Complexity analysis of morphological area openings and closings with set union

Area openings and closings are basic connected morphological operators that remove connected components which fail an area criterion. They are widely used in image filtering (e.g. for noise reduction) and segmentation and can be implemented efficiently using union-find-based algorithms. The authors show that the computational complexity of morphological area openings/closings based on disjoint set union is of order O(N) when N/ lambda, where lambda is an area threshold and N the image size, is sufficiently large, as in most practical applications.