Blurring-invariant Riemannian metrics for comparing signals and images

TitleBlurring-invariant Riemannian metrics for comparing signals and images
Publication TypeConference Papers
Year of Publication2011
AuthorsZhang Z, Klassen E, Srivastava A, Turaga P, Chellappa R
Conference Name2011 IEEE International Conference on Computer Vision (ICCV)
Date Published2011/11/06/13
ISBN Number978-1-4577-1101-5
Keywordsblurring-invariant Riemannian metrics, Estimation, Fourier transforms, Gaussian blur function, Gaussian processes, image representation, log-Fourier representation, measurement, Orbits, Polynomials, signal representation, Space vehicles, vectors

We propose a novel Riemannian framework for comparing signals and images in a manner that is invariant to their levels of blur. This framework uses a log-Fourier representation of signals/images in which the set of all possible Gaussian blurs of a signal, i.e. its orbits under semigroup action of Gaussian blur functions, is a straight line. Using a set of Riemannian metrics under which the group actions are by isometries, the orbits are compared via distances between orbits. We demonstrate this framework using a number of experimental results involving 1D signals and 2D images.