Image registration methods in high-dimensional space

Quantitative evaluation of similarity between feature densities of images is an important step in several computer vision and data-mining applications such as registration of two or more images and retrieval and clustering of images. Previously we had introduced a new class of similarity measures based on entropic graphs to estimate Renyi's alpha-entropy, alpha-Jensen difference divergence, alpha-mutual information, and other divergence measures for image registration. Entropic graphs such as the minimum spanning tree (MST) and k-Nearest neighbor (kNN) graph allow the estimation of such similarity measures in higher dimensional feature spaces. A major drawback of histogram-based estimates of such measures is that they cannot be reliably constructed in higher dimensional feature spaces. In this article, we shall briefly extrapolate upon the use of entropic graph based divergence measures mentioned above. Additionally, we shall present estimates of other divergence viz the Geometric-Arithmetic mean divergence and Henze-Penrose affinity. We shall present the application of these measures for pairwise image registration using features derived from independent component analysis of the images. An extension of pairwise image registration is to simultaneously register multiple images, a challenging problem that arises while constructing atlases of organs in medical imaging. Using entropic graph methods we show the feasibility of such simultaneous registration using graph based higher dimensional estimates of entropy measures. Finally we present a new nonlinear correlation measure that is invariant to nonlinear transformations of the underlying feature space and can be reliably constructed in higher dimensions. We present an image clustering experiment to demonstrate the robustness of this measure to nonlinear transformations and contrast it with the clustering performance of the linear correlation coefficient. (C) 2007 Wiley Periodicals, Inc.