Accelerating the pace of engineering and science

# 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 is a string having one of these 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.

• 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

fspecial supports the generation of efficient, production-quality C/C++ code from MATLAB. For best results, all inputs must be constants at compilation time. Expressions or variables are allowed if their values do not change. To see a complete list of toolbox functions that support code generation, see List of Supported Functions with Usage Notes.

## Class Support

h is of class double.

## Examples

expand all

### Create Various Filters and Filter an Image

```I = imread('cameraman.tif');
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);
```

expand all

### 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))
```