A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast exact euclidean distance (FEED) transforms. FEED class algorithms calculate the DT starting-directly from the definition or rather its inverse. The principle of FEED class algorithms is introduced, followed by strategies for their efficient implementation. It is shown that FEED class algorithms unite properties of ordered propagation, raster scanning, and independent scanning DT. Moreover, FEED class algorithms shown to have a unique property: they can be tailored to the images under investigation. Benchmarks are conducted on both the Fabbri et al. data set and on a newly developed data set. Three baseline, three approximate, and three state-of-the-art DT algorithms were included, in addition to two implementations of FEED class algorithms. It illustrates that FEED class algorithms i) provide truly exact Euclidean DT; ii) do no suffer from disconnected Voronoi tiles, which is a unique feature for non-parallel but fast DT; iii) outperform any other approximate and exact Euclidean DT with its time complexity O(N), even after their optimization; and iv) are unequaled in that they can be adapted to the characteristics of the image class at hand.

A new generic scheme for incremental implementations of distance transforms (DT) is presented: Incremental Distance Transforms (IDT). This scheme is applied on the city-block, Chamfer, and three recent exact Euclidean DT (E2DT). A benchmark shows that for all five DT, the incremental implementation results in a significant speedup: 3.4 × -10×. However, significant differences (i.e., up to 12.5×) among the DT remain present. The FEED transform, one of the recent E2DT, even showed to be faster than both city-block and Chamfer DT. So, through a very efficient incremental processing scheme for DT, a relief is found for E2DT's computational burden.