Skip to main content
Log in

Abstract

We present the design of parallel architectures for the computation of the Hough transform based on application-specific CORDIC processors. The design of the circular CORDIC in rotation mode is simplified by the a priori knowledge of the angles participating in the transform and a high throughput is obtained through a pipelined design combined with the use of redundant arithmetic (carry save adders in this paper). Saving area is essential to the design of a pipelined CORDIC and can be achieved through the reduction in the number of microrotations and/or the size of the coefficient ROM. To reduce the number of microrotations we incorporate radix 4, when it is possible, or mixed radix (radix 2 and radix 4) in the design of the processor, achieving a reduction by half and 25% microrotations, respectively, with respect to a totally radix 2 implementation. Furthermore, if we allocate two circular CORDIC rotators into one processors then the size of the shared coefficient ROM is only 50% of the ROM of a design based on two separated rotators. Finally, we have also incorporated additional microrotations in order to reduce the scale factor to one. The result is a pipelined architecture which can be easily integrated in VLSI technology due to its regularity and modularity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P.V.C. Hough, “Method and means for recognizing complex patterns”, U.S. Patent 3069654, 1962.

  2. R.D. Duda and P.E. Hart, “Use of the Hough transform to detect lines and curves in pictures,”J. Communications of the ACM, Vol. 15, pp. 11–15, 1972.

    Article  MATH  Google Scholar 

  3. C.W. Kang, R.H. Park, and K.H. Lee, “Extraction of straight line segments using rotation transformation: Generalized Hough transformation,”J. Pattern Recognition, Vol. 24, No. 7, pp. 663–641, 1991.

    Article  Google Scholar 

  4. D.D. Haule and A.S. Malowany, “Object recognition using fast adaptative Hough transform,”IEEE Computer Pacific Conf. on Communication, Computer and Signal Procesing, pp. 91–94, 1989.

  5. H.K. Muammar and M. Nixon, “Tristage Hough transform for multiple ellipse extraction”IEE Proc. Part E: Computer and Digital Techniques, Vol. 138, No. 1, 1991.

  6. H. Nishino and Y. Kobayashi, “Extraction of planar surfaces from a set of line segments using the 3-dimensional Hough transform,”J. System Computer in Japan, Vol. 21, No. 12, pp. 78–87, 1990.

    Article  MathSciNet  Google Scholar 

  7. I. da Silva, “Vectorization from aerial photographs applying the Hough transform method,”,Proc. SPIE, Vol. 1395, Pt. 2, pp. 956–963, 1990.

    Google Scholar 

  8. H. Koshimizu and M. Numada, “On a fast Hough transform method PLHT based on piecewise-linear Hough function,”J. System Computer in Japan, Vol. 21, No. 5, pp. 62–73, 1990.

    Article  Google Scholar 

  9. D. Ben-Tzvi and M. Sandler, “A combinatorial Hough transform”,J. Pattern Recognition Letters, Vol. 11, pp. 167–174, 1990.

    Article  MATH  Google Scholar 

  10. L. da Fontoura and M.B. Sandler, “A binary Hough transform and its efficient implementation in a systolic array architecture,”J. Pattern Recognition Letters Vol. 10, pp. 329–334, 1989.

    Article  MATH  Google Scholar 

  11. L. Xu, E. Oja, and P. Kultaken “A new curve detection method: Randomized Hough transform (RHT),”J. Pattern Recognition Letters, Vol. 11, pp. 331–338, 1990.

    Article  MATH  Google Scholar 

  12. H. Li, M.A. Lavin, and R.J. Le Master, “Fast Hough transform: A hierarchical approach,”J. Computer Vision Graphics Imagen Processing, Vol. 36, pp. 139–161, 1986.

    Article  Google Scholar 

  13. N. Guil, J. Villalba, and E.L. Zapata, “A fast Hough transform for segment detection,” (submitted).

  14. A.N. Choudhary and R. Ponnusamy, “Implementation and evaluation of Hough transform algorithms on a shared-memory multiprocessor,”J. Parallel and Distributed Computing, Vol. 12, pp. 178–188, 1991.

    Article  Google Scholar 

  15. A.L. Fisher, and P. T. Highnam, “Computing the Hough transform on a scan line array processor”IEEE Workshop on Computer Architecture for Pattern Analysis and Machine Intelligence, pp. 83–87, 1987.

  16. A. Rosenfeld, J. Ornelas, and Y. Hung. “Hough transform algorithms for mesh-connected SIMD parallel processor,”J. Computer Vision Graphics Imagen Processing, Vol. 41, pp. 293–305, 1988.

