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Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for binary images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image.
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 ...
The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
The etymology of the word "morphology" is from the Ancient Greek μορφή (morphḗ), meaning "form", and λόγος (lógos), meaning "word, study, research". [2] [3]While the concept of form in biology, opposed to function, dates back to Aristotle (see Aristotle's biology), the field of morphology was developed by Johann Wolfgang von Goethe (1790) and independently by the German anatomist ...
Generally, the basic morphologies are spheres (coccus) and round-ended cylinders or rod shaped (bacillus). But, there are also other morphologies such as helically twisted cylinders (example Spirochetes), cylinders curved in one plane (selenomonads) and unusual morphologies (the square, flat box-shaped cells of the Archaean genus Haloquadratum ...
Some of the earliest ideas and mathematical descriptions on how physical processes and constraints affect biological growth, and hence natural patterns such as the spirals of phyllotaxis, were written by D'Arcy Wentworth Thompson in his 1917 book On Growth and Form [2] [3] [note 1] and Alan Turing in his The Chemical Basis of Morphogenesis (1952). [6]
In the late twentieth century the field concept of ontogenesis was "rediscovered" as a useful part of developmental biology. It was found, for example, that different mutations could cause the same malformations, suggesting that the mutations were affecting a complex of structures as a unit, a unit that might correspond to the field of early ...
In morphological opening (), the erosion operation removes objects that are smaller than structuring element B and the dilation operation (approximately) restores the size and shape of the remaining objects. However, restoration accuracy in the dilation operation depends highly on the type of structuring element and the shape of the restoring ...