title: Gaussian blurring-invariant comparison of signals and images.
abstract: We present a Riemannian framework for analyzing signals and images in a manner that is invariant to their level of blurriness, under Gaussian blurring. Using a well known relation between Gaussian blurring and the heat equation, we establish an action of the blurring group on image space and define an orthogonal section of this action to represent and compare images at the same blur level. This comparison is based on geodesic distances on the section manifold which, in turn, are computed using a path-straightening algorithm. The actual implementations use coefficients of images under a truncated orthonormal basis and the blurring action corresponds to exponential decays of these coefficients. We demonstrate this framework using a number of experimental results, involving 1D signals and 2D images. As a specific application, we study the effect of blurring on the recognition performance when 2D facial images are used for recognizing people.
authors.affiliation: Department of Statistics, Florida State University, Tallahassee, FL 32304, USA. zhengwu@stat.fsu.edu
authors.forename: Zhengwu
authors.initials: Z
authors.lastname: Zhang
authors.forename: Eric
authors.initials: E
authors.lastname: Klassen
authors.forename: Anuj
authors.initials: A
authors.lastname: Srivastava
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D005145:Face / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016011:Normal Distribution; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique