# conv2

2-D convolution

## Description

returns
the two-dimensional
convolution of matrices `C`

= conv2(`A`

,`B`

)`A`

and `B`

.

## Examples

### 2-D Convolution

In applications such as image processing, it can be useful to compare the input of a convolution directly to the output. The `conv2`

function allows you to control the size of the output.

Create a 3-by-3 random matrix `A`

and a 4-by-4 random matrix `B`

. Compute the full convolution of `A`

and `B`

, which is a 6-by-6 matrix.

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

`Cfull = `*6×6*
0.7861 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 convolution `Csame`

, which is a submatrix of `Cfull`

with the same size as `A`

. `Csame`

is equal to `Cfull(3:5,3:5)`

.

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

`Csame = `*3×3*
3.5790 3.9432 2.9708
3.0052 3.7511 2.7593
2.4492 1.6082 1.7976

### Extract 2-D Pedestal Edges

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)

Convolve the rows of `A`

with the vector `u`

, and then convolve the rows of the result with the vector `v`

. The convolution extracts the horizontal edges of the pedestal.

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

To extract the vertical edges of the pedestal, reverse the order of convolution with `u`

and `v`

.

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

Compute and plot the combined edges of the pedestal.

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

## Input Arguments

`A`

— Input array

vector | matrix

Input array, specified as a vector or matrix.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

**Complex Number Support: **Yes

`B`

— Second input array

vector | matrix

Second input array, specified as a vector or a matrix to convolve
with `A`

. The array `B`

does not
have to be the same size as `A`

.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

**Complex Number Support: **Yes

`u`

— Input vector

row or column vector

Input vector, specified as a row or column vector. `u`

convolves
with each column of `A`

.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

**Complex Number Support: **Yes

`v`

— Second input vector

row or column vector

Second input vector, specified as a row or column vector. `v`

convolves
with each row of the convolution of `u`

with the
columns of `A`

.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

**Complex Number Support: **Yes

`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 as`A`

.`'valid'`

— Return only parts of the convolution that are computed without zero-padded edges.

## Output Arguments

`C`

— 2-D convolution

vector | matrix

2-D convolution, returned as a vector or matrix. When `A`

and `B`

are
matrices, then the convolution `C = conv2(A,B)`

has
size `size(A)+size(B)-1`

. When `[m,n] = size(A)`

, ```
p
= length(u)
```

, and `q = length(v)`

, then
the convolution `C = conv2(u,v,A)`

has `m+p-1`

rows
and `n+q-1`

columns.

When one or more input arguments to `conv2`

are
of type `single`

, then the output is of type `single`

.
Otherwise, `conv2`

converts inputs to type `double`

and
returns type `double`

.

**Data Types: **`double`

| `single`

## More About

### 2-D Convolution

For discrete, two-dimensional variables *A* and *B*,
the following equation defines the convolution of *A* and *B*:

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

*p* and *q* run over all values
that lead to legal subscripts of *A(p,q)* and *B(j-p+1,k-q+1)*.

## Extended Capabilities

### Tall Arrays

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

Usage notes and limitations:

If

`shape`

is`'full'`

(default), then the inputs`A`

and`B`

must not be empty and only one them can be a tall array.If

`shape`

is`'same'`

or`'valid'`

, then`B`

cannot be a tall array.`u`

and`v`

cannot be tall arrays.

For more information, see Tall 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, see Run 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, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

### Distributed Arrays

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

Usage notes and limitations:

Input vectors

`u`

and`v`

must not be distributed arrays.

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

## Version History

**Introduced before R2006a**

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