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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