[Mne_analysis] regarding morphing in matlab

[Pavan Ramkumar]

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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