Abstract
This study is devoted to the analysis of algorithms of calculating the fast Hough transform for two- and three-dimensional images. A method for calculating the fast Hough transform (FHT) for straight lines in a three-dimensional image is proposed; its space and time complexity are Θ(n4), where n is the characteristic linear size of the input image. The FHT algorithms for approximation in two- and three-dimensional spaces are considered, and properties of the accuracy and completeness of the corresponding sets of dyadic patterns are investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. V. C. Hough, “Machine analysis of bubble chamber pictures,” in Proc. Int. Conf. on High Energy Accelerators and Instrumentation, Geneva, Sept. 14–19, 1959 (Int. Union Pure & Appl. Phys., CERN, 1959).
P. Mukhopadhyay and B. Chaudhuri, “A survey of Hough transform,” Pattern Recogn. 48, 993–1010 (2015).
A. Shehata, S. Mohammad, M. Sameer, and E. Rahab, “A Survey on hough transform, theory, techniques and applications,” ArXiv, Preprint 1502.02160.
L. Xu, E. Oja, and P. Kultanan, “A new curve detection method: Randomized Hough transform (RHT),” Pattern Recogn., No. 11, 331–338 (1990).
M. A. Fischler and R. C. Bolles, “Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,” Comm. ACM 24, 381–395 (1981).
M. Jiri, C. Galambos, and J. Kittler, “Robust detection of lines using the progressive probabilistic hough transform,” Comp. Vision Image Understand. 78 (1), 119–137 (2000).
F. A. Limberger and M. M. Oliveira, “Real-time detection of planar regions in unorganized point clouds,” Pattern Recogn. 48, 2043–2053 (2014).
M. L. Brady and Yong Whanki, “Fast parallel discrete approximation algorithms for the Radon transform,” in Proc. 4th Ann. ACM Symp. on Parallel Algorithms and Architectures, San Diego, CA, USA, June 29–July 01, 1992 (ACM, 1992).
W. A. Gotz, Eine Schnelle Diskrete Radon Transformation Basierend auf Rekursiv Definiertern Digitalen Geraden, Dissertation (Univ. Insbruck, Insbruck, 1993).
J. E. Vuillemin, “Fast linear Hough transform,” in Proc. IEEE Conf. on Application-Specific Array Processors, San Francisco, CA, USA, 1994 (IEEE Comput. Soc., New York, 1994), pp. 91–99.
S. M. Karpenko, D. P. Nikolaev, P. P. Nikolaev, and V. V. Postnikov, “Fast Hough Transform with Controlled Robustness,” in Artificial Intellectual Systems and Intellectual CAD. Proc. Int. Conf. IEEE AIS’04 & CAD-2004, Divnomorskoe, Sept. 3–10, 2004 (Fizmatlit, Moscow, 2004), Vol. 2, pp. 303–309.
M. T. Frederick, N. A. VanderHorn, and A. K. Somani, “Real-time H/W implementation of the approximate discrete Radon transform,” in Proc. 16th IEEE Int. Conf. IEEE on Application-Specific Systems, Architectures and Processors, Samos, Greece, July 23–25, 2005 (IEEE, 2005), pp. 399–404.
V. V. Arlazarov, A. E. Zhukovskii, V. E. Krivtsov, D. P. Nikolaev, and D. V. Polevoi, “Analysis of the features of application of stationary and mobile little digital video cameras for recognition of documents,” Inf. Tekhnol. Vychisl. Sist. 3, 71–81 (2014).
D. Krokhina, V. Blinov, S. Gladilin, I. Tarhanov, and V. Postnikov, “Fast roadway detection using car cabin video camera,” in Proc. 8th Int. Conf. on Machine Vision, (ICMV, 2015); Proc. SPIE 9875, pp. 98751F1–5 (2015).
D. P. Nikolaev, S. M. Karpenko, I. P. Nikolaev, and P. P. Nikolayev, “Hough transform: underestimated tool in the computer vision field,” in Proc. 22nd Eur. Conf. on Modeling and Simulation, Nicosia, Cyprus, June 3–6, 2008 (ECMS, 2008), pp. 238–246.
V. E. Prun, A. V. Buzmakov, D. P. Nikolaev, M. V. Chukalina, and V. E. Asadchikov, “Computationally efficient version of the algebraic method of computer tomography,” Avtomat. Telemekh., No. 10, 86–97 (2013).
I. A. Kunina, S. A. Gladilin, and D. P. Nikolaev, “Blind compensation of the radial distortion on a single image with the use of the fast Hough transform,” Komp’yut. Opt. 40, 395–403 (2016).
E. Ershov, A. Terekhin, S. Karpenko, D. Nikolaev, and V. Postnikov, “Fast 3D Hough transform computation,” in Proc. 30th Eur. Conf. on Modeling and Simulation, 2016 (ECMS, 2016), pp. 227–230.
D. Rogers, Procedural Elements for Computer Graphics (McGraw-Hill, New York, 1985; Mir, Moscow, 1989).
E. I. Ershov, E. A. Shvets T. M. Khanipov, and D. P. Nikolaev, “Generation algorithms of fast generalized hough transform,” in Proc. 30th Eur. Conf. on Modeling and Simulation (ECMS, 2017), Budapest, May 23–26, 2017 (ECMS, 2017), pp. 534–538.
E. Ershov, A. Terekhin, D. Nikolaev, V. Postnikov, and S. Karpenko, “Fast Hough transform analysis: pattern deviation from line segment,” in Proc. 8th Int. Conf. on Machine Vision (ICMV 2015), Barcelona, Spain, Nov. 19–20, 2015, (Int. Soc. Optics and Photonics, 2015), pp. 987509–987509.
I. M. Gel’fand, S. G. Gindikin, and M. I. Graev, Selected Problems of Integral Geometry (Dobrosvet, Moscow, 2000).
P. V. Bezmaternykh, D. V. Vylegzhanin, S. A. Gladilin, and D. P. Nikolaev, “Generative recognition of 2D bar codes,” Iskusstv. Intellekt i Prinyatie Reshenii, No. 4, 63–69 (2010).
E. I. Ershov and S. M. Karpenko, “Fast Hough Transform and approximation properties of dyadic patterns,” arXiv: 2096256.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.I. Ershov, A.P. Terekhin, D.P. Nikolaev, 2017, published in Informatsionnye Protsessy, 2017, Vol. 17, No. 4, pp. 294–308.
Rights and permissions
About this article
Cite this article
Ershov, E.I., Terekhin, A.P. & Nikolaev, D.P. Generalization of the Fast Hough Transform for Three-Dimensional Images. J. Commun. Technol. Electron. 63, 626–636 (2018). https://doi.org/10.1134/S1064226918060074
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064226918060074