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6.3 Binary Morphological Operators

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Interestingly, Equations (6.3.1) and (6.3.2) resemble the familiar convolution sum formulation with OR replacing addition and AND replacing multiplication. Thus the structuring element plays an analogous role in morphological signal processing to the FIR filter in LSI signal processing.
Erosion is a morphological dual to dilation [Gon92, Har92, Pra91]. The set-theoretic definition of erosion follows.
Equivalently, erosion may be defined by the following correlation-like formulation. The erosion of image A with structuring element B, denoted C=AB, has the following matrix formulation:

Binary morphological functions.

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