Closing Operator


This morphological operator can be expressed as composition of a dilation followed by an erosion.

As in the opening operator, the key mechanism under the closing operator is the local comparision of a shape, the structural element, with the object that will be transformed. if, when positioned at a given point, the structural element is included in the complement of the image, then the whole structural element will appear in the complement of the transformed image, otherwise none of its points will appear in this image.

The following figures present a binary image and the result of its closing bu a small euclidian disk.

The following figure presents a colored composition of the original image, its closing by a small Euclidian disk and the structural element positioned in some critical points.

the next three figures show a binary image, the dilation by the sx3 square and the corresponding closing, that is, the erosion of the result of the dilation.

It is worth to note in the figures above the following properties of closing:

This last properties can be used to build dual granulommetries, that is, the separation of holes and their parts by their size relative to a family of homothetic structural elements.

The next two figures show a gray scale image and its closing by a small disk.



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