Mutual Information Narendhran Vijayakumar 03/14/2008

Definition Mutual Information – I(A,B) Similarity measure – Amount of information B contains about A Registration metric – Maximum MI corresponds to Perfect Alignment – Amount of information B contains about A is maximum when the images are aligned perfectly 2

Mathematical Definition I(A,B) = H(A)+H(B)-H(A,B) – A is the reference image – B is the floating image – H(.) is entropy – I(.,.) is mutual information 3

Entropy H(A) is defined as – H(A) = -∑p i log 2 p i – P i – Probability of the intensities in an image Measure of dispersion of pdf Measure of intensity 4

Joint Probability Image 1 Image 2 5

Joint Probability-Registered image

Misaligned image 567X 13124X 10511X 846X 7

Joint Probability-misregistered images

Conclusion Dispersion Increases (for misaligned images) Joint Probability Value Increases I(A,B) reduces Registration is achieved by minimizing H(A,B) 9