Grassmann manifold based shape matching and retrieval under partial occlusions

Abstract

Shape matching and recognition is a challenging task due to geometric distortions and occlusions. A novel shape matching approach based on Grassmann manifold is proposed that affine transformations and partial occlusions are both considered. An affine invariant Grassmann shape descriptor is employed which projects one shape contour to a point on Grassmann manifold and gives the similarity measurement between two contours based on the geodesic distance on the manifold. At first, shape contours are parameterized by affine length and accordingly divided into local affine-invariant shape segments, which are represented by the Grassmann shape descriptor, according to their curvature scale space images. Then the Smith-Waterman algorithm is employed to find the common parts of two shapesr segment sequences, and get the local similarity of shapes. The global similarity is given by the found common parts, and finally the shape recognition accomplished by the weighted sum of local similarity and global similarity. The robustness of the Grassmann shape descriptor is analyzed through subspace perturbation analysis theory. Retrieval experiments show that our approach is effective and robust under affine transformations and partial occlusions.