Gradient based optimization of an EMST image registration funtion

This paper examines the problem of registering images using an information theoretic metric (e.g., entropy) estimated using a Euclidean Minimum Spanning Tree (EMST). The objective is to find an extremum of the metric with respect to a vector of free parameters. One of the major difficulties posed by such graph theoretic metrics is concurrently obtaining gradient information as the metric is computed. Obtaining the gradient is a first step in efficiently optimizing the metric. Our main contribution is to show how to obtain a gradient-based descent direction from the computation of the EMST metric. We also indicate how this can be used for optimizing image registration over a vector set of parameters and provide some preliminary experimental results.