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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.
In mathematics, a dilation is a function from a metric space into itself that satisfies the identity. for all points , where is the distance from to and is some positive real number. [1] In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure.
For one gets a point reflection at point. Homothety of a pyramid. In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number called its ratio, which sends point to a point by the rule [1] for a fixed number . Using position vectors: .
Dilation and curettage, the opening of the cervix and surgical removal of the contents of the uterus. Dilation and evacuation, the dilation of the cervix and evacuation of the contents of the uterus. Esophageal dilation, a procedure for widening a narrowed esophagus. Pupillary dilation (also called mydriasis), the widening of the pupil of the eye.
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation ).
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. [1] It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is usually only noticeable at a substantial fraction of the speed of light ...
Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the ...
Erosion (morphology) The erosion of the dark-blue square by a disk, resulting in the light-blue square. Erosion (usually represented by ⊖) is one of two fundamental operations (the other being dilation) in morphological image processing from which all other morphological operations are based. It was originally defined for binary images, later ...