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.
Click here for a
postscript version of the entire paper (86k).