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The organ card reader software finishes with the Discrete Radon Transformation, a fast and exact method for detecting straight lines in an image. See • Image analysis: the punched card example for the full playlist of this series. For further video enjoyment, check out Cliff Stoll’s video on the Klein bottle. • Klein Bottles - Numberphile 00:00 Introduction 01:05 Review: the Hough transform 02:43 Problems with Hough transform 04:26 Discrete Radon transform 06:47 Why is discrete Radon slow? 07:42 Fast DRT - Setup 10:08 Fast DRT - Divide and conquer 12:15 Fast DRT - Error analysis 13:54 Fast DRT - Symmetry 15:34 Fast DRT - Topology 20:41 Conclusions 21:03 Coming attractions FOR FURTHER READING William H. Press. “Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines.” Proc. Nat. Acad. Sci. 103:51 (December 19, 2006), pp. 19249-19254 https://www.pnas.org/cgi/doi/10.1073/... Paul V.C. Hough. “Method and means for recognizing complex patterns”. U,S. Patent 3.069,654 (December 18, 1962). https://patents.google.com/patent/US3... George G. Moshos. “Error analysis of binary rate multipliers.” NASA Technical Note TN D-3124. Cleveland, O.: NASA Lewis Research Center, December, 1965. https://ntrs.nasa.gov/api/citations/1... IMAGES “Portrait of Johann Radon” https://commons.wikimedia.org/wiki/Fi... Copyright expired in US. Wannapik Studio, “Old West Gambling Gambler Poker Card Player” https://www.wannapik.com/vectors/4468#! CC-BY-3.0 https://creativecommons.org/licenses/... David Benbennick. “Möbius Strip” https://commons.wikimedia.org/wiki/Fi... GNU Free Documentation License, version 1.2 or later https://www.gnu.org/licenses/fdl-1.3.... Ole Husby, “Klein Bottle” https://www.flickr.com/photos/khianti... CC-BY-SA 2.0 https://creativecommons.org/licenses/... Conseil Européen pour la Récherche Nucléaire (CERN). “The decay of a lambda particle in the 32 cm hydrogen bubble chamber.” https://cds.cern.ch/record/39474 License terms:https://copyright.web.cern.ch/ Trammell Hudson (“autopilot”). “Space Rocks (game)” https://commons.wikimedia.org/wiki/Fi... CC-BY-SA 3.0 https://creativecommons.org/licenses/... “The M.I.T Numerical Controlled Machine Tool.” Douglas T. Ross, “Papers on Automatic Programming for Numerically Controlled Machine Tools.” Cambridge, Mass.:MIT, January 7, 1958, p. 3. http://www.bitsavers.org/pdf/mit/whir... Published in the US without notice of copyright prior to the enactment of the US Copyright Act of 1976. International Emergency Medicine Education Project. “Abdominal pain CT shows cholecyctitis” https://www.flickr.com/photos/iem-stu... CC-BY-NC-SA 2.0 https://creativecommons.org/licenses/... All other images are original to the videographer. MUSIC J.S. Bach, Prelude and Fugue No. 6 in A major, BWV 536 from Das Wohltempierte Klavier, Teil I. Recorded by Evgeniy E. Moshkin, 3 August 2018 using the Hauptwerk virtual pipe organ software with the Freisach sample set. https://imslp.org/wiki/File:PMLP11169... CC-BY-NC-SA 4.0 https://creativecommons.org/licenses/... © 2021 Kevin B. Kenny CC-SA-NC 4.0 https://creativecommons.org/licenses/...