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Granulometry (morphology)
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Granulometry (morphology) : ウィキペディア英語版
Granulometry (morphology)
In mathematical morphology, granulometry is an approach to compute a size distribution of grains in binary images, using a series of morphological opening operations. It was introduced by Georges Matheron in the 1960s, and is the basis for the characterization of the concept of ''size'' in mathematical morphology.
== Granulometry generated by a structuring element ==

Let ''B'' be a structuring element in an Euclidean space or grid ''E'', and consider the family \, k=0,1,\ldots, given by:
:B_k=\underbrace_, k=0,1,\ldots, given by:
:\gamma_k(X)=X\circ B_k,
where \circ denotes the morphological opening.
The ''granulometry function'' G_k(X) is the cardinality (i.e., area or volume, in continuous Euclidean space, or number of elements, in grids) of the image \gamma_k(X):
:G_k(X)=|\gamma_k(X)|.
The pattern spectrum or size distribution of ''X'' is the collection of sets \, k=0,1,\ldots, given by:
:PS_k(X) = G_(X)-G_(X).
The parameter ''k'' is referred to as ''size'', and the component ''k'' of the pattern spectrum PS_k(X) provides a rough estimate for the amount of grains of size ''k'' in the image ''X''. Peaks of PS_k(X) indicate relatively large quantities of grains of the corresponding sizes.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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