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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.
The element on the left (in the image) indicates the average height of an adult male in the US: 1.764 m (5 ft 9.4 in). This value is indicated by a horizontally written binary representation of the number 14, which is intended to be multiplied by the wavelength of the message (126 mm); 14 × 126 = 1,764 millimeters.
This simple "probe" is called structuring element, and is itself a binary image (i.e., a subset of the space or grid). Let E be a Euclidean space or an integer grid, and A a binary image in E. The erosion of the binary image A by the structuring element B is defined by: = {},
Binary translation. In computing, binary translation is a form of binary recompilation where sequences of instructions are translated from a source instruction set to the target instruction set. In some cases such as instruction set simulation, the target instruction set may be the same as the source instruction set, providing testing and ...
The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2F n. For example, out of the 16 binary strings of length 4, there are 2F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110. There is an equivalent statement about subsets.
Homogeneous relation. In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. [1] [2] [3] This is commonly phrased as "a relation on X " [4] or "a (binary) relation over X ".
Mathematical morphology. A shape (in blue) and its morphological dilation (in green) and erosion (in yellow) by a diamond-shaped structuring element. Mathematical morphology ( MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions.
Eta Carinae ( η Carinae, abbreviated to η Car ), formerly known as Eta Argus, is a stellar system containing at least two stars with a combined luminosity greater than five million times that of the Sun, located around 7,500 light-years (2,300 parsecs) distant in the constellation Carina. Previously a 4th-magnitude star, it brightened in 1837 ...