Abstract
In this Chapter, we address the problem of identifying and fitting more than one ellipse simultaneously, from a set of data points in the plane. This problem is an active research area with many applications in engineering and biology. Numerous studies attempted to solve this problem by detecting, fitting, and extracting the ellipses in a one-by-one approach from the set of data points. Although the one-by-one approach is effective and useful for many applications, recent studies have show that this approach is ill posed which led to the proposal of novel methods such as PEARL. PEARL is a multi-model fitting algorithm which minimizes an energy function. The PEARL algorithm requires to be initialized with random solutions. In this work we show that the performance of the PEARL algorithm, to solve the multi-ellipse fitting problem, can be improved by initializing it in a smarter way with solutions taken from a multi-objective genetic algorithm. Numerical results show that our approach can solve challenging data points instances, with high amount of outliers, and also with overlapping and nested ellipses.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bai, X., Sun, C., Zhou, F.: Splitting touching cells based on concave points and ellipse fitting. Pattern Recognit. 42(11), 2434–2446 (2009). https://doi.org/10.1016/j.patcog.2009.04.003
Charoenpong, T., Jantima, T., Chianrabupra, C., Mahasitthiwat, V.: A new method to estimate rotation angle of a 3D eye model from single camera. In: 2015 International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS), pp. 398–402 (2015). https://doi.org/10.1109/ICIIBMS.2015.7439474
Cheng, CW., Ou, WL., Fan, CP.: Fast ellipse fitting based pupil tracking design for human-computer interaction applications. In: 2016 IEEE International Conference on Consumer Electronics (ICCE), pp. 445–446 (2016). https://doi.org/10.1109/ICCE.2016.7430685
Cruz-Díaz, C., de la Fraga, LG., Schütze, O.: Fitness function evaluation for the detection of multiple ellipses using a genetic algorithm. In: 2011 8th International Conference on Electrical Engineering Computing Science and Automatic Control (CCE), pp. 1–6 (2011). https://doi.org/10.1109/ICEEE.2011.6106652
Cruz Hernández, H., de la Fraga, LG.: A multi-objective robust ellipse fitting algorithm. In: NEO 2016 Results of the Numerical and Evolutionary Optimization Workshop NEO 2016 and the NEO Cities 2016. Studies in Computational Intelligence, vol. 731, pp. 141–158. Springer, Cham (2018)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017
Delong, A., Osokin, A., Isack, H.N., Boykov, Y.: Fast approximate energy minimization with label costs. Int. J. Comput. Vis. 96(1), 1–27 (2012). https://doi.org/10.1007/s11263-011-0437-z
Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Commun. ACM 15(1), 11–15 (1972). https://doi.org/10.1145/361237.361242
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981). https://doi.org/10.1145/358669.358692
Fitzgibbon, A., Pilu, M., Fisher, R.B.: Direct least square fitting of ellipses. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 476–480 (1999). https://doi.org/10.1109/34.765658
Fornaciari, M., Prati, A., Cucchiara, R.: A fast and effective ellipse detector for embedded vision applications. Pattern Recognit. 47(11), 3693–3708 (2014). https://doi.org/10.1016/j.patcog.2014.05.012
de la Fraga, LG., Cruz-Diaz, C.: Fitting an ellipse is equivalent to find the roots of a cubic equation. In: 2011 8th International Conference on Electrical Engineering, Computer Science and Automatic Control, pp. 743–746 (2011)
Isack, H., Boykov, Y.: Energy-based geometric multi-model fitting. Int. J. Comput. Vis. 97(2), 123–147 (2012). https://doi.org/10.1007/s11263-011-0474-7
Johansson, E., Johansson, D., Skog, J., Fredriksson, M.: Automated knot detection for high speed computed tomography on Pinus sylvestris L. and Picea abies (L.) Karst. using ellipse fitting in concentric surfaces. Comput. Electron. Agric. 96, 238–245 (2013). https://doi.org/10.1016/j.compag.2013.06.003
Jung, Y., Lee, D., Bang, H.: Study on ellipse fitting problem for vision-based autonomous landing of an UAV. In: 2014 14th International Conference on Control, Automation and Systems (ICCAS), pp. 1631–1634 (2014). https://doi.org/10.1109/ICCAS.2014.6987819
Kanatani, K.: Motion segmentation by subspace separation and model selection. In: Proceedings of the Eighth IEEE International Conference on Computer Vision, ICCV 2001, vol. 2, pp. 586–591 (2001). https://doi.org/10.1109/ICCV.2001.937679
Kim, J.S., Gurdjos, P., Kweon, I.: Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005)
Liang, J., Wang, Y., Zeng, X.: Robust ellipse fitting via half-quadratic and semidefinite relaxation optimization. IEEE Trans. Image Process. 24(11), 4276–4286 (2015). https://doi.org/10.1109/TIP.2015.2460466
Liao, M., Zhao, Y.Q., Li, X.H., Dai, P.S., Xu, X.W., Zhang, J.K., Zou, B.J.: Automatic segmentation for cell images based on bottleneck detection and ellipse fitting. Neurocomputing 173, 615–622 (2016). https://doi.org/10.1016/j.neucom.2015.08.006
Ma, Z., Ho, K.C.: Asymptotically efficient estimators for the fittings of coupled circles and ellipses. Digit. Signal Process. Rev. J. 25(1), 28–40 (2014). https://doi.org/10.1016/j.dsp.2013.10.022
Mahajan, M., Nimbhorkar, P., Varadarajan, K.: The planar k-means problem is NP-hard. Theor. Comput. Sci. 442, 13–21 (2012). https://doi.org/10.1016/j.tcs.2010.05.034
Masuzaki, T., Sugaya, Y., Kanatani, K.: Floor-wall boundary estimation by ellipse fitting. In: 2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), pp. 30–35 (2015). https://doi.org/10.1109/ICCIS.2015.7274592
Mukhopadhyay, P., Chaudhuri, B.B.: A survey of Hough transform. Pattern Recognit. 48(3), 993–1010 (2015). https://doi.org/10.1016/j.patcog.2014.08.027
Panagiotakis, C., Argyros, A.: Parameter-free modelling of 2D shapes with ellipses. Pattern Recognit. 53, 259–275 (2016). https://doi.org/10.1016/j.patcog.2015.11.004
Rousseeuw, P., Leroy, A.: Robust Regretion and Outlier Detection. Wiley, New York (2003)
Rueda, S., Knight, CL., Papageorghiou, AT., Noble, JA.: Oriented feature-based coupled ellipse fitting for soft tissue quantification in ultrasound images. In: 2013 IEEE 10th International Symposium on Biomedical Imaging, pp. 1014–1017 (2013). https://doi.org/10.1109/ISBI.2013.6556649
Vincent, E., Laganiere R.: Detecting planar homographies in an image pair. In: Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis ISPA 2001, In Conjunction with 23rd International Conference on Information Technology Interfaces, pp. 182–187. IEEE (2001). https://doi.org/10.1109/ISPA.2001.938625
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Cruz Hernández, H., de la Fraga, L.G. (2019). Fitting Multiple Ellipses with PEARL and a Multi-objective Genetic Algorithm. In: Trujillo, L., Schütze, O., Maldonado, Y., Valle, P. (eds) Numerical and Evolutionary Optimization – NEO 2017. NEO 2017. Studies in Computational Intelligence, vol 785. Springer, Cham. https://doi.org/10.1007/978-3-319-96104-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-96104-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-96103-3
Online ISBN: 978-3-319-96104-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)