An Analytical Theory of Mathematical Morphology

Leo Dorst and Rein van den Boomgaard
in: Mathematical Morphology and its Applications to Signal Processing, J. Serra, P. Salembier, eds., Universitat Politecnica de Catalunya, Barcelona, Spain, May 1993, pp. 245-250.

We extend morphology to tangential morphology of differentiable surfaces, described by set-valued functions. We show that there is a preserved logarithmic inner product, and a standard basis of morphological eigenfunctions. The components on this basis form the slope transform. In (logarithmic) analogy to linear signal processing, the slope transform of a dilation equals the sum of the slope transforms.

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