Shape Representation using Gaussian Process mixture models
This work addresses storage and computational inefficiencies in 3D modeling for applications like computer graphics or CAD, though it appears incremental as it builds on existing functional representation ideas.
The authors tackled the problem of inefficient 3D shape representation by proposing a lightweight functional method using Gaussian Process mixture models, which achieved efficient and accurate representation of complex geometries on ShapeNetCore and IndustryShapes datasets.
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.