Signal Processing Toolbox

conv2

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 one less than the sum of the corresponding dimensions of the input matrices. When [ma,na] = size(A) and [mb,nb] = size(B),

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 code extracts the horizontal edges.

h = conv2(I,s);

The following code extracts the vertical edges first, and then extracts both horizontal and vertical edges combined.

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

See Also

conv	Convolution and polynomial multiplication.
convn	N-dimensional convolution (see the MATLAB documentation).
deconv	Deconvolution and polynomial division.
filter2	Apply a two-dimensional filter to data.
xcorr	Cross-correlation function estimate.
xcorr2	Two-dimensional cross-correlation.

conv

convmtx