element is defined by

where is the translation of by the vector , i.e.,

When the structuring element has a center (e.g., is a disk or a square), and this center is located on the origin of , then the erosion of by can be understood as the locus of points reached by the center of when moves inside . For example, the erosion of a square of side , centered at the origin, by a disc of radius , also centered at the origin, is a square of side centered at the origin.

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