# strel

Morphological structuring element

## Description

A `strel` object represents a flat morphological structuring element, which is an essential part of morphological dilation and erosion operations.

A flat structuring element is a binary valued neighborhood, either 2-D or multidimensional, in which the `true` pixels are included in the morphological computation, and the `false` pixels are not. The center pixel of the structuring element, called the origin, identifies the pixel in the image being processed. Use the `strel` function (described below) to create a flat structuring element. You can use flat structuring elements with both binary and grayscale images. The following figure illustrates a flat structuring element. To create a nonflat structuring element, use `offsetstrel`.

## Creation

### Syntax

``SE = strel(nhood)``
``SE = strel('arbitrary',nhood)``
``SE = strel('diamond',r)``
``SE = strel('disk',r,n)``
``SE = strel('octagon',r)``
``SE = strel('line',len,deg)``
``SE = strel('rectangle',[m n])``
``SE = strel('square',w)``
``SE = strel('cube',w)``
``SE = strel('cuboid',[m n p])``
``SE = strel('sphere',r)``

### Description

````SE = strel(nhood)` creates a flat structuring element with specified neighborhood `nhood`.You can also use the syntax `SE = strel('arbitrary',nhood)` to create a flat structuring element with a specified neighborhood.```
````SE = strel('diamond',r)` creates a diamond-shaped structuring element, where `r` specifies the distance from the structuring element origin to the points of the diamond.```

example

````SE = strel('disk',r,n)` creates a disk-shaped structuring element, where `r` specifies the radius and `n` specifies the number of line structuring elements used to approximate the disk shape. Morphological operations using disk approximations run much faster when the structuring element uses approximations.```
````SE = strel('octagon',r)` creates a octagonal structuring element, where `r` specifies the distance from the structuring element origin to the sides of the octagon, as measured along the horizontal and vertical axes. `r` must be a nonnegative multiple of 3.```

example

````SE = strel('line',len,deg)` creates a linear structuring element that is symmetric with respect to the neighborhood center, with approximate length `len` and angle `deg`.```
````SE = strel('rectangle',[m n])` creates a rectangular structuring element of size ```[m n]```.```

example

````SE = strel('square',w)` creates a square structuring element whose width is `w` pixels.```
````SE = strel('cube',w)` creates a 3-D cubic structuring element whose width is `w` pixels.```
````SE = strel('cuboid',[m n p])` creates a 3-D cuboidal structuring element of size ```[m n p]```. ```

example

````SE = strel('sphere',r)` creates a 3-D spherical structuring element whose radius is `r` pixels.```
Compatibility

The following syntaxes still work, but `offsetstrel` is the preferred way to create these nonflat structuring element shapes:

• `SE = strel('arbitrary',nhood,h)`

• `SE = strel('ball',r,h,n)`

The following syntaxes still work, but are not recommended for use:

• `SE = strel('pair',offset)`

• `SE = strel('periodicline',p,v)`

### Input Arguments

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Neighborhood, specified as numeric array of any dimension. All nonzero pixels of `nhood`belong to the neighborhood for the morphological operation. The center (or origin) of `nhood` is its center element, given by `floor((size(nhood) + 1)/2)`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical`

Radius of the structuring element in the x-y plane, specified as a positive integer.

• For the disk shape, `r` is the distance from the origin to the edge of the disk.

• For the diamond shape, `r` is the distance from the structuring element origin to the points of the diamond.

• For the octagon shape, `r` is the distance from the structuring element origin to the sides of the octagon, as measured along the horizontal and vertical axes. `r` must be a multiple of 3.

Data Types: `double`

Number of periodic line structuring elements used to approximate shape, specified as `0`, `4`, `6`, or `8`. When `n` is greater than 0, the disk-shaped structuring element is approximated by a sequence of `n` periodic-line structuring elements. When `n` is `0`, `strel` does no approximation, and the structuring element members comprise all pixels whose centers are no greater than `r` away from the origin. Morphological operations using disk approximations run much faster when the structuring element uses approximations (`n` > 0). Sometimes it is necessary for `strel` to use two extra line structuring elements in the approximation, in which case the number of decomposed structuring elements used is `n+2`.

