A two-dimensional filter kernel is separable if it can be expressed as the outer product of two vectors. For example, let's look at a Sobel kernel. This kernel can be written as a matrix product of a column and a row vector.

How do I know if my kernel is separable?

4 Answers. A kernel h is separable if and only if all its rows are multiples of each other. Then you can pick one, call it f, make a column of the multiplicative factors, call it g, and find that h=f∗g.

How do I know if my filter is separable?

If the filter is separable, all energy is in the first singular value. If it's not, then it will be distributed among multiple singular values.