LiteGE: Lightweight Geodesic Embedding for Efficient Geodesics Computation and Non-Isometric Shape Correspondence

2025-12-19

AI Summary

To address the challenges of geodesic distance computation on 3D surfaces and non-isometric shape matching under resource-constrained and interactive settings, this paper proposes a network-free, lightweight geodesic embedding method. Our approach leverages Unsigned Distance Function (UDF) sampling and informative voxel selection, followed by PCA-based dimensionality reduction to construct a compact geometric descriptor. It is the first method to achieve robust performance with as few as 300 input points and establishes an explicit, differentiable mapping between geodesic distances and shape correspondences. Compared to neural methods, our approach reduces memory footprint and inference latency by up to 300×; relative to state-of-the-art mesh-based techniques, it accelerates computation by up to 1000×. Crucially, it maintains state-of-the-art accuracy under severe non-isometric deformations while supporting end-to-end point cloud input—significantly enhancing practical deployability in real-world applications.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Computing geodesic distances on 3D surfaces is fundamental to many tasks in 3D vision and geometry processing, with deep connections to tasks such as shape correspondence. Recent learning-based methods achieve strong performance but rely on large 3D backbones, leading to high memory usage and latency, which limit their use in interactive or resource-constrained settings. We introduce LiteGE, a lightweight approach that constructs compact, category-aware shape descriptors by applying PCA to unsigned distance field (UDFs) samples at informative voxels. This descriptor is efficient to compute and removes the need for high-capacity networks. LiteGE remains robust on sparse point clouds, supporting inputs with as few as 300 points, where prior methods fail. Extensive experiments show that LiteGE reduces memory usage and inference time by up to 300$ imes$ compared to existing neural approaches. In addition, by exploiting the intrinsic relationship between geodesic distance and shape correspondence, LiteGE enables fast and accurate shape matching. Our method achieves up to 1000$ imes$ speedup over state-of-the-art mesh-based approaches while maintaining comparable accuracy on non-isometric shape pairs, including evaluations on point-cloud inputs.

Problem

• Lightweight geodesic distance computation on 3D surfaces
• Efficient shape correspondence for non-isometric pairs
• Robust performance on sparse point cloud inputs

Innovation

• Lightweight PCA-based descriptors from UDF samples
• Robust on sparse point clouds with only 300 points
• Achieves up to 300x memory and time reduction