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Groupwise Congealing Algorithm

Learned-Miller et. al. [24] originally introduced their 'congealing' algorithm for registering a set of hand-written digits. The aim was to avoid the arbitrary selection of a co-ordinate frame, by repeatedly registering each image with an evolving "average" model. Given the current set of transformed images (initially the original images), for each pixel position, 2#2, the probability density function of intensities, 89#89, at that position across the set of images, 90#90 is estimated. The objective function is then the sum of entropies of these distributions across the whole image, 91#91. A set of image deformations were optimised to minimise this. In later work on registering sets of 3D medical images [25], the objective function was approximated by 92#92, where 93#93 is the value of pixel 2#2 in deformed image 94#94. During optimisation, each image was warped so as to bring pixels with similar intensities into correspondence across the set. We implemented this later approach.

Roy Schestowitz 2007-03-11