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Mathematical Morphology was developed in 1964 by the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France.Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and ...
A binary image is viewed in mathematical morphology as a subset of a Euclidean space R d or the integer grid Z d, for some dimension d. Let E be a Euclidean space or an integer grid, A a binary image in E, and B a structuring element regarded as a subset of R d. The dilation of A by B is defined by
Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0-12-637240-3 (1982) Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances by Jean Serra, ISBN 0-12-637241-1 (1988) An Introduction to Morphological Image Processing by Edward R. Dougherty, ISBN 0-8194-0845-X (1992)
The closing of the dark-blue shape (union of two squares) by a disk, resulting in the union of the dark-blue shape and the light-blue areas. In mathematical morphology, the closing of a set (binary image) A by a structuring element B is the erosion of the dilation of that set,
In binary morphology, an image is viewed as a subset of a Euclidean space or the integer grid, for some dimension d.. The basic idea in binary morphology is to probe an image with a simple, pre-defined shape, drawing conclusions on how this shape fits or misses the shapes in the image.
Structuring elements are particular cases of binary images, usually being small and simple. In mathematical morphology, binary images are subsets of a Euclidean space R d or the integer grid Z d, for some dimension d. Here are some examples of widely used structuring elements (denoted by B): Let E=R 2; B is an open disk of radius r, centered at ...
The image to the right shows the extent of what skeleton morphology can accomplish. Given a partial image, it is possible to extract a much fuller picture. Properly pre-processing the image with a simple Auto Threshold grayscale to binary converter will give the skeletonization function an easier time thinning.
In mathematical morphology, granulometry is an approach to compute a size distribution of grains in binary images, using a series of morphological opening operations. It was introduced by Georges Matheron in the 1960s, and is the basis for the characterization of the concept of size in mathematical morphology.