Maximum Likelihood Image Registration With Subpixel Accuracy

Michael S. Mort M. D. SrinathSignal Analytics374 Maple Ave. East Suite 200Vienna, VA 22180ABSTRACTDepartment of Electrical EngineeringSouthern Methodist UniversityDallas, TX 75275The problem addressed in this paper is to estimate, with an error which is substantially less than the dimensions of a pixel,the unknown displacement d between two images of a common scene, given only the image data. Assuming a Gauss - Markovmodel for the scene, the joint probability density function of the two images is obtained and an implicit expression for themaximum likelihood estimate of the displacement is found as the maximum of a functional J( d). The sensitivity of thealgorithm to the model parameters has been determined by experiments on 32 real images. The experiments show that amean absolute error of 1/20 of a pixel dimension is achievable for rms signal to nus noise ratios down to a value of 5.1. INTRODUCTIONLet g(i,k,0) and g(i,k,1) be two frames of sampled image data formed by imaging the same continuous scene r(u), uE R2. Weassume that the imaging process is noisy and that the two frames are displaced by an unknown amount dE R2, so thatg(i,k,0) = r(iAxl,k6,x2) + w(i,k,0)g(i,k,l) = r(iAxl +dl,kAx2 +d2) + w(i,k,l)where (ixi3Ox2) is the image sample spacing, and w(i,k,t), t =1,2, is sensor noise. If r(nJ is known, then it can be shown1that the maximum likelihood estimate of d is given by