How can I determine if my convolution is separable?

What makes a convolution kernel separable? Ho开发者_StackOverfloww would I be able to tell what those separable parts were in order to do two 1D convolutions instead of a 2D convolution>

Thanks

If the 2D filter kernel has a rank of 1 then it is separable. You can test this in e.g. Matlab or Octave:

octave-3.2.3:1>     sobel = [-1 0 1 ; -2 0 2 ; -1 0 1];
octave-3.2.3:2>     rank(sobel)
ans =  1
octave-3.2.3:3> 

See also: http://blogs.mathworks.com/steve/2006/11/28/separable-convolution-part-2/ - this covers using SVD (Singular Value Decomposition) to extract the two 1D kernels from a separable 2D kernel.

See also this question on DSP.stackexchange.com: Fast/efficient way to decompose separable integer 2D filter coefficients

you can also split the matrix into symmetric and skew parts and separate each part, which can be effective for larger 2d convolutions.