Blurring-Invariant Riemannian Metrics for Comparing Signals and Images

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.

• Type: Journal
• Year: 2011
• Where: ICCV
• Authors: Zhengwu Zhang, Eric Klassen, Anuj Srivastava, Pavan Turaga, Rama Chellappa
• Keywords: 2D Images, Computer Vision, Gaussian Blur, ICCV 2011, Riemannian Metrics