Determining the separability of a 3D kernel

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AP 2014-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/166261-determining-the-separability-of-a-3d-kernel

编辑： AP 2014-12-11

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