A Bayesian theoretic approach to multi-scale complex phase order representations

This paper explores a Bayesian theoretic approach to constructing multi-scale complex phase order representations. We formulate the construction of complex phase order representations at different structural scales based on scale space theory. Linear and nonlinear deterministic approaches are explored, and a Bayesian theoretic approach is introduced for constructing representations in such a way that strong structure localization and noise resilience is achieved. Experiments illustrate its potential for constructing robust multi-scale complex phase order representations with well-localized structures across all scales under high noise situations. Illustrative examples of applications of the proposed approach is presented in the form of multimodal image registration and feature extraction.