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Structuring Elements

An essential part of the morphological dilation and erosion operations is the structuring element used to probe the input image. A structuring element is a matrix that defines the neighborhood used to process each pixel in the image. The center pixel of the structuring element, called the origin, identifies the pixel in the image being processed.

You typically choose a structuring element of the same size and shape as the objects you want to process in the input image. For example, to find lines in an image, create a linear structuring element.

There are two types of structuring elements: flat and nonflat. A flat structuring element is a binary valued neighborhood, either 2-D or multidimensional, in which the true (1-valued) pixels are included in the morphological operation, and the false (0-valued) pixels are not. Use the strel function 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.

A 3-by-3 structuring element includes true-valued pixels in the morphological operation and excludes false-valued pixels

You can use nonflat structuring elements only with grayscale images. A nonflat structuring element includes an additive offset for each pixel in the neighborhood. Pixels in the neighborhood that have a finite real value are used in the morphological operation. Pixels in the neighborhood with the value -Inf are not used in the operation. Use the offsetstrel function to create a nonflat structuring element.

Pixels in the 3-by-3 neighborhood of a nonflat structuring element have different additive offsets, such as 3.0, 4.0, and -Inf.

Determine the Origin of a Structuring Element

The morphological functions use this code to get the coordinates of the origin of structuring elements of any size and dimension:

origin = floor((size(nhood)+1)/2)

where nhood is the neighborhood defining the structuring element. To see the neighborhood of a flat structuring element, view the Neighborhood property of the strel object. To see the neighborhood of a nonflat structuring element, view the Offset property of the offsetstrel object.

For example, the following illustrates the origin of a flat, diamond-shaped structuring element.

The origin of a flat diamond-shaped structuring element is the center pixel.

Structuring Element Decomposition

To enhance performance, the strel and offsetstrel functions might break structuring elements into smaller pieces, a technique known as structuring element decomposition.

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 speed improvement of a factor of 5.5, although in practice the actual speed improvement is somewhat less.

Structuring element decompositions used for the "disk" and "ball" shapes are approximations; all other decompositions are exact. Decomposition is not used with an arbitrary structuring element unless it is a flat structuring element whose neighborhood matrix is all 1's.

To see the sequence of structuring elements used in a decomposition, use the decompose method. Both strel objects and offsetstrel objects support decompose methods. The decompose method returns an array of the structuring elements that form the decomposition. For example, here are the structuring elements created in the decomposition of a diamond-shaped structuring element.

SE = strel("diamond",4)
SE = 

strel is a diamond shaped structuring element with properties:

      Neighborhood: [9x9 logical]
    Dimensionality: 2

Call the decompose method. The method returns an array of structuring elements.

ans = 

  3x1 strel array with properties:


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