Two Linear Time Union-Find Strategies for Image Processing

Abstract : We consider Union-Find as an appropriate data structure to obtain two linear time algorithms for the Segmentation of images. The linearity is obtained by restricting the Order in which Union's are performed. For one algorithm the complexity bound is proven by amortizing the Find operations. For the other we use periodic updates to keep the relevant part of our Union-Find-tree of constant height. Both algorithms are generalized and lead to new linear strategies for Union-Find that are neither covered by the algorithm of Gabow and Tarjan (1984) nor by the one of Dillencourt et al. (1992).