conv2

2-D convolution

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Syntax

C = conv2(A,B)

C = conv2(u,v,A)

C = conv2(___,shape)

Description

example

C= conv2(A,B)returns thetwo-dimensional convolution矩阵的AandB.

example

C= conv2(u,v,A)first convolves each column ofAwith the vectoru, and then it convolves each row of the result with the vectorv.

example

C= conv2(___,shape)returns a subsection of the convolution according toshape. For example,C = conv2(A,B,'same')returns the central part of the convolution, which is the same size asA.

Examples

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2-D Convolution

Open Live Script

In applications such as image processing, it can be useful to compare the input of a convolution directly to the output. Theconv2function allows you to control the size of the output.

Create a 3-by-3 random matrixAand a 4-by-4 random matrixB. Compute the full convolution ofAandB, which is a 6-by-6 matrix.

A = rand(3); B = rand(4); Cfull = conv2(A,B)

Cfull =6×60.7861 1.2768 1.4581 1.0007 0.2876 0.0099 1.0024 1.8458 3.0844 2.5151 1.5196 0.2560 1.0561 1.9824 3.5790 3.9432 2.9708 0.7587 1.6790 2.0772 3.0052 3.7511 2.7593 1.5129 0.9902 1.1000 2.4492 1.6082 1.7976 1.2655 0.1215 0.1469 1.0409 0.5540 0.6941 0.6499

Compute the central part of the convolutionCsame, which is a submatrix ofCfullwith the same size asA.Csameis equal toCfull(3:5,3:5).

Csame = conv2(A,B,'same')

Csame =3×33.5790 3.9432 2.9708 3.0052 3.7511 2.7593 2.4492 1.6082 1.7976

Extract 2-D Pedestal Edges

Open Live Script

The Sobel edge-finding operation uses a 2-D convolution to detect edges in images and other 2-D data.

Create and plot a 2-D pedestal with interior height equal to one.

A = zeros(10); A(3:7,3:7) = ones(5); mesh(A)

Figure contains an axes object. The axes object contains an object of type surface.

Convolve the rows ofAwith the vectoru, and then convolve the rows of the result with the vectorv. The convolution extracts the horizontal edges of the pedestal.

u = [1 0 -1]'; v = [1 2 1]; Ch = conv2(u,v,A); mesh(Ch)

Figure contains an axes object. The axes object contains an object of type surface.

To extract the vertical edges of the pedestal, reverse the order of convolution withuandv.

Cv = conv2(v,u,A); mesh(Cv)

Figure contains an axes object. The axes object contains an object of type surface.

Compute and plot the combined edges of the pedestal.

figure mesh(sqrt(Ch.^2 + Cv.^2))

Figure contains an axes object. The axes object contains an object of type surface.

Input Arguments

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`A`—Input array
vector|matrix

Input array, specified as a vector or matrix.

`B`—Second input array
vector|matrix

Second input array, specified as a vector or a matrix to convolve withA. The arrayBdoes not have to be the same size asA.

`u`—Input vector
row or column vector

Input vector, specified as a row or column vector.uconvolves with each column ofA.

`v`—Second input vector
row or column vector

Second input vector, specified as a row or column vector.vconvolves with each row of the convolution ofuwith the columns ofA.

`shape`—Subsection of convolution
`'full'`(default) |`'same'`|`'valid'`

Subsection of the convolution, specified as one of these values:

'full'— Return the full 2-D convolution.
'same'— Return the central part of the convolution, which is the same size asA.
'valid'— Return only parts of the convolution that are computed without zero-padded edges.

Output Arguments

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`C`——二维卷积
vector | matrix

2-D convolution, returned as a vector or matrix. WhenAandBare matrices, then the convolutionC = conv2(A,B)has sizesize(A)+size(B)-1. When[m,n] = size(A),p = length(u), andq = length(v), then the convolutionC = conv2(u,v,A)hasm+p-1rows andn+q-1columns.

When one or more input arguments toconv2are of typesingle, then the output is of typesingle. Otherwise,conv2converts inputs to typedoubleand returns typedouble.

Data Types:double|single

More About

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2-D Convolution

For discrete, two-dimensional variablesAandB, the following equation defines the convolution ofAandB:

$C (j, k) = \sum_{p} \sum_{q} A (p, q) B (j - p + 1, k - q + 1)$

pandqrun over all values that lead to legal subscripts ofA(p,q)andB(j-p+1,k-q+1).

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

使用笔记和限制:

Ifshapeis'full'(default), then the inputsAandBmust not be empty and only one them can be a tall array.
Ifshapeis'same'or'valid', thenBcannot be a tall array.
uandvcannot be tall arrays.

For more information, seeTall Arrays.

C / C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, seeRun MATLAB Functions on a GPU(Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

使用笔记和限制:

Input vectorsuandvmust not be distributed arrays.

For more information, seeRun MATLAB Functions with Distributed Arrays(Parallel Computing Toolbox).

Version History

Introduced before R2006a

conv2

Syntax

Description

Examples

2-D Convolution

Extract 2-D Pedestal Edges

Input Arguments

A—Input arrayvector|matrix

B—Second input arrayvector|matrix

u—Input vectorrow or column vector

v—Second input vectorrow or column vector

shape—Subsection of convolution'full'(default) |'same'|'valid'

Output Arguments

C——二维卷积vector | matrix

More About

2-D Convolution

Extended Capabilities

Tall ArraysCalculate with arrays that have more rows than fit in memory.

C / C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

GPU Code GenerationGenerate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based EnvironmentRun code in the background using MATLAB®backgroundPoolor accelerate code with Parallel Computing Toolbox™ThreadPool.

GPU ArraysAccelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

See Also

`A`—Input array
vector|matrix

`B`—Second input array
vector|matrix

`u`—Input vector
row or column vector

`v`—Second input vector
row or column vector

`shape`—Subsection of convolution
`'full'`(default) |`'same'`|`'valid'`

`C`——二维卷积
vector | matrix

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C / C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.