Grad student seminar | Daniel Otero, Function-valued mappings in imaging

Speaker

Daniel Otero, PhD Candidate
Department of Applied Mathematics, University of Waterloo

Title

Function-valued mappings in imaging

Abstract

The concept of a function whose range is infinite dimensional has been studied by mathematicians since the third decade of the last century. Given this, nowadays there is a vast literature on how the classical results of real-valued functions carry over functions that assume values in a Banach space. Several fields have benefited from these contributions, among them partial differential equations, statistics and harmonic analysis. Surprisingly, the image processing community has barely explored the potential of these mathematical objects. In this talk we discuss how this type of functions, which we call function-valued mappings (FVMs), can be employed in an image processing context. In particular, we present a Fourier transform and a new class of fractal transforms for FVMs. Practical applications are also discussed.