[VBMEG-users:00149] About the coregistration matrix

[Chang Cai]

Dear VBMEG users

Here is a part of description about the coregistration matrix for
inter-subject analysis from VBMEG manual.

There are several points I still cannot understand.

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-----------------

. Each component of the projection matrix, C_{ij}, is proportional to
exp(-(d_{ij}/R)^{2}), where R is a tunable coefficient and d_{ij} is the
distance between the i-th vertex of the template model and the j-th vertex
of the source model, on a common coordinate system .

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-----------------

(1) About "C_{ij}, is proportional to exp(-(d_{ij}/R)^{2})", I understand
the "proportional" as

C_{ij} = Z exp(-(d_{ij}/R)^{2}).

If I am correct, is Z a constant or varies across vertices? What is the
physical meaning by Z? What determines Z?

(2) About "R is a tunable coefficient", what is the physical meaning by
R? Is R a constant or varies across vertices?

(3) About "{2}", why should there be "{ }"? Can I just rewrite the
"exp(-(d_{ij}/R)^{2})" to "exp(-(d_{ij}/R)^2)"?



Sorry for so many small questions.

Because we might put the definition of the coregistration matrix
(exp(-(d_{ij}/R)^{2})) into paper, so we need to know every detail about it.



Best Regards

Chang Cai

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[佐藤雅昭]

Dear Cai-san

This coregistration program is written by Yoshioka-san.
Then, I am not so confident of my answer.
I wrote the following by looking at the corresponding program
'vb_job_coreg_brain.m'

>(1) About "C_{ij}, is proportional to exp(-(d_{ij}/R)^{2})", I understand
>the "proportional" as
>
>C_{ij} = Z exp(-(d_{ij}/R)^{2}).
>
>If I am correct, is Z a constant or varies across vertices? What is the
>physical meaning by Z? What determines Z?

Z is a normalization constant such that C_{ij} satisfy
sum_{j} C_{ij} = 1
then Z depends on 'i'.

>(2) About "R is a tunable coefficient", what is the physical meaning by
>R? Is R a constant or varies across vertices?

R is a constant.
R controls the serch range around the neighborhood of the vertex.

% R : <optional> <<double>> Scaling parameter for
% coregistration matrix (default = 0.01).

>(3) About "{2}", why should there be "{ }"? Can I just rewrite the
>"exp(-(d_{ij}/R)^{2})" to "exp(-(d_{ij}/R)^2)"?

Yes, you can remove {}.

>Because we might put the definition of the coregistration matrix
>(exp(-(d_{ij}/R)^{2})) into paper, so we need to know every detail about it.

If possible, please send your manuscript.

Best regard,


Masa-aki Sato

Best regard,

Masa-aki Sato