Continuous image representations avoid the histogram binning problem in mutual information based image registration

Mutual information (MI) based image-registration methods that use histograms are known to suffer from the so-called binning problem, caused by the absence of a principled technique for choosing the "optimal" number of bins to calculate the joint or marginal distributions. In this paper, we show that foregoing the notion of an image as a set of discrete pixel locations, and adopting a continuous representation is the solution to this problem. A new technique to calculate joint image histograms is proposed, which makes use of such a continuous representation. We report results on affine registration of a pair of 2D medical images under high noise, and demonstrate the smoothness of various information-theoretic similarity measures such as joint entropy (JE) or MI w.r.t. the transformation, when our proposed technique (referred to as the "robust histogram") is adopted to compute the required probability distributions