# Documentation

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# fspecial

Create predefined 2-D filter

## Syntax

h = fspecial(type)
h = fspecial(type, parameters)

## Description

h = fspecial(type) creates a two-dimensional filter h of the specified type. fspecial returns h as a correlation kernel, which is the appropriate form to use with imfilter. type can have any of the following values:

Value

Description

'average'

Averaging filter

'disk'

Circular averaging filter (pillbox)

'gaussian'

Gaussian lowpass filter

'laplacian'

Approximates the two-dimensional Laplacian operator

'log'

Laplacian of Gaussian filter

'motion'

Approximates the linear motion of a camera

'prewitt'

Prewitt horizontal edge-emphasizing filter

'sobel'

Sobel horizontal edge-emphasizing filter

h = fspecial(type, parameters) accepts the filter specified by type plus additional modifying parameters particular to the type of filter chosen. If you omit these arguments, fspecial uses default values for the parameters.

The following list shows the syntax for each filter type. Where applicable, additional parameters are also shown.

• h = fspecial('average', hsize) returns an averaging filter h of size hsize. The argument hsize can be a vector specifying the number of rows and columns in h, or it can be a scalar, in which case h is a square matrix. The default value for hsize is [3 3].

• h = fspecial('disk', radius) returns a circular averaging filter (pillbox) within the square matrix of size 2*radius+1. The default radius is 5.

• h = fspecial('gaussian', hsize, sigma) returns a rotationally symmetric Gaussian lowpass filter of size hsize with standard deviation sigma (positive). hsize can be a vector specifying the number of rows and columns in h, or it can be a scalar, in which case h is a square matrix. The default value for hsize is [3 3]; the default value for sigma is 0.5. Not recommended. Use imgaussfilt or imgaussfilt3 instead.

• h = fspecial('laplacian', alpha) returns a 3-by-3 filter approximating the shape of the two-dimensional Laplacian operator. The parameter alpha controls the shape of the Laplacian and must be in the range 0.0 to 1.0. The default value for alpha is 0.2.

• h = fspecial('log', hsize, sigma) returns a rotationally symmetric Laplacian of Gaussian filter of size hsize with standard deviation sigma (positive). hsize can be a vector specifying the number of rows and columns in h, or it can be a scalar, in which case h is a square matrix. The default value for hsize is [5 5] and 0.5 for sigma.

• h = fspecial('motion', len, theta) returns a filter to approximate, once convolved with an image, the linear motion of a camera by len pixels, with an angle of theta degrees in a counterclockwise direction. The filter becomes a vector for horizontal and vertical motions. The default len is 9 and the default theta is 0, which corresponds to a horizontal motion of nine pixels.

To compute the filter coefficients, h, for 'motion':

1. Construct an ideal line segment with the desired length and angle, centered at the center coefficient of h.

2. For each coefficient location (i,j), compute the nearest distance between that location and the ideal line segment.

3. h = max(1 - nearest_distance, 0);

4. Normalize h:h = h/(sum(h(:)))

• h = fspecial('prewitt') returns the 3-by-3 filter h (shown below) that emphasizes horizontal edges by approximating a vertical gradient. If you need to emphasize vertical edges, transpose the filter h'.

[ 1  1  1
0  0  0
-1 -1 -1 ]

To find vertical edges, or for x-derivatives, use h'.

• h = fspecial('sobel') returns a 3-by-3 filter h (shown below) that emphasizes horizontal edges using the smoothing effect by approximating a vertical gradient. If you need to emphasize vertical edges, transpose the filter h'.

[ 1  2  1
0  0  0
-1 -2 -1 ]

Code Generation support: Yes.

MATLAB Function Block support: Yes.

## Class Support

h is of class double.

## Examples

collapse all

imshow(I);

Create a motion filter and use it to blur the image. Display the blurred image.

H = fspecial('motion',20,45);
MotionBlur = imfilter(I,H,'replicate');
imshow(MotionBlur);

Create a disk filter and use it to blur the image. Display the blurred image.

H = fspecial('disk',10);
blurred = imfilter(I,H,'replicate');
imshow(blurred);

collapse all

### Code Generation

This function supports the generation of C code using MATLAB® Coder™. For more information, see Code Generation for Image Processing.

When generating code, all inputs must be constants at compilation time.

### MATLAB Function Block

You can use this function in the MATLAB Function Block in Simulink.

When generating code, all inputs must be constants at compilation time.

### Algorithms

fspecial creates Gaussian filters using

${h}_{g}\left({n}_{1},{n}_{2}\right)={e}^{\frac{-\left({n}_{1}^{2}+{n}_{2}^{2}\right)}{2{\sigma }^{2}}}$

$h\left({n}_{1},{n}_{2}\right)=\frac{{h}_{g}\left({n}_{1},{n}_{2}\right)}{\sum _{{n}_{1}}\sum _{{n}_{2}}{h}_{g}}$

fspecial creates Laplacian filters using

${\nabla }^{2}=\frac{{\partial }^{2}}{\partial {x}^{2}}+\frac{{\partial }^{2}}{\partial {y}^{2}}$

${\nabla }^{2}=\frac{4}{\left(\alpha +1\right)}\left[\begin{array}{ccc}\frac{\alpha }{4}& \frac{1-\alpha }{4}& \frac{\alpha }{4}\\ \frac{1-\alpha }{4}& -1& \frac{1-\alpha }{4}\\ \frac{\alpha }{4}& \frac{1-\alpha }{4}& \frac{\alpha }{4}\end{array}\right]$

fspecial creates Laplacian of Gaussian (LoG) filters using

${h}_{g}\left({n}_{1},{n}_{2}\right)={e}^{\frac{-\left({n}_{1}^{2}+{n}_{2}^{2}\right)}{2{\sigma }^{2}}}$

$h\left({n}_{1},{n}_{2}\right)=\frac{\left({n}_{1}^{2}+{n}_{2}^{2}-2{\sigma }^{2}\right){h}_{g}\left({n}_{1},{n}_{2}\right)}{2\pi {\sigma }^{6}\sum _{{n}_{1}}\sum _{{n}_{2}}{h}_{g}}$

fspecial creates averaging filters using

ones(n(1),n(2))/(n(1)*n(2))