Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods

Abstract

We propose a new exact Euclidean distance transformation (DT) by propagation, using bucket sorting. A fast but approximate DT is first computed using a coarse neighborhood. A sequence of larger neighborhoods is then used to gradually improve this approximation. Computations are kept short by restricting the use of these large neighborhoods to the tile borders in the Voronoi diagram of the image. We assess the computational cost of this new algorithm and show that it is both smaller and less image-dependent than all other DTs recently proposed. Contrary to all other propagation DTs, it appears to remain o(n 2 ) even in the worst-case scenario.

Serial registration of intraoperative MR images of the brain

“…To increase the robustness and the convergence rate of the surface deformation, we compute our forces as a steepest gradient descent on a Euclidean distance transform of the edges of the object to be tracked in the target image. The distance transform is computed with optimal efficiency (linear computational cost with respect to the amount of voxels in the image) using a fast Euclidean distance transformation algorithm (Cuisenaire and Macq, 1999;Cuisenaire, 1999). To prevent the surface from sticking on a wrong edge, or to prevent two sides of a thin surface from sticking together on the same edge, we have included the expected gradient sign of the edges of the structure to be segmented in the force expression (Ferrant et al, 1999a(Ferrant et al, , 2000a.…”

Distance Transforms: Academics Versus Industry

“…For a large majority of cases, they were able to determine exact EDT. One year later, Cuisenaire and Macq [60] also introduced an exact EDT. First, they calculated an approximate EDT, using ordered propagation by bucket sorting.…”

“…Shortly after [59] and [60], Costa et al [67] presented a method to determine EDT, using the concept of exact dilations. Their work was closely followed by Borgefors and colleagues, who presented several DT in two special issues of journals: [44,45].…”

Locally adaptable mathematical morphology using distance transformations

“…The most intuitive method would be to use a dynamic list of propagating pixels to scan the image by order of increasing values of D X,S (p), adapting the algorithms of Ragnelmam [18,11] or Cuisenaire [14] for the Euclidean DT. Nevertheless, this is needlessly complex.…”

“…for which numerous efficient algorithms exist [12][13][14][15][16]. Hence, the dilation is im- In what follows, we consider the Euclidean distance transformation and therefore balls that are circular, i.e.…”