Unsupervised Label Learning on Manifolds by Spatially Regularized Geometric Assignment

Abstract

Manifold models of image features abound in computer vision. We present a novel approach that combines unsupervised computation of representative manifold-valued features, called labels, and the spatially regularized assignment of these labels to given manifold-valued data. Both processes evolve dynamically through two Riemannian gradient flows that are coupled. The representation of labels and assignment variables are kept separate, to enable the flexible application to various manifold data models. As a case study, we apply our approach to the unsupervised learning of covariance descriptors on the positive definite matrix manifold, through spatially regularized geometric assignment.