The optimal implementation of morphological operations on neighborhood connected array processors

Neighborhood-connected array processors can implement Minkowski addition and Minkowski subtraction operations with structuring elements larger than the neighborhood size by breaking the operation into a sequence of successive neighborhood operations. The author provides a complete solution to the problem of decomposing convex polygons into subsets of the 3×3 neighborhood set. With the help of the Freeman chain code notation, it is proved that all convex polygons have neighborhood decompositions. Based on this result, an efficient algorithm is developed which can find an optimal decomposition for any convex polygon. The decomposition produced by the algorithm can be used to determine the most efficient implementation of a morphological operation with convex polygonal structuring elements as a sequence of successive neighborhood operations. Therefore, the algorithm is applicable to neighborhood-connected array processors, or any machine structure that can quickly perform 3×3 neighborhood operations