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Hit-or-miss transform
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Hit-or-miss transform : ウィキペディア英語版
Hit-or-miss transform

In mathematical morphology, hit-or-miss transform is an operation that detects a given configuration (or pattern) in a binary image, using the morphological erosion operator and a pair of disjoint structuring elements. The result of the hit-or-miss transform is the set of positions, where the first structuring element fits in the foreground of the input image, and the second structuring element misses it completely.
== Mathematical definition ==

In binary morphology, an image is viewed as a subset of an Euclidean space \mathbb^d or the integer grid \mathbb^d, for some dimension ''d''. Let us denote this space or grid by ''E''.
A structuring element is a simple, pre-defined shape, represented as a binary image, used to probe another binary image, in morphological operations such as erosion, dilation, opening, and closing.
Let C and D be two structuring elements satisfying C\cap D=\emptyset. The pair (''C'',''D'') is sometimes called a ''composite structuring element''. The hit-or-miss transform of a given image ''A'' by ''B''=(''C'',''D'') is given by:
::A\odot B=(A\ominus C)\cap(A^c\ominus D),
where A^c is the set complement of ''A''.
That is, a point ''x'' in ''E'' belongs to the hit-or-miss transform output if ''C'' translated to ''x'' fits in ''A'', and ''D'' translated to ''x'' misses ''A'' (fits the background of ''A'').

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Hit-or-miss transform」の詳細全文を読む



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