On Thursday 10 February 2005 05:38, Eddie Deng wrote:
> What is the theory for high dimensional warping? Symmetric Priors?
It's all in the following paper:
@article{ashburner00a,
author = {J. Ashburner and J. Andersson and K. J. Friston},
title = {Image Registration using a Symmetric Prior - in Three-Dimensions},
journal = {{H}uman {B}rain {M}apping},
volume = {9},
number = {4},
pages = {212--225},
year = {2000},
}
Two summarise. The registration minimises the sum of two terms. One is the
mean squared difference between the images, and the other is the
regularisation (which penalises unlikely distortions). The idea behind the
regularisation was that the penalty for a forward warp should be the same as
the penalty for its inverse.
Since that paper, I have seen the light, and think that the diffeomorphic
framework of Miller et al is a much better way of doing such stuff (although
I haven't had the chance to do a full 3D implementation yet). See the recent
special issue of NeuroImage for more info on such things (although there is
probably a need for some sort of "Diffeomorphisms for Dummies" paper to be
written before the framework becomes more widely adopted).
Best regards,
-John
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