March 3, 2008
Rami Hagege
Title: Explicit Estimation of Function Deformations (joint work with Joseph M. Francos)
We present a novel theory that rigorously and explicitly solves a fundamental problem in understanding the multiplicity of appearances of the same object in different scenes. This problem has been a long standing challenge in diverse fields of applications, such as image processing, sound analysis and mass spectrometry analysis. However, no satisfactory answer was known: All existing solutions to this highly nonlinear and high dimensional problem are partial, complicated and rely on intuition developed separately for each sub problem. Using some fundamentally new representations of the basic problem, and a new methodology for modeling errors, we show that the original problem can be mapped into an equivalent linear problem defined on a new coordinate system that is natural to the problem. In this framework all classical linear analysis methods are applicable, thus reducing the previously intractable nonlinear problem into a well understood one.