3D Object Recognition Based on Canonical Angles between Shape Subspaces

Our goal is to realize a framework for 3D object recognition, which is invariant to camera rotation and object motion. How was the framework achieved? We establish an index of shape similarity by measuring the geometrical relation between two shape subspaces using canonical angles. To obtain a similarity, we must solve the point matching problem. We introduce a new method to solve the problem by comparing the orthogonal projection matrices of two shape subspaces. Concept of our framework for 3D object recognition (1) The feature points are tracked through image sequence for each object. (2) The shape subspaces are derived from the sets of the tracked feature points by the factorization method. (3) Canonical angles between the shape subspaces are calculated and used to construct a measure of shape similarity. 1. Calculation of shape subspace with factorization of an image sequence The measurement matrix W is factored into the product of three matrices. The column vectors of shape matrix V span shape subspace. 2. Similarity based on canonical angles between shape subspaces Let QA and QB denote the orthogonal projection matrices of the shape subspaces SA and SB. Then, cos 2θi for the canonical angle θi is equal to the i-th largest eigenvalue of QAQB. We define the shape similarity Sim as follows