Erosion (morphology) - Grayscale Erosion

Grayscale Erosion

In grayscale morphology, images are functions mapping a Euclidean space or grid E into, where is the set of reals, is an element larger than any real number, and is an element smaller than any real number.

Denoting an image by f(x) and the grayscale structuring element by b(x), the grayscale erosion of f by b is given by

,

where "inf" denotes the infimum.

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