$O(N)$ , even after their optimization; and iv) are unequaled in that they can be adapted to the characteristics of the image class at hand." /> $O(N)$ , even after their optimization; and iv) are unequaled in that they can be adapted to the characteristics of the image class at hand." /> $O(N)$ , even after their optimization; and iv) are unequaled in that they can be adapted to the characteristics of the image class at hand." /> Fast Exact Euclidean Distance (FEED): A New Class of Adaptable Distance Transforms
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Issue No.11 - Nov. (2014 vol.36)
pp: 2159-2172
Theo E. Schouten , Institute for Computing and Information Science (ICIS), Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands
Egon L. van den Broek , Department of Information and Computing Sciences, Utrecht University; Human Media Interaction (HMI), University of Twente; and Karakter University Center, Radboud University Medical Center Nijmegen, The Netherlands
ABSTRACT
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 startingdirectly 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.
INDEX TERMS
Feeds, Search problems, Euclidean distance, Transforms, Approximation algorithms, Algorithm design and analysis,distance transform, Feeds, Search problems, Euclidean distance, Transforms, Approximation algorithms, Algorithm design and analysis, benchmark, Geometric algorithms, languages, and systems, Computational Geometry and Object Modeling, Computer Graphics, Region growing, partitioning, Segmentation, Computing Methodologies, Morphological, Image Representation, Image Processing and Computer Vision, distance transformation,benchmark, Fast exact euclidean distance (FEED), distance transform, distance transformation, Voronoi, computational complexity, adaptive
CITATION
Theo E. Schouten, Egon L. van den Broek, "Fast Exact Euclidean Distance (FEED): A New Class of Adaptable Distance Transforms", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.36, no. 11, pp. 2159-2172, Nov. 2014, doi:10.1109/TPAMI.2014.25
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