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

TL;DR

LiteGE introduces a memory-efficient pipeline for geodesic distance prediction on 3D shapes by applying PCA to unsigned distance field (UDF) samples over informative voxels. Through shape canonicalization, informative-voxel selection, and a compact UDF-PCA representation, LiteGE replaces heavy 3D backbones with lightweight MLPs that predict geodesic distances and enable fast, robust shape matching across meshes and point clouds, including sparse inputs. The method achieves large practicality gains (up to 300x memory/time reductions) and strong performance on non-isometric shape matching, with up to 1000x speedups over mesh-based approaches while maintaining accuracy. A coarse-to-fine matching strategy and gradient-based geodesic path tracing further enhance efficiency, and results demonstrate good generalization across diverse datasets and input modalities, highlighting LiteGE’s utility for interactive 3D tasks and beyond.

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$\times$ 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.

Figures (5)

• Figure 1: Illustration of shape descriptor creation process in LiteGE. First, each input point cloud is aligned to a canonical upright orientation. Next, the shape is voxelized and the informative voxels near the shapes surface are selected. Finally, we compute the unsigned distance (UDF) from the informative voxels to the shape to construct the final shape descriptor. This is as shown on the rightmost figure where we depicted the cross-section slice of the UDF heatmap through the center of the shape.
• Figure 2: Cumulative variance captured by principal components of UDFs on the SMAL dataset."Point Cloud UDF" denotes shape canonicalization using bounding-box scaling and PCA-based axis alignment, while "Unit Area Mesh UDF" refers to T-Net alignment with unit-area scaling. In both settings, the first 50 principal components account for over 95% of the total UDF variance, highlighting the effectiveness of PCA in creating compact shape descriptors.
• Figure 3: Architecture of LiteGE for geodesic regression. The UDF-PCA shape descriptor and the coordinates of source and destination points are embedded using separate MLPs. These embeddings are combined to produce two shape-specific point embeddings. The geodesic distance is predicted from the difference between the point embeddings.
• Figure 4: Visual comparison of geodesic distance predictions on a sparse (300-point) pig model, with the source point located on the left front paw. Distances are visualized using a heatmap: warmer colors indicate larger distances, while cooler colors indicate smaller ones. The mean prediction errors are 24 for NeuroGF and 2.5 for LiteGE, with ground-truth distances normalized to a mean of 100. This highlights LiteGE's accuracy on sparse point clouds.
• Figure 5: Visual results on shape matching. Left: LiteGE accurately performs point cloud matching on an 8K-sample point cloud derived from a unit-area mesh, achieving a mean geodesic error of 0.022. Matched point pairs are connected by lines. Right: Shape matching performance of LiteGE and SMS on remeshed 5K-vertex models and their broken variants (with 40% of faces randomly removed). Average errors across all test shape pairs are visualized on a dog model.