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Top-hat transform : ウィキペディア英語版
Top-hat transform
In mathematical morphology and digital image processing, top-hat transform is an operation that extracts small elements and details from given images. There exist two types of top-hat transform: The ''white top-hat transform'' is defined as the difference between the input image and its opening by some structuring element; The ''black top-hat transform'' is defined dually as the difference between the closing and the input image. Top-hat transforms are used for various image processing tasks, such as feature extraction, background equalization, image enhancement, and others.
==Mathematical definitions==

Let f:E\mapsto R be a grayscale image, mapping points from an Euclidean space or discrete grid ''E'' (such as ''R''2 or ''Z''2) into the real line. Let b(x) be a grayscale structuring element.
Then, the white top-hat transform of ''f'' is given by:
:T_w(f)=f-f \circ b,
where \circ denotes the opening operation.
The black top-hat transform of ''f'' (sometimes called the ''bottom-hat'' transform
) is given by:
:T_b(f)=f\bullet b-f,
where \bullet is the closing operation.

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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