Fast morphological attribute operations using Tarjan's union-find algorithm

Morphological attribute openings and closings and related operators are generalizations of the area opening and closing, and allow filtering of images based on a wide variety of shape or size based criteria. A fast union-find algorithm for the computation of these operators is presented in this paper. The new algorithm has a worst case time complexity of O(N logN) where N is the image size, as opposed to O(N^2 logN) for the existing algorithm. Memory requirements are O(N) for both algorithms