[Mne_analysis] regarding morphing in matlab

[Alexandre Gramfort]

Hi,

if you feel like making this accessible to the MNE community
it would be great to have it directly in the MNE matlab toolbox

https://github.com/mne-tools/mne-matlab

It would be another mne_* function. I can give you access to the
code repository, or you can just send me the m files if you
prefer.

Alex
-- 
Alexandre Gramfort, PhD
gramfort at nmr.mgh.harvard.edu
Dept. of Radiology MGH Martinos Center / Harvard Medical School
http://www-sop.inria.fr/members/Alexandre.Gramfort/

On Tue, Mar 15, 2011 at 8:06 PM, Pavan Ramkumar <pavan at neuro.hut.fi> wrote:
> Dear Matti, Justin, Hari, Dan, Sheraz, and others!
>
> Thanks very much for clarifying and proposing a solution. I guess Justin's
> interpolation method (nearpoints) and Matti's iterative method are
> slightly different in how sparse they allow the 'destination' surface to
> be. I have tested the nearpoints function and it seems to work really well
> & fast! I will also test Matti's suggestion and report back in case I find
> something unexpected.
>
> Thanks again,
> Pavan
>
>>
>> Hi Pavan, Hari, Justin, and others,
>>
>> On Mar 14, 2011, at 12:09 PM, Pavan Ramkumar wrote:
>>
>>> Hi Hari (and others),
>>>
>>> Thanks very much for the suggestions and apologies for the lengthy
>>> reply!
>>>
>>> I did check that most rows are entirely zero (about 2300/2562).
>>> Secondly,
>>> I did look at the vertex numbering and they seem to make sense.
>>> Also, I
>>> visualized the result as stc and they do seem as sparse as the data
>>> matrix
>>> suggests.
>>>
>>> It seems to me that smoothing (or as Matti recommends to call it in
>>> Section 8.3 of the manual v2.6.1 : smudging/blurring) is the root of
>>> the
>>> difference between the mne_make_movie result and my MATLAB
>>> implemenation.
>>
>> The smoothing or spreading operator is, indeed, essential. Here is how
>> the morphing works in mne_make_movie:
>>
>> 1. A morphing map is composed. Using the aligned spherical surfaces (?
>> h.sphere.reg) of the two subjects, you get a linear interpolation
>> (sparse) matrix which interpolates the values at the vertices of a
>> triangle of a "source" surface to get the value at a vertex of the
>> "destination" surface.
>>
>> 2. The vertices of interest on the "destination" surface are
>> determined. This is done by finding the vertices nearest to the
>> vertices of a recursively subdivided icosahedron on the sphere.reg
>> surfaces. Only the rows corresponding to these vertices are retained
>> in the morphing map.
>>
>> 3. Since the interpolation (morphing) matrix not only assumes but
>> requires that data are available on all vertices of the source
>> surface, the spreading operator is applied. This is the one step not
>> currently implemented in Matlab.
>>
>> 4. The smeared data are multiplied by the (restricted) morphing matrix.
>>
>> Here is the recipe we came up with Alex Gramfort during lunch to make
>> the spreading operator matrix. The C code uses direct iteration
>> instead of forming this matrix explicitly. By "valid neigboring
>> vertex" I mean a vertex which is adjacent to the vertex of interest
>> AND belongs to the source space OR has been defined during previous
>> iterations of the spreading operator.
>>
>> This is what you need to do:
>>
>> 0. Initialize the spreading operator as an nvert x nvert identity
>> matrix (S_0)
>> 1. Create an nvert x nvert empty matrix (S)
>> 2. On each row, insert ones to the columns corresponding to the
>> vertices adjacent to the vertex corresponding to the row.
>> 3. Zero columns corresponding to vertices that are not valid.
>> 4. Divide each row by the number of non-zero entries on that row.
>> 4. Compute the spreading operator corresponding to the k'th smoothstep
>> as S_k = S*S_{k-1}
>>
>> I hope this helps.
>>
>> - Matti
>>
>>
>>
>>
>> ---------
>>
>> Matti Hamalainen, Ph.D.
>> Athinoula A. Martinos Center for Biomedical Imaging
>> Massachusetts General Hospital
>>
>> msh at nmr.mgh.harvard.edu
>>
>>
>>
>>
>>
>>
>>
>>
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