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The dilation of a dark-blue square by a disk, resulting in the light-blue square with rounded corners. In binary morphology, dilation is a shift-invariant (translation invariant) operator, equivalent to Minkowski addition.
The opening of the dark-blue square by a disk, resulting in the light-blue square with round corners. In mathematical morphology, opening is the dilation of the erosion of a set A by a structuring element B:
The dilation of the dark-blue square by a disk, resulting in the light-blue square with rounded corners. The dilation of A by the structuring element B is defined by A ⊕ B = ⋃ b ∈ B A b . {\displaystyle A\oplus B=\bigcup _{b\in B}A_{b}.}
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,
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.
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Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
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 k called its ratio, which sends point X to a point X ′ by the rule, [1]