Hello Silviu,
You're right about the meaning of kernel-weighted ( in this case a 7x7x7 box kernel, the weighting is 1 for each voxel in the box ). Normalisation is how we refer to dividing the convolved values by the sum of the kernel weights, which also corrects for the edge case where not all the kernel voxels are relevant. This is the conventional option, the un-normalised version is provided for more unusual kernels ( e.g. a zero-sum kernel ). The outputs can then be used as in 2).
Hope this helps,
Matthew
>
>
> 1. To be more specific, consider the filtering group, where i used the
> command like:
>
> fslmaths aFile -kernel box 7 -fmean outFile
>
> I think i am taking, around each voxel, a 7x7x7 box centered at that
> voxel, and i believe i am placing the arithmetic mean value in the
> image, at that voxel. (loop over all voxels implied)
>
> I am, however puzzled by the meaning of 'kernel weighted' coupled with
> '(conventionally used with gauss kernel)' and also by the
> 'un-normalised' attribute present in the -fmeanu option. What does
> this mean? :)
>
> (i suppose kernel-weighted simply means in this case that only the
> voxels in the 7x7x7 box are included, i.e. treating the averaging
> process as a convolution with a 7x7x7 uniform box function as a
> symmetric kernel, which is, basically, 1/7^3 * chi_box (the
> 'charactersitic function of the box'). Where does the additional
> 'gauss kernel' fit into this picture? And how about the
> edge-effects in the option below?)
>
> 2. As an extension, suppose i wanted to compute, for a single volume
> image aFile as above, the estimated variance around each voxel over a
> 7x7x7 box as above. Then, since for a sample of size n, this can be
> computed as
>
> estVar = n/(n-1) * (<SqVals> - <Vals>^2) ,
>
> i would have to:
> - square aFile
> - take average over the same box of the squares -> aveSqVals.nii
>
> - take average of aFile
> - square it -> sqAveVals.nii
>
> - subtract the latter from the former and multiply the result
> with n/(n-1), where n=7*7*7=343.
>
> Thank you for your help and patience with me,
>
> Silviu
>
|