[Insight-users] General question about registration

[jj perico]

Thanks Martin.

Then,

   Registration is solved in one step (for a rigid or affine transformation 
models) by using
a simple system of linear equations for the truth matches. For instance, if 
I (manually)
intentionally select a set of relevant features, all of them with their 
right match in the
other image, it'll be solved in one step. I know, if there is no knowledge 
about truth
matches, an iterative (optimization fashion) procedure should be used 
instead, I mean.

Thanks again.

>From: Martin Urschler <martin at urschler.info>
>To: jj perico <ciriushall at hotmail.com>
>Subject: Re: [Insight-users] General question about registration
>Date: Tue, 16 May 2006 11:43:24 +0200
>
>hi
>
>I guess you are right.
>Basically you have to distinguish between feature- and intensity based 
>registration. I assume that you refer to rigid or at most affine 
>registration.
>If you are using intensity based methods for rigid/affine registration you 
>have between 6 and 12 unknowns that parameterize your transformation. These 
>unknowns are determined from a start solution by varying the unknowns and 
>comparing intensity based cost metrics which should decrease. Since this 
>cost function landscape is nonlinear you won't be able to come up with a 
>direct solution. Therefore you need an optimization algorithm in an 
>iterative fashion.
>However if you are using feature based methods you generally can set up a 
>direct solution provided that you have identified corresponding features 
>(e.g. point landmarks). In the rigid case you might align the images by a 
>simple procrustes analysis of the correspondences. Note that you need at 
>least as many feature correspondences as you have unknowns in your assumed 
>transformation you want to derive. In general, since you have uncertainties 
>in feature extraction and/or matching, you will need more correspondences 
>than you have features and you will perform least squares fitting.
>
>For nonlinear registration, the same principle is valid, in feature based 
>registration you can come up with a direct solution using e.g. thin plate 
>splines given a certain minimal number of feature correspondences.
>
>hth,
>Martin

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