Disjoint set data structure for morphological area operators

Morphological openings and closings are basic operators in mathematical morphology. Morphological area openings and area closings have the same functions as standard morphological openings and closings but avoid distorting object boundaries. The conventional implementation of morphological area operators is based on the heap data structure. A new methodology for implementing morphological area operators, which relies on the disjoint set data structure, is proposed in this paper. The computational complexity of our method is O(N) where N is the image size, and not related to the area parameter. Experiments show that the new implementation of grayscale area operators runs faster than the conventional implementations. The computational complexity of binary area operators is also studied in this paper.