Improving accuracy and efficiency of mutual information for multi-modal retinal image registration using adaptive probability density estimation

Mutual information (MI) is a popular similarity measure for performing image registration between different modalities. MI makes a statistical comparison between two images by computing the entropy from the probability distribution of the data. Therefore, to obtain an accurate registration it is important to have an accurate estimation of the true underlying probability distribution. Within the statistics literature, many methods have been proposed for finding the 'optimal' probability density, with the aim of improving the estimation by means of optimal histogram bin size selection. This provokes the common question of how many bins should actually be used when constructing a histogram. There is no definitive answer to this. This question itself has received little attention in the MI literature, and yet this issue is critical to the effectiveness of the algorithm. The purpose of this paper is to highlight this fundamental element of the MI algorithm. We present a comprehensive study that introduces methods from statistics literature and incorporates these for image registration. We demonstrate this work for registration of multi-modal retinal images: colour fundus photographs and scanning laser ophthalmoscope images. The registration of these modalities offers significant enhancement to early glaucoma detection, however traditional registration techniques fail to perform sufficiently well. We find that adaptive probability density estimation heavily impacts on registration accuracy and runtime, improving over traditional binning techniques.