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Determining the separability of a 3D kernel

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AP
AP on 11 Dec 2014
Edited: AP on 11 Dec 2014
I have three kernels of size 2×2×2 (as define below by ker1, ker2, ker3). I wanted to know how I can determine whether these kernels are separable (for 3D convolution purposes). I read online how this can be done in MATLAB for 2D kernels. But rank of a 3D array! mmmm, I don't think there's such thing. Maybe other methods?
The main question is: can a 1D kernel get the 3D convolution result (not using FFT)?
I would be thankful to have the thoughts of my friends in the community on this matter.
>> % I am investigating this in MATLAB
ker1(:,:,1) =
-1 1
-1 1
ker1(:,:,2) =
-1 1
-1 1
>>
ker2(:,:,1) =
-1 -1
-1 -1
ker2(:,:,2) =
1 1
1 1
>>
ker3(:,:,1) =
-1 -1
1 1
ker3(:,:,2) =
-1 -1
1 1

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