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.
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Mathematical definitions
Let
Then, the white top-hat transform of f is given by:
where
The black top-hat transform of f (sometimes called the bottom-hat transform ) is given by:
where
Properties
The white top-hat transform returns an image, containing those "objects" or "elements" of an input image that:
The black top-hat returns an image, containing the "objects" or "elements" that:
The size, or width, of the elements that are extracted by the top-hat transforms can be controlled by the choice of the structuring element
Both top-hat transforms are images that contain only non-negative values at all pixels.