Entropic graphs for image registration.

Abstract

Given 2D or 3D images gathered via multiple sensors located at different positions, the multi-sensor image registration problem is to align the images so that they have an identical pose in a common coordinate system. Image registration methods depend crucially upon a robust image similarity measure to guide the image alignment. This thesis concerns itself with a new class of such similarity measures. The launching point of this thesis is the entropic graph based estimate of Renyi's alpha-entropy developed by Ma for image registration. This thesis extends this initial work to develop other entropic graph-based divergence measures to be used with advanced higher dimensional features. A detailed analysis of entropic graphs is followed by a demonstration of their performance advantages relative to conventional similarity measures. This thesis introduces techniques to extend image registration to higher dimension feature spaces using Renyi's generalized alpha-entropy. The alpha-entropy is estimated directly through continuous quasi-additive power-weighted graphs such as the minimal spanning tree (MST) and k-Nearest Neighbor graph (kNN). Entropic graph methods are further used to approximate similarity measures like the alpha-mutual information, non-linear correlation coefficient, alpha-Jensen divergence, Henze-Penrose affinity and Geometric-Arithmetic mean affinity. Entropic-graph similarity measures are applied to problems in breast Ultrasound image registration for cancer management, geo-stationary satellite registration, feature clustering and classification and for atlas based multi-image registration. This last work is a novel and significant application of divergence estimation for registering several images simultaneously. These similarity measures offer robust registration benefits in a multisensor environment. Higher dimensional features used for this work include basis functions like multidimensional wavelets, independent component analysis (ICA) and discrete cosine transforms.