Algorithms for connected component labeling based on quadtrees

Abstract

AbstractAn algorithm of linear time complexity is presented to label connected components of a binary image by a quadtree. For a given node, the search for all adjacent nodes is carried out in O(1) (i.e., constant time complexity for the worst case) using our formerly presented algorithm in (Aizawa et al., 3rd International Symposium on Communications, Control, and Signal Processing,2008, 505–510), whereas it explores all possible adjacencies for each node in a usual way. Then during the process of tree formulation in the search, all equivalent relations of labels are stored as lists. Time complexity of the algorithm is O(B+W) for the worst case and its auxiliary space is no more than O(B), where B and W correspond to the number of leaf nodes in a quadtree representing black and white quadrants, respectively. Empirical tests of the algorithm are employed in comparison with another linear time connected component labeling algorithm based on top‐down quadtree traversal algorithm (Samet, IEEE Trans Pattern Anal Mach Intell PAMI‐7 (1985), 94–98), as well as traditional row‐by‐row scanning algorithm using linear time Union‐Find (Fiorio and Gustedt, Theor Comput Sci 154 (1996), 165–181). Our algorithm has shown the best performance in large images. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 158–166, 2009.