Abstract
The subject of this paper is very high precision parameter estimation using the Hough transform. We identify various problems that adversely affect the accuracy of the Hough transform and propose a new, high accuracy method that consists of smoothing the Hough arrayH(ρ, θ) prior to finding its peak location and interpolating about this peak to find a final sub-bucket peak. We also investigate the effect of the quantizations Δρ and Δθ ofH(ρ, θ) on the final accuracy. We consider in detail the case of finding the parameters of a straight line. Using extensive simulation and a number of experiments on calibrated targets, we compare the accuracy of the method with results from the standard Hough transform method of taking the quantized peak coordinates, with results from taking the centroid about the peak, and with results from least squares fitting. The largest set of simulations cover a range of line lengths and Gaussian zero-mean noise distributions. This noise model is ideally suited to the least squares method, and yet the results from the method compare favorably. Compared to the centroid or to standard Hough estimates, the results are significantly better—for the standard Hough estimates by a factor of 3 to 10. In addition, the simulations show that as Δρ and Δθ are increased (i.e., made coarser), the sub-bucket interpolation maintains a high level of accuracy. Experiments using real images are also described, and in these the new method has errors smaller by a factor of 3 or more compared to the standard Hough estimates.
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References
Ambs P, Lee SH, Tian Q, Fainman Y (1986) Optical implementation of the Hough transform by a matrix of holograms. Applied Optics 25:4039–4045
Ballard DH (1981) Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition 13:111–122
Ballard DH (1987) Interpolation coding: A representation for numbers in neural models. Biological Cybernetics 57:389–402
Ballard DH, Brown CM (1982) Computer vision, Prentice-Hall, Englewood Cliffs, NJ, pp 123–130
Baringer WB, Richards BC, Brodersen RW, Sanz JLC, Petkovic D (1987) A VLSI implementation of PPPE for real-time image processing in Random space — Work in progress. Proceedings of IEEE Workshop on Computer Architectures for Pattern Analysis and Machine Intelligence, Seattle, WA
Bracewell RN (1978) The Fourier transform and its applications. McGraw-Hill New York
Brown CM (1983) Inherent bias and noise in the Hough transform. IEEE Pattern Analysis and Machine Intelligence PAMI-5 (5):493–505
Canny J (1986) A computational approach to edge detection. IEEE Pattern Analysis and Machine Intelligence PAMI-8 (6):679–698
Cohen M, Toussaint GT (1977) On the detection of structures in noisy pictures. Pattern Recognition 9:95–98
Davies ER (1987) A new framework for analysing the properties of the generalized Hough transform. Pattern Recognition Letters 6:1–7
Deans SR (1981) Hough transform from the Randon transform. IEEE Pattern Analysis and Machine Intelligence PAMI-3(2):185–188
Deans SR (1983) The Radon transform and some of its applications. John Wiley and Sons, New York
Duda RO, Hart PE (1972) Use of the Hough transform to detect lines and curves in pictures. Communication of the ACM 15:11–15
Dyer CR (1983) Gauge inspection using Hough transform. IEEE Pattern Analysis Machine Intelligence PAMI-5(6):621–623
Eichmann G, Dong BZ (1983) Coherent optical production of the Hough transform, Applied Optics 22:830–834
Galkowski JT, Galkowski PJ (1986) On the importance of signal-to-noise measures in machine vision: A case study of the Hough transform. IBM Federal Systems Division Technical Report 86-L57-003, Owego, NY
Gindi GR, Gmitro AF (1984) Optical feature extraction via the Radon transform. Optical Engineering 23:499–506
Gordon SJ, Seering WP (1986) Accuracy issues in measuring quantized images of straight-line features. IEEE International Conference on Robotics and Automation, San Francisco, CA, pp 931–936
Gordon SJ, Seering WP (1988) Real-time part position sensing. IEEE Pattern Analysis and Machine Intelligence PAMI-10(3):373–386
GRAFSTAT User's Guide (1986), available from IBM
