Three-dimensional Object Recognition via Subspace Representation on a Grassmann Manifold

In this paper, we propose a method for recognizing three-dimensional (3D) objects using multi-view depth images. To derive the essential 3D shape information extracted from these images for stable and accurate 3D object recognition, we need to consider how to integrate partial shapes of a 3D object. To address this issue, we introduce two ideas. The first idea is to represent a partial shape of the 3D object by a three-dimensional subspace in a high-dimensional vector space. The second idea is to represent a set of the shape subspaces as a subspace on a Grassmann manifold, which reflects the 3D shape of the object more completely. Further, we measure the similarity between two subspaces on the Grassmann manifold by using the canonical angles between them. This measurement enables us to construct a more stable and accurate method based on richer information about the 3D shape. We refer to this method based on subspaces on a Grassmann manifold as the Grassmann mutual subspace method (GMSM). To further enhance the performance of the GMSM, we equip it with powerful feature-extraction capabilities. The validity of the proposed method is demonstrated through experimental comparisons with several conventional methods on a hand-depth image dataset.