Using fundamental operators from image algebra, the authors present simple closed-form expressions for dilation, erosion, and convolution. Algebraically, these expressions appear as terms within the algebra. Moreover, the methodology for obtaining the expressions reveals a universal operational structure within image algebra, of which the three aforementioned operations are particular instances. The result is a natural parallel mechanism for computation and a representation of convolution that naturally overcomes the difficulties arising from the variability of image domains in the defining relation.
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