Orientation-based representations for Mathematical Morphology

Leo Dorst and Rein van den Boomgaard
The paper was first presented as invited paper at the 4th DGCI, Grenoble, France, Sept. 1994; this version is an invited paper for SSPR94, Nahariya, Israel, Oct.94, published in: Shape, Structure and Pattern Recognition, D. Dori, A. Bruckstein, eds., World Scientific, 1995, pp. 13--22.

Dilation is the basic operation of mathematical morphology, and it can be defined on objects or functions. Locally, it preserves the direction of the normal to a boundary. A representation of objects or functions based on this property reduces the dilation to a simple addition operation. This is most clearly demonstrated on tangential dilation, a reformulation of the operation which describes the local touching contact of surfaces (object boundaries or function graphs). Four orientation-based representations are presented and compared: slope diagrams, supporting functions, the normal transform and the slope transform. We also present a discretization method which is especially suited for digital implementation of morphological computations.

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