Continuous Procrustes Analysis to Learn 2D Shape Models from 3D objects

Abstract

Two dimensional shape models have been successfully applied to solve many problems in computer vision such as object tracking, recognition and segmentation. Typically, 2D shape models (e.g. Point Distribution Models, Active Shape Models) are learned from a discrete set of image landmarks once the rigid transformations are removed applying Procrustes Analysis (PA). However, the standard PA process suffers from two main limitations: (i) the 2D training samples do not necessarily cover a uniform sampling of all 3D transformations of an object. This can bias the estimate of the shape model; (ii) it can be computationally expensive to learn the shape model by sampling 3D transformations; To solve these problems, we propose Continuous Procrustes Analysis (CPA). CPA uses a continuous formulation that avoids the need to generate 2D projections from all 3D rigid transformations. Furthermore, it builds an efficient (space and time) non-biased 2D shape model from a 3D model of an object. Preliminary experimental results to build 2D shape models of objects and faces show the benefits of CPA over PA.