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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.

Click here for a
postscript version of the entire paper (90k).

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