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

TL;DR

LiteGE is a lightweight, PCA-based method for efficient geodesic distance computation and shape correspondence, significantly reducing memory and computation while maintaining accuracy, suitable for resource-constrained settings.

Contribution

We propose LiteGE, a novel PCA-based shape descriptor that enables fast, memory-efficient geodesic computation and shape matching without high-capacity neural networks.

Findings

Reduces memory and inference time by up to 300×

Supports sparse point clouds with as few as 300 points

Achieves up to 1000× speedup over mesh-based 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 Principal Component Analysis (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$\times$ 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$\times$ speedup over state-of-the-art mesh-based approaches while maintaining comparable accuracy on non-isometric shape pairs, including evaluations on point-cloud inputs.