Hanahara K, Maruyama T, Uchiyama T (1988) A real time processor for the Hough transform. IEEE Pattern Analysis and Machine Intelligence PAMI-10(1):121–125
Hinkle E, Sanz JLC, Jain AK, Petkovic D (1987) PPPE: New life for projection-based image processing. Journal of Parallel and Distributed Computing (4):45–78
Holland PW, Welsch RE (1977) Robust regression using iteratively reweighted least squares. Communications Statistics-Theoretical Methods A6(9):813–827
Hough PVC (1962) Method and means for recognizing complex patterns. U.S. Patent 3069654
Huber PJ (1981) Robust statistics. John Wiley and Sons, New York
Hunt DJ, Nolte LW, Ruedger WH (1988) Performance of the Hough transform and its relationship to statistical signal detection theory. Computer Vision, Graphics, and Image Processing 43(2):221–238
Illingworth J, Kittler J (1987) The adaptive Hough transform. IEEE Pattern Analysis and Machine Intelligence PAMI-9(5):690–698
Illingworth J, Kittler J. (1988) A survey of the Hough transform. Computer Vision, Graphics, and Image Processing 44:87–116
Kimme C, Ballard DH, Sklansky J (1975) Finding circles by an array of accumulators. Communications of the ACM 18:120–122
Kiryati N, Bruckstein AM (1988) Antialiasing the Hough transform. EE Publication 697, Department of Electrical Engineering, Technion, Haifa, Israel
Leavers VF, Boyce JF (1986) An implementation of the Hough transform using a linear array processor in conjunction with a PDP/11. National Physical Laboratory, Teddington, Middlesex, England, NPL Report DITC 74/86
Li CC, Mancuso JF, Shu DB, Sun YN, Roth LD (1983) A preliminary study of automated inspection of VLSI resist patterns. Proceedings of the IEEE International Conference on Robotics and Automation, pp 474–480
Li H, Lavin MA, LeMaster RJ (1986) Fast Hough transform: A hierarchical approach. Computer Vision, Graphics, and Image Processing 36:139–161
Maitre H (1986) Contribution to the prediction of performance of the Hough transform. IEEE Patten Analysis and Machine Intelligence PAMI-8(5)669–674
Niblack W, Petkovic D (1986) On improving the accuracy of the Hough transform, theory, simulation, and experiments. Proceedings of Computer Vision and Pattern Recognition, Ann Arbor, Michigan, June, pp 574–579
Rhodes FM, Dituri JJ, Chapman GH, Emerson BE, Soares AM, Raffel JI (1988) A monolithic Hough transform processor based on restructurable VLSI. IEEE Pattern Analysis and Machine Intelligence PAMI-10(1):106–110
Rosenfeld A, Kak AC (1982) Digital picture processing. Second Edition. Volume 1. Academic Press, New York
Shapiro SD (1978) Generalization of the Hough transform for curve detection in noisy digital images. Fourth International Joint Conference on Pattern Recognition, Kyoto, Japan
Shapiro SD (1978) Properties of transforms for the detection of curves in noisy pictures. Computer Graphics and Image Processing 8:219–236
Shapiro SD, Iannino A (1979) Geometric constructions for predicting Hough transform performance. IEEE Pattern Analysis and Machine Intelligence PAMI-1(3):310–317
Sheinvald J, Dom B, Niblack W (1989) Multiple curve detection using the MDL principle and the Hough transform. IBM Almaden Research Center
Sklansky J (1978) On the Hough technique for curve detection. IEEE Transactions on Computers C-27, (10):923–926
Srihari SN, Govindaraju V, (1989) Analysis of textual images using the Hough transform. Machine Vision and Applications 2(3): 141–153
Steier WH, Shori RK (1986) Optical Hough transform. Applied Optics 25:2734–2738
Thrift PR, Dunn SM (1983) Approximating point set images by line segments using a variation of the Hough transform. Computer Vision, Graphics and Image Processing 21:383–394
Van Veen TM, Groen FCA (1981) Discretization errors in the Hough transform. Pattern Recognition 14:137–145
Young RA (1986) Locating parts with subpixel accuracies. SPIE, Boston, MA
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Niblack, W., Petkovic, D. On improving the accuracy of the Hough transform. Machine Vis. Apps. 3, 87–106 (1990). https://doi.org/10.1007/BF01212193
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DOI: https://doi.org/10.1007/BF01212193