Learning Grassmann manifolds for object state discovery

Abstract

In this paper, we advocate the use of Grassmann manifolds for discovering object images in different states (e.g., unripe, peeled, etc.). We propose a novel dictionary learning algorithm, which derives the subspaces on a Grassmann manifold for describing each object state. By our introduced geodesic-flow constraint, our Grassmann manifold exhibits excellent capabilities in relating objects in distinct states (i.e., subspaces on the derived manifold), while the geodesics connecting different states can be viewed as transformations between the associated states. This is the reason why the use of our proposed Grassmann manifold can be applied to perform object state classification with improved performance. In our experiments, we provide quantitative and qualitative results to verify the effectiveness of our proposed method.