The design of morphological filters using multiple structuring elements, Part I: openings and closings

Morphological filters with very selective action often cannot be implemented using a single structuring element. Combining multiple structuring elements is one method which constrains the filtering action. Decomposition of the multiple elements into basis closing sets provides insight into which shapes should be chosen and how they shoule be combined to produce a filter with the desired selective characteristics. The selectivity constraints evolve as a natural consequence of the geometry of the interacting element shapes and the strength of filtering is sequenced by the size of the shapes in the closing joint decomposition basis set. A line-preserving filter is discussed as an example of this approach.