Data-Driven Sparse Priors of 3D Shapes

Abstract

We present a sparse optimization framework for extracting sparse shape priors from a collection of 3D models. Shape priors are defined as point-set neighborhoods sampled from shape surfaces which convey important information encompassing normals and local shape characterization. A 3D shape model can be considered to be formed with a set of 3D local shape priors, while most of them are likely to have similar geometry. Our key observation is that the local priors extracted from a family of 3D shapes lie in a very low-dimensional manifold. Consequently, a compact and informative subset of priors can be learned to efficiently encode all shapes of the same family. A comprehensive library of local shape priors is first built with the given collection of 3D models of the same family. We then formulate a global, sparse optimization problem which enforces selecting representative priors while minimizing the reconstruction error. To solve the optimization problem, we design an efficient solver based on the Augmented Lagrangian Multipliers method (ALM). Extensive experiments exhibit the power of our data-driven sparse priors in elegantly solving several high-level shape analysis applications and geometry processing tasks, such as shape retrieval, style analysis and symmetry detection.