Calculation of a vanishing point by the maximum likelihood estimation method

I. A. Konovalenko ; J. A. Shemiakina ; I. A. Faradjev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 13 (2020) no. 1, pp. 107-117

Résumé

The paper presents a method to estimate the position of the vanishing point of a set of converging noisy segments. As a model of segment noise, we use normal noise applied to the end points of the segment. We construct a functional that depends on the position of the considered segments and determine the vanishing point as the point at which the functional reaches its minimum. In order to set such a functional, we use the maximum likelihood estimation method. The obtained functional allows both to pose the problem on numerical minimization and to set the function of correspondence of the segment to the beam, if it is necessary to filter out the emission segments from the initial set. The application of the proposed method is illustrated by the example of correction of projective distortions and the subsequent localization of the pages of the Russian Federation passport on the images of the passport pages. In the framework of this problem, we assume that the segments highlighted in an image correspond to several beams and contain emissions. In order to ensure stability and ability to estimate a set of vanishing points, we propose an algorithm based on the RANSAC scheme. The use of the projective normalization method allows to reduce the number of page localization errors from 6,4% to 1,8%.

Détail

Keywords: vanishing point, maximum likelihood estimation method
Mots-clés : segments, image rectification.

Bibliographie

[1] P. Clark, M. Mirmehdi, “Rectifying Perspective Views of Text in 3D Scenes Using Vanishing Points”, Pattern Recognition, 36:11 (2003), 2673–2686 | DOI

[2] C. Hughes, P. Denny, M. Glavin, E. Jones, “Equidistant Fish-Eye Calibration and Rectification by Vanishing Point Extraction”, IEEE Transaction on Pattern Analysis and Machine Intelligence, 32:12 (2010), 2289–2296 | DOI

[3] Xu Cheng, Cai Youqi, Tian Ya Zheng, Li Tao, Liu Bin Yan, “Principal Orientation and Generalized Vanish Point Based Road Detection”, Proceedings of 3rd International Conference on Computer Science and Service System (13–15 June, Bangkok, 2014), 394–397 | DOI

[4] M. Hornacek, S. Maierhofer, “Extracting Vanishing Points Across Multiple Views”, Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition (20–25 June, Colorado, 2011), 953–960 | DOI

[5] Xu-Cheng Yin, Hong-Wei Hao, Jun Sun, S. Naoi, “Robust Vanishing Point Detection for MobileCam-Based Documents”, Proceeding of 2011 International Conference on Document Analysis and Recognition (18–21 September, Beijing, 2011), 136–140 | DOI

[6] R. Grompone von Gioi, J. Jakubowicz, J. Morel, G. Randall, “LSD: a Line Segment Detector. Image Processing on Line”, Image Processing On Line, 2 (2012), 35–55 | DOI

[7] C. Akinlar, C. Topal, “EDLines: a Real-Time Line Segment Detector with a False Detection Control”, Pattern Recognition Letters, 32:13 (2011), 1633–1642 | DOI | MR

[8] Qiang He, Chee-Hung Henry Chu, “Lane Detection and Tracking Through Affine Rectification”, Proceeding of IAPR Conference on Machine Vision Applications (16–18 May, Tokyo, 2007), 536–539

[9] D.P. Nikolaev, S.M. Karpenko, I.P. Nikolaev, P.P. Nikolayev, “Hough Transform: Underestimated Tool in The Computer Vision Field”, Proceedings of the 22th European Conference on Modelling and Simulation (3–6 June, Nicosia, 2008), 238–246 | DOI

[10] Shemiakina J., “The Usage of Points and Lines for the Calculation of Projective Transformation by Two Images of One Plane Object”, Information Technologies and Computation Systems, 2017, no. 3, 79–91 (in Russian)

[11] D. Liebowitz, A. Zisserman, “Metric Rectification for Perspective Images of Planes”, Proceedings 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (23–25 June, Santa Barbara, 1998), 482–488 | DOI

[12] F. Schaffalitzky, A. Zisserman, “Planar Grouping for Automatic Detection of Vanishing Lines and Points”, Image and Vision Computing, 18:9 (2000), 647–658 | DOI

[13] J.P. Tardif, “Non-Iterative Approach for Fast and Accurate Vanishing Point Detection”, Proceeding of 12th IEEE International Conference on Computer Vision (29 September–2 October, Kyoto, 2009), 1250–1257 | DOI

[14] Yiliang Xu, Sangmin Oh, A. Hoogs, “A Minimum Error Vanishing Point Detection Approach for Uncalibrated Monocular Images of Man-Made Environments”, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (23–28 June, Portland, 2013), 1376–1383 | DOI

[15] Lloyd E., Lederman U., Applied Statistics Manual, v. 1, Financy i statistika, M., 1989

[16] Seber G. A.F., Lee A. J., Linear Regression Analysis, John Wiley and Sons, Hoboken, New Jersey, 2003 | MR | MR

[17] K. Pearson, “On Lines and Planes of Closest Fit to Systems of Points in Space”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2:11 (1901), 559–572 | DOI

[18] Tropin D. V., Shemiakina J. A., Konovalenko I. A., Faradjev I. A., “Localization of Planar Objects on the Images with Complex Structure of Projective Distortion”, Information Processes, 2019, no. 2, 208–229 (in Russian)

[19] S. Usilin, D. Nikolaev, V. Postnikov, G. Schaefer, “Visual Appearance Based Document Image Classification”, Proceedings of International Conference on Image Processing (ICIP) (12–15 September, Hong Kong, 2010), 2133–2136

[20] Gill P., Murray W., Wright M., Practical Optimization, Academic Press, San Diego, 1981 | MR | MR | Zbl