[Math] Looking for techniques of How to measure the Similarity/Dissimilarity between two images

Question

I would like to compute the similarity/dissimilarity between two images L and R.

I know one way which is : computing the histogram of blocks of each image, and then using Bhattacharyya measure I asset if the blocs are similar or not. The histogram are normalized the result are between 0 and 1. The reference to this is on this article :

Bhattacharyya, A., “On a measure of divergence between two statistical
populations defined by their probability distribution,” Bulletin of
the Calcutta Mathematical Society 35, 99–110 (1943).

Well, I know that there is other measures (MI, Tanimoto, etc) and I would like to know if there is other ways to compute the Similarity/Dissimilarity between two images. I mean using histograms , it is kind of region based similarity measure, but is there some pixels related similarity techniques or more region based ones ?

Update 1

To illustrate what I want, here is an example of two images to be compared. As you can see it is related to medical imaging (here there is two parts of the brain but I am talking about a more general case) :

If only I can get a MAP of simmilarity/dissimilarity between those two images. The technique I proposed above works fine , but i am requesting some references for other similar techniques.

Answer 1

One particular application to medical scans, that may be relevant for your problem, is the alignment and fusion of information in images of the same tissue obtained by different methods (MRI, CT, ultrasound). This application goes by the name of image registration, and it has a very extensive literature, with a variety of software tools that you can download.

• The mathematical connections are explored in Mathematics Meets Medicine: An Optimal Alignment. See also this more general review: Mathematical Methods In Medical Image Processing.

• Here is a comparison of 8 different similarity measures that have been tested in this context:

In this paper, eight intensity-based similarity measures for CT and ultrasound scans are evaluated. Six of these use the information from the histogram of images while two of them use the spatial information and intensity values. They are: mutual information, normalized mutual information, entropy correlation coefficient, joint entropy, point similarity measure based on mutual information, histogram energy, correlation ratio, and Woods criterion. Each intensity-based similarity measure was assessed for its capability to align and fuse complementary information in CT and ultrasound images. We compared its accuracy, capture range, distinctiveness of the optimum, risk and non-convergence, and number of minima.

• You can find algorithms for some of these similarity measures in a Matlab toolbox.