Shape Representation using Gaussian Process mixture models

2026-04-01

AI Summary

This work proposes a lightweight functional shape representation that models geometric surfaces by learning a continuous directional distance field over sparse point clouds, circumventing the high storage overhead and complex indexing requirements of traditional explicit 3D representations such as point clouds and meshes. The approach employs a mixture of local Gaussian processes anchored at structural reference points, integrated with structure-aware decomposition strategies—including skeletonization and distance-based clustering—to flexibly capture complex topologies without relying on heavy neural networks. Experimental results demonstrate that the method achieves efficient and accurate reconstruction of intricate geometries on both the ShapeNetCore and IndustryShapes datasets.

Abstract

Traditional explicit 3D representations, such as point clouds and meshes, demand significant storage to capture fine geometric details and require complex indexing systems for surface lookups, making functional representations an efficient, compact, and continuous alternative. In this work, we propose a novel, object-specific functional shape representation that models surface geometry with Gaussian Process (GP) mixture models. Rather than relying on computationally heavy neural architectures, our method is lightweight, leveraging GPs to learn continuous directional distance fields from sparsely sampled point clouds. We capture complex topologies by anchoring local GP priors at strategic reference points, which can be flexibly extracted using any structural decomposition method (e.g. skeletonization, distance-based clustering). Extensive evaluations on the ShapeNetCore and IndustryShapes datasets demonstrate that our method can efficiently and accurately represent complex geometries.

Problem

• shape representation
• 3D geometry
• storage efficiency
• surface lookup
• functional representation

Innovation

• Gaussian Process mixture models
• functional shape representation
• directional distance fields
• sparse point clouds
• topology-aware modeling