Nonlinear Smart Diffusion: A Probabilistic Approach

North Carolina State University, Raleigh NC

Investigators

Abstract

This research focuses on some fundamental problems in pattern/object recognition/classification, such as gleaning geometric information from images/signals. The investigator proposes to develop nonlinear estimation and filtering techniques capable of coping with noise while preserving the features of interest. Starting with the celebrated Perona-Malik partial differential equation, the investigator proposes to develop a fully probabilistic approach naturally compatible with the presence of the perturbation noise as well as with the underlying geometry typically crucial in this class of problems. Nonlinear diffusions techniques may then be formulated by way of nonlinear stochastic differential equations which in turn, lead to nonhomogeneous Markov chains. In addition to the education goal of motivating and improving the classroom experience, this research has four main objectives: 1. To construct a stochastic framework for interpreting and analyzing Nonlinear Scale Space Analysis. They intend to apply the Stochastic Differential Equations (SDE) mathematical machinery and intuition to advance the understanding of nonlinear scale space analysis. 2. To recast the variational formulation usually corresponding to a nonlinear evolution equation in a ``{\em controlled diffusion}'' setting, and thereby facilitate the choice of evolution and impose constraints for a desired solution. 3. To fully use the above insights to construct a unifying framework that embraces the multiscale wavelet-based and the scale space analyses, and by the same token provide an analytical track to facilitate performance assessment as well as exploit the respective strengths of the two frameworks. The interplay and expected synergy will in addition provide a mechanism for analyzing/extracting other features in an image, such as texture, shapes, specific junctions and others. 4. Apply their theoretical/algorithmic results to specific tasks in pattern classification and recognition problems (in particular shape recognition for wood lumber applications) which have recently been posed to them by some industrial partners.