Maximization of Mutual Information

Maximization of mutual information is a general approach applicable to a wide range of multi-modality registration applications [1,2,6,11]. One of the strengths of using mutual information (and perhaps in some special cases, one of the weaknesses) is that MI does not use any prior information about the relationship between joint intensity distributions.

Given two random variables X and Y, mutual information is defined as [1]:

 

MI(X, Y) = H(X) + H(Y) - H(X, Y) (1)

The first two terms on the right are the entropies of the two random variables, and encourage transformations that project X into complex parts of Y. The third term, the (negative) joint entropy of X and Y, takes on large values if Xand Y are functionally related, and encourages transformations where X explains Y well. Mutual information does not use an a priori model of the relationships between the intensities of the different images. Our method not only expects the relationship between the intensity values of registered images to be maximal in mutual information, but also to be similar to that of the pre-registered training data of the same modalities. The prior joint intensity model provides the registration algorithm with additional guidance which results in convergence on the correct alignment more quickly, more reliably and from further initial starting points.