att_abstract={{Understanding the effect of blur is an important problem in unconstrained visual analysis. We address this problem in
the context of image-based recognition, by a fusion of image-formation models, and differential geometric tools. First, we discuss
the space spanned by blurred versions of an image and then under certain assumptions, provide a differential geometric analysis
of that space. More specifically, 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 show that the
corresponding 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 study the practical utility of this subspace representation for
the problem of direct recognition of blurred faces, 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 analyze the
effect of noise, as well as the presence of other facial variations between the gallery and probe images, and provide comparisons
with existing approaches on standard datasets.}},
	att_copyright_notice={{This version of the work is reprinted here with permission of IEEE for your personal use. Not for redistribution. The definitive version was published in IEEE Transactions on Pattern Analysis and Machine Intelligence {{, Volume 34}}{{, Issue 6}}{{, 2012-03-31}}
	att_tags={Blur,  Grassmann manifold,  Face recognition},
	author={Raghuraman Gopalan and Sima Taheri and Pavan Turaga and Rama Chellappa},
	institution={{IEEE Transactions on Pattern Analysis and Machine Intelligence}},
	title={{A Blur-robust Descriptor with Applications to Face Recognition}},