Fast distance transformation on irregular two-dimensional grids

In this article, we propose a new fast algorithm to compute the squared Euclidean distance transform (E²DT) on every two-dimensional (2-D) irregular isothetic grids (regular square grids, quadtree based grids, etc.). Our new fast algorithm is an extension of the E²DT method proposed by Breu et al. [3]. It is based on the implicit order of the cells in the grid, and builds a partial Voronoi diagram of the centers of background cells thanks to a data structure of lists. We compare the execution time of our method with the ones of others approaches we developed in previous works. In those experiments, we consider various kinds of classical 2-D grids in imagery to show the interest of our methodology, and to point out its robustness. We also show that our method may be interesting regarding an application where we extract an adaptive medial axis construction based on a quadtree decomposition scheme.