Title: 3D Shape Generation via Tri-Vectors: a Parsimonious Representation
Primary area: learning on graphs and other geometries & topologies
Keywords: 3D shape representation, generative model, flow matching

Abstract: The pursuit of optimal 3D representations remains both a long-standing challenge and an exciting frontier within the vision and graphics communities. We argue that compressing 3D data into low-dimensional components improves parameter efficiency and captures essential features, providing a parsimonious representation that enhances shape generation. To this end, we propose Tri-Vectors, a parsimonious 3D representation tailored for shape generation. Tri-Vectors instantiates the classical CANDECOMP/PARAFAC (CP) decomposition of a shape’s continuous signed distance field (SDF) into orthogonal tri-vector sets, yielding a compact, resolution-independent, and highly adaptable structure. Specifically, Tri-Vectors has three major advantages: (i) direct shape reconstruction through linear combinations of components, (ii) adjustable dimension and number of components to suit varying shape complexities, and (iii) robustness across arbitrary resolutions. Extensive experiments across multiple datasets show that Tri-Vectors outperforms state-of-the-art methods in terms of parameter efficiency and geometric fidelity. Moreover, we extend its application to textured and deformable shapes, demonstrating the scalability and versatility of the representation.