Value of nBehavior
`n` > 0`strel` uses a sequence of `n` (or sometimes `n+2`) periodic line-shaped structuring elements to approximate the shape.
`n` = 0`strel` does not use any approximation. The structuring element members comprise all pixels whose centers are no greater than `r` away from the origin and the corresponding height values are determined from the formula of the ellipsoid specified by `r` and `h`.

Data Types: `double`

Length of linear structuring element, specified as a positive number. `len` is approximately the distance between the centers of the structuring element members at opposite ends of the line.

Data Types: `double`

Angle of linear structuring element, in degrees, specified as numeric scalar. The angle is measured in a counterclockwise direction from the horizontal axis.

Data Types: `double`

Size of rectangular structuring element, specified as a 2-element vector of positive integers. The structuring element has m rows and n columns.

Data Types: `double`

Width of square or cubic structuring element, specified as a positive integer.

Data Types: `double`

Size of cuboidal structuring element, specified as a 3-element vector of positive integers. The structuring element has m rows, n columns, and p planes.

Data Types: `double`

## Properties

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Structuring element neighborhood, specified as a logical array.

Data Types: `logical`

Dimensions of structuring element, specified as a nonnegative scalar.

Data Types: `double`

## Object Functions

 `imdilate` Dilate image `imerode` Erode image `imclose` Morphologically close image `imopen` Morphologically open image `imbothat` Bottom-hat filtering `imtophat` Top-hat filtering `bwhitmiss` Binary hit-miss operation
 `decompose` Return sequence of decomposed structuring elements `reflect` Reflect structuring element `translate` Translate structuring element

## Examples

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Create an 11-by-11 square structuring element.

`SE = strel('square', 11)`
```SE = strel is a square shaped structuring element with properties: Neighborhood: [11x11 logical] Dimensionality: 2 ```

Create a line-shaped structuring element with a length of 10 at an angle of 45 degrees.

`SE = strel('line', 10, 45)`
```SE = strel is a line shaped structuring element with properties: Neighborhood: [7x7 logical] Dimensionality: 2 ```

View the structuring element.

`SE.Neighborhood`
```ans = 7x7 logical array 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 ```

Create a disk-shaped structuring element with a radius of 15.

`SE3 = strel('disk', 15)`
```SE3 = strel is a disk shaped structuring element with properties: Neighborhood: [29x29 logical] Dimensionality: 2 ```

Display the disk-shaped structuring element.

```figure imshow(SE3.Neighborhood)``` Create a 3-D sphere-shaped structuring element with a radius of 15.

`SE = strel('sphere', 15)`
```SE = strel is a sphere shaped structuring element with properties: Neighborhood: [31x31x31 logical] Dimensionality: 3 ```

Display the structuring element.

```figure isosurface(SE.Neighborhood)``` ## Tips

• Structuring elements that do not use approximations (`n` = 0) are not suitable for computing granulometries.

## Algorithms

For all shapes except `'arbitrary'`, structuring elements are constructed using a family of techniques known collectively as structuring element decomposition. The principle is that dilation by some large structuring elements can be computed faster by dilation with a sequence of smaller structuring elements. For example, dilation by an 11-by-11 square structuring element can be accomplished by dilating first with a 1-by-11 structuring element and then with an 11-by-1 structuring element. This results in a theoretical performance improvement of a factor of 5.5, although in practice the actual performance improvement is somewhat less. Structuring element decompositions used for the `'disk'` shape is an approximations—all other decompositions are exact.

## Compatibility Considerations

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Behavior changed in R2017b

 van den Boomgard, R, and R. van Balen, "Methods for Fast Morphological Image Transforms Using Bitmapped Images," Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, Vol. 54, Number 3, pp. 252–254, May 1992.

 Adams, R., "Radial Decomposition of Discs and Spheres," Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, Vol. 55, Number 5, pp. 325–332, September 1993.

 Jones, R., and P. Soille, "Periodic lines: Definition, cascades, and application to granulometrie," Pattern Recognition Letters, Vol. 17, pp. 1057–1063, 1996.