Fast 2-D convolution

Speeds up many 2-D convolutions using the SVD; also finds a fast approximation in other cases.

CONVOLVE2 can be used wherever CONV2 is used, taking the same arguments and returning the same results to within a small tolerance. The computation is speeded up by using the singular value decomposition of the mask to express it as a sum of outer products. Each of these can be computed efficiently as convolution with a row and a column vector. CONV2 is used to carry out the individual convolutions.

Separable masks are a particular case and are handled by CONVOLVE2 much as FILTER2 does. Many other masks which are not separable have low rank (e.g. Gabor function masks) and are handled more efficiently by CONVOLVE2.

The function will also compute a reduced-rank approximation to a given mask if required and will use this if it will speed up the computation. An extra argument allows control over the error.

Additional shape options allow: (a) 2-D "circular" convolution - that is, the input array is taken to be periodic rather than surrounded by zeros; (b) a "reflection" boundary condition - that is, the input array is taken to be surrounded by reflected copies of itself.

See 'Computer and Robot Vision' Vol I, by R.M. Haralick and L.G. Shapiro (Addison-Wesley 1992), pp. 298-299.