CONV2 Matrix Convolution

Usage

The conv2 function performs a two-dimensional convolution of matrix arguments. The syntax for its use is

    Z = conv2(X,Y)

which performs the full 2-D convolution of X and Y. If the input matrices are of size [xm,xn] and [ym,yn] respectively, then the output is of size [xm+ym-1,xn+yn-1]. Another form is

    Z = conv2(hcol,hrow,X)

where hcol and hrow are vectors. In this form, conv2 first convolves Y along the columns with hcol, and then convolves Y along the rows with hrow. This is equivalent to conv2(hcol(:)*hrow(:)',Y). You can also provide an optional shape argument to conv2 via either

    Z = conv2(X,Y,'shape')
    Z = conv2(hcol,hrow,X,'shape')

where shape is one of the following strings

'full' - compute the full convolution result - this is the default if no shape argument is provided.
'same' - returns the central part of the result that is the same size as X.
'valid' - returns the portion of the convolution that is computed without the zero-padded edges. In this situation, Z has size [xm-ym+1,xn-yn+1] when xm>=ym and xn>=yn. Otherwise conv2 returns an empty matrix.

Function Internals

The convolution is computed explicitly using the definition:

If the full output is requested, then m ranges over 0 <= m < xm+ym-1 and n ranges over 0 <= n < xn+yn-1. For the case where shape is 'same', the output ranges over (ym-1)/2 <= m < xm + (ym-1)/2 and (yn-1)/2 <= n < xn + (yn-1)/2.