Shape Representation using Gaussian Process mixture models

TL;DR

This paper introduces a compact, continuous shape representation using Gaussian Process mixture models that efficiently captures complex 3D geometries from sparse data without heavy neural networks.

Contribution

It proposes a novel object-specific functional shape representation with GPs, enabling efficient modeling of complex geometries from sparse point clouds.

Findings

Accurately models complex geometries on ShapeNetCore and IndustryShapes datasets.

Uses local GP priors anchored at reference points for topology capture.

Achieves efficient shape representation without neural network reliance.

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.