Pitta Santhosh Kumar, Ankush Jain
Abstract: Understanding the effect of blur is an important problem in unconstrained visual analysis. We concentrate on this problem in the context of image-based recognition, by a fusion of image-formation models, as well as differential geometric tools. First, we talk about the space spanned by blurred versions of an image and then under certain assumptions, present a differential geometric analysis of that space. More exclusively, we create a subspace resulting from convolution of an image with a complete set of orthonormal basis functions of a pre-specified maximum size (that can represent an arbitrary blur kernel within that size), and explain that the equivalent subspaces created from a clean image and its blurred versions are equal under the ideal case of zero noise, and some assumptions on the properties of blur kernels. We then learn the practical utility of this subspace representation for the problem of direct recognition of blurred faces and by viewing the subspaces as points on the Grassmann manifold and present methods to perform recognition for cases where the blur is both homogenous and spatially varying. We empirically evaluate the effect of noise, as well as the presence of other facial variations between the gallery and probe images, and give comparisons with existing approaches on usual datasets.
Keywords: Blur, Convolution, Subspace, Grassmann manifold, Face recognition