The level sets of a map are the sets of points with level above a given threshold. The connected components of the level sets, thanks to the inclusion relation, can be organized in a tree structure, that is called the component tree. This tree, under several variations, has been used in numerous applications. Various algorithms have been proposed in the literature for computing the component tree. The fastest ones have been proved to run in 0(nln(n)) complexity. In this paper, we propose a simple to implement quasi-linear algorithm for computing the component tree on symmetric graphs, based on Tarjan’s union-find principle.
We propose a concise definition of the skew angle of document, based on mathematical morphology. This definition has the advantages to be applicable both for binary and grey-scale images. We then discuss various possible implementations of this definition, and show that results we obtain are comparable to those of other existing algorithms.