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Structuring Elements

The field of mathematical morphology provides a number of important image processing operations, including erosion, dilation, opening and closing. All these morphological operators take two pieces of data as input. One is the input image, which may be either binary or grayscale for most of the operators. The other is the structuring element. It is this that determines the precise details of the effect of the operator on the image.

The structuring element is sometimes called the kernel, but we reserve that term for the similar objects used in convolutions.

The structuring element consists of a pattern specified as the coordinates of a number of discrete points relative to some origin. Normally cartesian coordinates are used and so a convenient way of representing the element is as a small image on a rectangular grid. Figure 1 shows a number of different structuring elements of various sizes. In each case the origin is marked by a ring around that point. The origin does not have to be in the center of the structuring element, but often it is. As suggested by the figure, structuring elements that fit into a 3×3 grid with its origin at the center are the most commonly seen type.

Figure 1 Some example structuring elements.

Note that each point in the structuring element may have a value. In the simplest structuring elements used with binary images for operations such as erosion, the elements only have one value, conveniently represented as a one. More complicated elements, such as those used with thinning or grayscale morphological operations, may have other pixel values.

An important point to note is that although a rectangular grid is used to represent the structuring element, not every point in that grid is part of the structuring element in general. Hence the elements shown in Figure 1 contain some blanks. In many texts, these blanks are represented as zeros, but this can be confusing and so we avoid it here.

When a morphological operation is carried out, the origin of the structuring element is typically translated to each pixel position in the image in turn, and then the points within the translated structuring element are compared with the underlying image pixel values. The details of this comparison, and the effect of the outcome depend on which morphological operator is being used.


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