3D Object Recognition with Enhanced Grassmann Discriminant Analysis

Abstract

Subspace representation has become a promising choice in the classification of 3D objects such as face and hand shape, as it can model compactly the appearance of an object, represent effectively the variations such as the change in pose and illumination condition. Subspace based methods tend to require complicated formulation, though, we can utilize the notion of Grassmann manifold to cast the complicated formulation into a simple one in a unified manner. Each subspace is represented by a point on the manifold. Thank to this useful correspondence, various types of conventional methods have been constructed on a manifold by the kernel trick using a Grassmann kernel. In particular, discriminant analysis on Grassmann manifold (GDA) have been known as one of the useful tools for image set classification. GDA can work as a powerful feature extraction method on the manifold. However, there remains room to improve its ability in that the discriminative space is determined depending on the set of data points on the manifold. This suggests that if the data on a manifold are not so discriminative, the ability of GDA may be limited. To overcome this limitation, we construct a set of more discriminative class subspaces as the input for GDA. For this purpose, we propose to project class subspaces onto a generalized difference subspace (GDS), before mapping class subspaces onto the manifold. The GDS projection can magnify the angles between class subspaces. As a result, the separability of data points between different classes is improved and the ability of GDA is enhanced. The effectiveness of our enhanced GDA is demonstrated through classification experiments with CMU face database and hand shape database.