Editing Hough transform (section)

{{Short description|Method of detecting shapes within images}}
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The '''Hough transform''' ({{IPAc-en|h|ʌ|f}}) is a [[feature extraction]] technique used in [[image analysis]], [[computer vision]], [[pattern recognition]], and [[digital image processing]].<ref>[[Linda Shapiro|Shapiro, Linda]] and Stockman, George. "Computer Vision", Prentice-Hall, Inc. 2001</ref><ref>{{Cite journal |last1=Romanengo |first1=Chiara |last2=Falcidieno |first2=Bianca |last3=Biasotti |first3=Silvia |date=2024-09-01 |title=Extending the Hough transform to recognize and approximate space curves in 3D models |journal=Computer Aided Geometric Design |volume=113 |pages=102377 |doi=10.1016/j.cagd.2024.102377 |issn=0167-8396 |doi-access=free }}</ref> The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure. This voting procedure is carried out in a [[parameter space]], from which object candidates are obtained as local maxima in a so-called accumulator space that is explicitly constructed by the algorithm for computing the Hough transform.  Mathematically it is simply the  [[Radon transform]] in the plane, known since at least 1917, but the Hough transform refers to its use in image analysis. 

The classical Hough transform was concerned with the identification of [[Line (mathematics)|lines]] in the image, but later the Hough transform has been extended to identifying positions of arbitrary shapes, most commonly [[circle]]s or [[ellipse]]s. The Hough transform as it is universally used today was invented by [[Richard Duda]] and [[Peter E. Hart|Peter Hart]] in 1972, who called it a "generalized Hough transform"<ref>Duda, R. O. and P. E. Hart, "Use of the Hough Transformation to Detect Lines and Curves in Pictures", ''Comm. ACM'', vol.&nbsp;15, pp.&nbsp;11–15 (January, 1972).</ref> after the related 1962 patent of Paul Hough.<ref>Hough, P. V. C. ''Method and means for recognizing complex patterns'', U.S. Patent 3,069,654, Dec.&nbsp;18, 1962.</ref><ref>P. V. C. Hough, ''[http://inspirehep.net/record/919922/files/HEACC59_598-602.pdf Machine Analysis of Bubble Chamber Pictures]'', Proc. Int. Conf. High Energy Accelerators and Instrumentation, 1959.</ref> The transform was popularized in the [[computer vision]] community by [[Dana H.&nbsp;Ballard]] through a 1981 journal article titled "[[Generalised Hough transform|Generalizing the Hough transform to detect arbitrary shapes]]".