Abstract
The standard Hough transform does not provide length and width of a line-segment detected in an image; it just detects the normal parameters of the line. We present a novel method for determining also length and width of a line segment by using the Hough transform. Our method uses statistical analysis of voting cells around a peak in the Hough space. In image space, the voting cells and voting values are analysed. The functional relationship between voting variance and voting angle is deduced. We approximate this relationship by a quadratic polynomial curve. In Hough space, the statistical variances of columns around a peak are computed and used to fit a quadratic polynomial function. The length and width of a line segment are determined simultaneously by resolving the equations generated by comparing the corresponding coefficients of two functions. We tested and verified the proposed method on simulated and real-world images. Obtained experimental results demonstrate the accuracy of our novel method for determining length and width of detected line segments.
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Aggarwal, N., Karl, W.: Line detection in images through regularized Hough transform. IEEE Trans. Image Processing 15, 582–591 (2006)
Akhtar, M.W., Atiquzzaman, M.: Determination of line length using Hough transform. Electronics Letters 28, 94–96 (1992)
Atiquzzaman, M., Akhtar, M.W.: Complete line segment description using the Hough transform. Image and Vision Computing 12, 267–273 (1994)
Atiquzzaman, M., Akhtar, M.W.: A robust Hough transform technique for complete line segment description. Real-Time Imaging 1, 419–426 (1995)
Costa, L.F., Ben-Tzvi, B., Sandler, M.: Performance improvements to the Hough transform. In: UK IT 1990 Conference, pp. 98–103 (1990)
Du, S., Tu, C., van Wyk, B.J., Chen, Z.: Collinear segment detection using HT neighborhoods. IEEE Trans. Image Processing 20, 3912–3920 (2011)
Du, S., Tu, C., van Wyk, B.J., Ochola, E.O., Chen, Z.: Measuring straight line segments using HT butterflies. PLoS ONEÂ 7(3), e33790 (2012)
Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Comm. ACM 15, 11–15 (1972)
EISATS: .enpeda.. image sequence analysis test site (2013), http://www.mi.auckland.ac.nz/EISATS
Furukawa, Y., Shinagawa, Y.: Accurate and robust line segment extraction by analyzing distribution around peaks in Hough space. Computer Vision Image Understanding 92, 1–25 (2003)
Hough, P.V.C.: Methods and means for recognizing complex patterns. U.S. Patent 3.069.654 (1962)
Ioannou, D.: Using the Hough transform for determining the length of a digital straight line segment. Electronics Letters 31, 782–784 (1995)
Kamat, V., Ganesan, S.: A robust Hough transform technique for description of multiple line segments in an image. In: Int. Conf. Image Processing, pp. 216–220 (1998)
Kamat, V., Ganesan, S.: Complete description of multiple line segments using the Hough transform. Image Vision Computing 16, 597–613 (1998)
Kiryati, N., Bruckstein, A.M.: What’s in a Set of Points? IEEE Trans. Pattern Analysis Machine Intelligence 14, 496–500 (1992)
Klette, R.: Concise Computer Vision. Springer, London (2014)
Netanyahu, N.S., Weiss, I.: Analytic line fitting in the presence of uniform random noise. Pattern Recognition 34, 703–710 (2001)
Nguyen, T.T., Pham, X.D., Jeon, J.: An improvement of the standard Hough transform to detect line segments. In: IEEE Int. Conf. Industrial Technology, pp. 1–6 (2008)
Qjidaa, H., Radouane, L.: Robust line fitting in a noisy image by the method of moments. IEEE Trans. Pattern Analysis Machine Intelligence 21, 1216–1223 (1999)
Radon, J.: Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte Sächsische Akademie Wissenschaften, Math.-Phys. Kl. 69, 262–267 (1917)
Shin, B.-S., Xu, Z., Klette, R.: Visual lane analysis and higher-order tasks: A concise review. Machine Vision Applications (to appear, 2014)
Weiss, I.: Line fitting in a noisy image. IEEE Trans. Pattern Analysis Machine Intelligence 11, 325–329 (1989)
Xu, Z., Shin, B.-S.: Line segment detection with Hough transform based on minimum entropy. In: Klette, R., Rivera, M., Satoh, S. (eds.) PSIVT 2013. LNCS, vol. 8333, pp. 254–264. Springer, Heidelberg (2014)
Xu, Z., Shin, B.-S.: A statistical method for peak localization in Hough space by analysing butterflies. In: Klette, R., Rivera, M., Satoh, S. (eds.) PSIVT 2013. LNCS, vol. 8333, pp. 111–123. Springer, Heidelberg (2014)
Yamato, J., Ishii, I., Makino, H.: Highly accurate segment detection using Hough transformation. Systems and Computers in Japan 21, 68–77 (1990)
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Xu, Z., Shin, BS., Klette, R. (2014). Determination of Length and Width of a Line-Segment by Using a Hough Transform. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2014. Lecture Notes in Computer Science, vol 8668. Springer, Cham. https://doi.org/10.1007/978-3-319-09955-2_16
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DOI: https://doi.org/10.1007/978-3-319-09955-2_16
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