{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T03:10:46Z","timestamp":1791169846464,"version":"4.1.0"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>\n                    This paper addresses fast parallel methods for the computation of the Radon (or Hough) transform. The Radon transform of an image is a set of projections of the image taken at different angles. Its computation is important in image processing and computer vision for problems such as pattern recognition and reconstruction of medical images. A unique new method for combining partial results is presented, from which an algorithm is constructed that computes a provably good approximation to the discrete Radon transform. The approximate discrete Radon transform (ADRT) algorithm computes 4, N - 4 projections through an $N \\times N$ image in time $O(N^2\\mathrm{lg}N)$ (the majority of previous algorithms are O(N\n                    <jats:sup>3,<\/jats:sup>\n                    )). The method is quite simple and easy to parallelize. A parallel version of the ADRT requires only $O(\\mathrm{lg}N)$ parallel steps on O(N\n                    <jats:sup>2<\/jats:sup>\n                    ) processors, ignoring communication time. An additional property of the algorithm is that it can be applied directly to compute the backprojection step of the inverse RT.\n                  <\/jats:p>","DOI":"10.1137\/s0097539793256673","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"107-119","source":"Crossref","is-referenced-by-count":104,"title":["A Fast Discrete Approximation Algorithm for the Radon Transform"],"prefix":"10.1137","volume":"27","author":[{"given":"Martin L.","family":"Brady","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(78)90022-5"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"M. Brady, W. Higgins, K. Ramaswamy, and R. Srinivasan,\n                      Interactive navigation inside 3D radiological images\n                      , in Proc. Biomedical Visualization \u201995, Atlanta, GA, IEEE Computer Society Press, Los Alamitos, CA, pp. 33\u201340; 85.","DOI":"10.1109\/BIOVIS.1995.528703"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"M. Brady and W. Yong,\n                      Fast parallel discrete approximation algorithms for the Radon transform\n                      , in Proc. 4th ACM Symp. on Parallel Algorithms and Architectures, ACM, New York, 1992, pp. 91\u201399.","DOI":"10.1145\/140901.140911"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0219056"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1145\/361237.361242"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.1987.4307847"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/42.7788"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0743-7315(89)90039-7"},{"key":"R9","unstructured":"P. V. C. Hough,\n                      Method and means of recognizing complex patterns\n                      , U.S. Patent 3069654, 1962."},{"key":"R10","unstructured":"J.\u2010F. Jenq and S. Sahni,\n                      Reconfigurable algorithms for the Hough transform\n                      , in Proc. 1991 Intl. Conf. on Parallel Processing, St. Charles, IL, CRC Press, Boca Raton, FL, 1991, pp. 34\u201341."},{"key":"R11","unstructured":"A. C. Kak, Guest ed.\n                      Computerized Medical Images\n                      , special issue of IEEE Trans. Biomed. Eng., BME\u201028 (Feb. 1981)."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/S0734-189X(88)80033-1"},{"key":"R13","unstructured":"H. Liu,\n                      Parallel Implementation of a Fast Radon Transform Algorithm\n                      , M. S. thesis, Dept. of ECE, The Pennsylvania State University, University Park, PA, 1993."},{"key":"R14","unstructured":"Y. Pan and Y. H. Chuang,\n                      Parallel Hough transform algorithms on SIMD hypercube arrays\n                      , in Proc. 1990 Intl. Conf. on Parallel Processing, St. Charles, IL, Penn. State Univ. Press, University Park, PA, 1990, pp. 83\u201386."},{"key":"R15","first-page":"262","volume":"69","author":"Radon J.","year":"1917","journal-title":"Math.\u2010Phys. Kl."},{"key":"R16","unstructured":"J. Ramakrishnan,\n                      Approximate Fast Radon Transform Algorithm for Image Reconstruction\u2014Implementation and Analysis\n                      , M. S. Thesis, Dept. of ECE, The Pennsylvania State University, University Park, PA, 1993."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1987.1165123"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"T.\u2010K. Wu and M. Brady,\n                      Parallel approximate computation of projection for animated volume rendered displays\n                      , in Proc. 1993 Parallel Rendering Symp., pp. 61\u201366; The Visual Computer, to appear.","DOI":"10.1145\/166181.166190"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539793256673","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:32Z","timestamp":1787336072000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539793256673"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S0097539793256673"],"URL":"https:\/\/doi.org\/10.1137\/s0097539793256673","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}