A new implementation for the binary and Minkowski operators

The binary and Minkowski operators are considered here to be the set of Boolean functions on binary pictures that perform the functions and, or not, exclusive-or, shrink, dilate, open, close and medial-axis transform. Through proper coding of the objects in a binary picture it is shown that these operators can be implemented in such a way as to decrease significantly computational complexity. The complexity is measured here as the number of primitive operations that must be executed on a picture of size N x N. A primitive operation is, or example, the algebraic comparison of two integer numbers. Except for pathological conditions, the implementation leads to complexities on the order of N; conventional implementations lead to complexities on the order of N/sup 2/.

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