Closed-form representation of convolution, dilation, and erosion in the context of image algebra

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