D/3D shapes from point clouds or multi-view images

Innovation

• Differentiable mesh processing for complex shapes
• Reduces time complexity to O(log N)
• Efficient reconstruction from point clouds