Separable algorithms for distance transformations on irregular grids

In this article, we propose to investigate two extensions of the E2DT (squared Euclidean Distance Transformation) on irregular isothetic grids (or I-gridsI-grids), such as quadtree/octree or run-length encoded d  -dimensional images. We enumerate the advantages and drawbacks of the I-CDTI-CDT, based on the cell centres, and the ones of the I-BDTI-BDT, which uses the cell borders. One of the main problem we mention is that no efficient algorithm has been designed to compute both transforms in arbitrary dimensions. To tackle this problem, we describe in this paper two algorithms, separable in dimension, to compute these distance transformations in the two-dimensional case, and we show that they can be easily extended to higher dimensions.

Research highlights
► We make a complete review of distance transformation (DT) on irregular grids.
► We propose 2 separable algorithms to compute squared Euclidean DT on irregular grids.
► These methods are efficient and fast algorithms in arbitrary dimensions.