conv2 (Signal Processing Toolbox)

Two-dimensional convolution.

Syntax

C = conv2(A,B)
C = conv2(A,B,'shape')

Description

C = conv2(A,B)

computes the two-dimensional convolution of matrices A and B. If one of these matrices describes a two-dimensional FIR filter, the other matrix is filtered in two dimensions.

Each dimension of the output matrix C is equal in size to the sum of the corresponding dimensions of the input matrices minus 1. For [ma,na] = size(A) and [mb,nb] = size(B), then

size(C) = [ma+mb-1,na+nb-1]

C = conv2(A,B,'shape')

returns a subsection of the two-dimensional convolution with size specified by shape, where:

full returns the full two-dimensional convolution (default)
same returns the central part of the convolution that is the same size as A
valid returns only those parts of the convolution that are computed without the zero-padded edges. Using this option, size(C) = [ma-mb+1,na-nb+1] when size(A) > size(B)

conv2 executes most quickly when size(A) > size(B).

The conv2 function is part of the standard MATLAB language.

Examples

In image processing, the Sobel edge-finding operation is a two-dimensional convolution of an input array with the special matrix

s = [1 2 1; 0 0 0; -1 -2 -1];

Given any image, the following line extracts the horizontal edges:

h = conv2(I,s);

The lines below extract first the vertical edges, then both horizontal and vertical edges combined:

v = conv2(I,s');
v2 = (sqrt(h.^2 + v.^2))

`conv`	Convolution and polynomial multiplication.
`convn`	N-dimensional convolution (see the online MATLAB Function Reference).
`deconv`	Deconvolution and polynomial division.
`filter2`	Two-dimensional digital filtering.
`xcorr`	Cross-correlation function estimate.
`xcorr2`	Two-dimensional cross-correlation.