3D Object Recognition Based on Canonical Angles between Shape Subspaces

Abstract. We propose a method to measure similarity of shape for 3D objects using 3-dimensional shape subspaces produced by the factoriza-tion method. We establish an index of shape similarity by measuring the geometrical relation between two shape subspaces using canonical angles. The proposed similarity measure is invariant to camera rotation and ob-ject motion, since the shape subspace is invariant to these changes under affine projection. However, to obtain a meaningful similarity measure, we must solve the difficult problem that the shape subspace changes de-pending on the ordering of the feature points used for the factorization. To avoid this ambiguity, and to ensure that feature points are matched between two objects, we introduce a method for sorting the order of fea-ture points by comparing the orthogonal projection matrices of two shape subspaces. The validity of the proposed method has been demonstrated through evaluation experiments with synthetic feature points and actual face images.