Image registration using alpha-entropy measures and entropic graphs

Registration of a reference image to a secondary image extracted from a database of transformed exemplars constitutes an important image retrieval and indexing application. Two important problems are: specification of a general class of discriminatory image features and an appropriate similarity measure to rank the closeness of the query to the database. In this paper we propose a solution using high dimensional image features, which can be either continuous or discrete valued, and a general class of feature similarity measures based on Rényi’s -entropy function. This class of measures contains the well known mutual information measure, its mutual -information ( -MI) variants, and the -Jensen difference. When the features are discrete valued, the -MI can be estimated from the joint feature histogram constructed from the reference and the secondary images using a data structure called a feature coincidence tree. However, histogram estimation techniques become impractical for continuous valued features in high dimension. For such features we propose an alternative similarity measure: the -Jensen difference which can be accurately estimated using an entropic-graph estimator such as the minimal spanning tree (MST). A low time-memory complexity MST is used to compare a variety of continuous and discrete features including single pixel gray levels, tag subimages, and independent component analysis (ICA) coefficient vectors. The methodology is illustrated for ultrasound breast image registration for which we find that the best small angle registration performance is attained by implementing minimal graph entropy estimators on a set of ICA feature vectors.