An Analytical Theory of Mathematical Morphology

Leo Dorst and Rein van den Boomgaard Faculty of Mathematics and Computer Science University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands [email protected] or [email protected] Abstract We extend morphology to tangential morphology of di erentiable 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.