Image foresting transform: Difference between revisions

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In the practice of [[digital image processing]] Alexandre X. Falcao, Jorge Stolfi, and Roberto de Alencar Lotufo have created and proven that the '''Image Foresting Transform''' (IFT) can be used as a time saver in processing 2-D, 3-D images, and moving images.<ref name="Falcao">Falcao, A.X. Stolfi, J. de Alencar Lotufo, R. : "[https://www.researchgate.net/profile/Roberto_Lotufo/publication/8331682_The_image_foresting_transform_theory_algorithms_and_applications/links/0912f50b724229bf0d000000.pdf The image foresting transform: theory, algorithms, and applications]", In IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 26, NO. 1, JANUARY 2004</ref>
 
==History <ref name="Falcao"/>==
 
In 1959 Dijkstra used a [[Heap (data structure)|balanced heap data structure]]<ref name="Falcao"/><ref name="Dij">E.W. Dijkstra, “[http://www.cs.yale.edu/homes/lans/readings/routing/dijkstra-routing-1959.pdf A Note on Two Problems in Connexion with Graphs],” Numerische Mathematik, vol. 1, pp. 269-271, 1959</ref> to improve upon an algorithm presented by Moore in 1957<ref name="Falcao"/><ref name="Moo">E.F. Moore, “The Shortest Path through a Maze,” Proc. Int’l Symp. Theory of Switching, pp. 285-292, Apr. 1959</ref> and Bellman in 1958<ref name="Falcao"/><ref name="Bell">R. Bellman, “On“[https://apps.dtic.mil/dtic/tr/fulltext/u2/606258.pdf On a Routing Problem],” Quarterly of Applied Math., vol. 16, pp. 87-90, 1958</ref> that computed the cost of the paths in a general graph. The [[Bucket sort]]ing technique is how Dial improved on the algorithm a decade later.<ref name="Falcao"/><ref name="Dial">R.B. Dial, “Shortest“[https://www.sciencedirect.com/science/article/pii/0191261580900144 Shortest-Path Forest with Topological Ordering],” Comm. ACM, vol. 12, no. 11, pp. 632-633, Nov. 1969</ref> The algorithm has been tweaked and modified in many ways since then. It is on this version that Falcao, Stolfi, and Lotufo improved upon.<ref name="Falcao"/>
 
==Definition <ref name="Falcao"/>==