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("diamond",r)

SE = strel("disk",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

Arbitrary Neighborhood Shape

SE = strel(nhood) creates a flat structuring element with specified neighborhood nhood.

2-D Geometric Neighborhood Shapes

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.

SE = strel("disk",r) creates a disk-shaped structuring element, where r specifies the radius.

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 run much faster when the structuring element uses approximations.

SE = strel("octagon",r) creates an 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.

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-by-n.

SE = strel("square",w) creates a square structuring element whose width is w pixels.

3-D Geometric Neighborhood Shapes

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-by-n-by-p pixels.

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), where h is a matrix of the same size as nhood containing the height values associated with each nonzero element of nhood.

• SE = strel("ball",r,h,n)

Input Arguments

nhood — Neighborhood

numeric array

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

r — Radius of structuring element

positive integer

Radius of the structuring element, 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.

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

Data Types: double

n — Number of periodic line structuring elements used to approximate shape

4 (default) | 0 | 6 | 8

Number of periodic line structuring elements used to approximate shape, specified as 0, 4, 6, or 8. Morphological operations using disk approximations run much faster when the structuring element uses approximations (n > 0).

Value of n	Behavior
n > 0	strel uses a sequence of n periodic line-shaped structuring elements to approximate the shape. Sometimes strel must use two extra line structuring elements in the approximation, in which case the actual number of decomposed structuring elements is n+2.
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.

Data Types: double

len — Length of linear structuring element

positive number

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

deg — Angle of linear structuring element

numeric scalar

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

[m n] — Size of rectangular structuring element

2-element vector of positive integers

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

w — Width of square or cubic structuring element

positive integer

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

Data Types: double

[m n p] — Size of cuboidal structuring element

3-element vector of positive integers

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

Neighborhood — Structuring element neighborhood

logical array

Structuring element neighborhood, specified as a logical array.

Data Types: logical

Dimensionality — Dimensions of structuring element

nonnegative scalar

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

Create Square Structuring Element

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 Line-Shaped Structuring Element

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 Disk-Shaped Structuring Element

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 3-D Sphere-shaped Structuring Element

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 of the geometrical shapes, 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.

References

[1] 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.

[2] 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.

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• strel supports the generation of C code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

• All input arguments of type char must be compile-time constants.

• The methods associated with strel objects are not supported in code generation.

• Arrays of strel objects are not supported.

Version History

Introduced before R2006a

R2017b: Linear Structuring Elements Use Angle in Range [0, 180]

Starting in R2017b, strel constrains linear structuring elements to have an angle in the range [0, 180]. If you specify a value of deg outside this range, then strel calculates the angle as mod(deg,180).

Prior to R2017b, in some situations, strel would create different linear structuring elements for angles that differ by a factor of 180 degrees.