    Article  Google Scholar 

  17. D. Ben-Tzvi, A. Naovi, and M. Sandler, “Synchronous multiprocessor implementation of the Hough transform,”J. Computer Vision, Graphics and Image Processing, Vol. 52, pp. 437–446, 1990.

    Article  Google Scholar 

  18. M. Ferretti, “Mapping the generalized Hough transform on a mesh connected computer,”IEEE Int'l Conf. CompEuro'91, pp. 248–252, 1991.

  19. M.G. Albanesi, “Time complexity evaluation of algorithms for the Hough transform on mesh connected computers,”IEEE Int'l Conf. CompEuro'91, pp. 253–257, 1991.

  20. R.E. Cypher, J.L.C. Sanz, and L. Snyder, “The Hough transform hasO (N) complexity onN×N mesh connected computers,”SIAM Journal of Computing, Vol. 19, No. 5, pp. 805–820, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  21. K.W. Bowyer, “Computing the Hough transform on an MIMD hypercube,”6th Scandinavian Conf. on Image Analysis, Vol. 2, pp. 1172–1181, 1989.

    Google Scholar 

  22. R.V. Shankar and N. Asokan, “A parallel implementation of the Hough transform method to detect lines and curves in pictures,”IEEE 32th Midwest Symp. on Circuits & Systems, pp. 321–324, 1990.

  23. X. Cao, F. Deravi, and M.G. Rodd, “Parallel implementation of the tuned generalized Hough transform on transputer networks,” InApplication of Transputers I, IOS Press, London, pp. 113–121, 1990.

    Google Scholar 

  24. H.Y.H. Chuang and C.C. Li, “A systolic processor for straight line detection by modified Hough transform,”IEEE Conf. on Computer Architecture for Pattern Analysis and Image Database Management, pp. 300–304, 1985.

  25. H.F. Li, D. Pao, and R. Jayakumar, “Improvements and systolic implementation of the Hough transformation for straight line detection,”J. Pattern Recognition, Vol. 22, No. 6, pp. 697–706, 1989.

    Article  Google Scholar 

  26. K. Hanahara, T. Maruyama, and T. Uchiyama, “A real time processor for the Hough transform,”IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 10, No. 1, pp. 121–125, 1988.

    Article  Google Scholar 

  27. “L64250 Histogram/Hough transform processor (HHP)”, LSI Logic, 1989.

  28. D. Timmermann, H. Hahn, and B.J. Hosticka, “Hough transform using CORDIC method,”J. Electronics Letters, Vol. 25, No. 3, pp. 205–206, 1989.

    Article  Google Scholar 

  29. J.E. Volder, “The CORDIC trigonometric computing technique,”IRE Transactions on Electronic Computers, Vol. EC-8, No. 3, pp. 330–334, 1959.

    Article  Google Scholar 

  30. J.S. Walther, “A unified algorithm for elementary functions,”Proc. Spring Joint Computers Conference, pp. 379–385, 1971.

  31. H.M. Ahmed. “Efficient elementary function generation with multipliers,”8th IEEE Int'l Symp. on Computer Arithmetic, pp. 52–59, 1989.

  32. H.M. Ahmed, “Signal processing algorithms and architectures,” Ph.D. Dissertation, Dept. of Electrical Engineering, Stanford University, Stanford, C.A., 1982.

    Google Scholar 

  33. J.R. Cavallaro and F.T. Luk, “CORDIC arithmetic for an SVD processor,”J. Parallel and Distributed Computing, Vol. 5, pp. 271–290, 1988.

    Article  Google Scholar 

  34. A. Despain, “Fourier transform computers using CORDIC iterations,”IEEE Trans on Computers, Vol. C-23, No. 10, pp. 993–1001, 1974.

    Article  MATH  Google Scholar 

  35. G.L. Haviland and A.A. Tuszynski, “A CORDIC arithmetic processor chip,”IEEE Trans. on Computers, Vol. C-29, No. 2, pp. 68–79, 1980.

    Article  Google Scholar 

  36. D. Timmermann, H. Hahn, B.J. Hosticka, and G. Schmidt, “A programmable CORDIC chip for digital signal processing applications,”IEEE Journal of Solid-State Circuits, Vol. 26, No. 9, pp. 1317–1321, 1991.

    Article  Google Scholar 

  37. Y.H. Hu, “CORDIC-based VLSI architectures for digital signal processing,”IEEE Signal Processing Magazine, Vol. 9, No. 3, pp. 16–35, 1992.

