A comparison of algorithms for connected set openings and closings

The implementation of morphological connected set operators for image filtering and pattern recognition is discussed. Two earlier algorithms based on priority queues and hierarchical queues, respectively, are compared to a more recent union-find approach. Unlike the earlier algorithms which process regional extrema in the image sequentially, the union-find method allows simultaneous processing of extrema. In the context of area openings, closings, and pattern spectra, the union-find algorithm outperforms the previous methods on almost all natural and synthetic images tested. Finally, extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms, and memory usages are compared.