    Article  Google Scholar 

  38. D. König and J.F.Böhme, “Optimizing the CORDIC algorithm for processors with pipeline architecture,” InSignal Processing V: Theories and Applications, Elsevier Science Publishers, pp. 1391–1394, 1990.

  39. R. Künemund, H. Sölder, S. Wohlleben, and T. Noll, “CORDIC processor with carry save architecture,”16th European Solid State Citcuits Conference, pp. 193–196, 1990.

  40. A.A. de Lange and E.F. Deprettere, “Design and implementation of a floating-point quasi-systolic general purpose CORDIC rotator for high-rate parallel data and signal processing,”IEEE 10th Int'l Symp. on Computer Arithmetic, pp. 272–281, 1991.

  41. D.E. Metafas and C.E. Goutis, “A DSP processor with a powerfull set of elementary arithmetic operations based on CORDIC and CCM algorithms,”J. Microprocessing and Microprogramming, Vol. 30, pp. 51–58, 1990.

    Article  Google Scholar 

  42. J. Duprat and J.M. Muller, “The CORDIC algorithm: New results for fast VLSI implementation,” Report No. 90-04, Ecole Normale Superieure de Lyon, France, 1990.

    Google Scholar 

  43. X. Hu, R.G. Harber, and S.C. Bass, “Expanding the range of convergence of the CORDIC algorithm”IEEE Trans. on Computers, Vol. C-40, No. 1, pp. 13–21, 1991.

    Article  Google Scholar 

  44. Y.H. Hu, “The quantization effects of the CORDIC algorithm,”IEEE Trans. on Signal Processing, Vol. 40, No. 4, pp. 834–844, 1992.

    Article  MATH  Google Scholar 

  45. N. Takagi, T. Asada, and S. Yajima, “Redundant CORDIC methods with a constant scale factor for sine and cosine computation,”IEEE Trans. on Computers, Vol. C-40, No. 9, pp. 989–995, 1991.

    Article  MathSciNet  Google Scholar 

  46. D. Timmermann, H. Hahn, and B.J. Hosticka, “Low latency time CORDIC algorithms,”IEEE Trans. on Computers, Vol. 41, No. 8, pp. 1010–1015, 1992.

    Article  Google Scholar 

  47. J.M. Delosme, “VLSI implementation of rotations in pseudo Euclidean spaces,”IEEE Int'l Conf. Acoustics, Speech, and Signal Processing, pp. 927–930, 1983.

  48. F. Argüello, J.D. Bruguera, R. Doallo, T.Lang, and E.L. Zapata, “CORDIC based application specific processor for orthogonal transforms,” (submitted).

  49. J. Villalba, J.A. Hidalgo, E. Antelo, J. D. Bruguera, and E.L. Zapata, “CORDIC architecture with parallel compensation of the scale factor,”Proc. Int. Conf. on Application Specific Array Processors (ASAP'95), pp. 258–269, July 1995.

  50. J. Bruguera, E. Antelo, and E.L. Zapata, “Design of a pipelined radix 4 CORDIC processor,”J. Parallel Computing, Vol. 19, pp. 729–744, 1993.

    Article  MATH  Google Scholar 

  51. M.D. Ercegovac and T. Lang, “Redundant and on-line CORDIC: Application to matrix triangularization and SVD,”IEEE Trans. on Computers, Vol. C-39, No. 6, pp. 725–740, 1990.

    Article  Google Scholar 

  52. J. Harding, T. Lang, and J. Lee, “A comparasion of redundant CORDIC rotator engines,”IEEE Int'l Conf. Computer Design, pp. 556–559, 1991.

  53. J. Lee and T. Lang, “SVD by constant-factor-redundant-CORDIC,”IEEE 10th Int'l Symp. on Computer Arithmetic, pp. 264–271, 1991.

  54. J. Lee and T. Lang, “Constant-factor redundant CORDIC for angle calculation and rotation,”IEEE Trans. on Computers, Vol. 41, No. 8, pp. 1016–1025, 1992.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported by the Ministry of Education and Science (CICYT) of Spain under project TIC-92-0942.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruguera, J.D., Guil, N., Lang, T. et al. Cordic based parallel/pipelined architecture for the Hough transform. J VLSI Sign Process Syst Sign Image Video Technol 12, 207–221 (1996). https://doi.org/10.1007/BF00924986

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00924986

Keywords

Navigation