Implicit equation description and fitting method for cylinder perspective contours

XIE Ying; YANG Xiangdong; RUI Xiaofei; REN Shunan; CHEN Ken

doi:10.16511/j.cnki.qhdxxb.2016.22.025

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Journal of Tsinghua University(Science and Technology) ›› 2016, Vol. 56 ›› Issue (6) : 640-645. DOI: 10.16511/j.cnki.qhdxxb.2016.22.025

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Implicit equation description and fitting method for cylinder perspective contours

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Abstract

A constrained implicit equation is developed to enhance the robustness and precision of perspective contour extraction for cylinders. The contour curve fitting problem is converted to a nonlinear optimization problem containing nonlinear constraints by a linear approximation. The problem is then solved with a rough estimate of the curve parameters and the noisy points filtered to find reasonable points based on the rough estimate of the curve parameters. This constrained problem is then converted to an unconstrained problem using the penalty function method to find the solution. This method takes advantage of the constraint between the lines and the ellipse to give better anti-noise performance for perspective cylinder contour extraction than separate methods using lines or ellipses. Tests of synthetic and real images show that this method effectively improves perspective contour curve fitting for cylinders.

Key words

image recognition / contour curve / implicit equation / curve fitting / nonlinear optimization

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XIE Ying, YANG Xiangdong, RUI Xiaofei, REN Shunan, CHEN Ken. Implicit equation description and fitting method for cylinder perspective contours[J]. Journal of Tsinghua University(Science and Technology). 2016, 56(6): 640-645 https://doi.org/10.16511/j.cnki.qhdxxb.2016.22.025

References

[1] Doignon C, De Mathelin M. A degenerate conic-based method for a direct fitting and 3-D pose of cylinders with a single perspective view [C]// IEEE International Conference on Robotics and Automation. Roma, 2007: 4220-4225.
[2] Huang J, Chen Z, Chia T. Pose determination of a cylinder using reprojection transformation [J]. Pattern Recognition Letters, 1996, 17(10): 1089-1099.
[3] Shiu Y C, Huang C. Pose determination of circular cylinders using elliptical and side projections [C]// IEEE International Conference on Systems Engineering. Dayton, OH, 1991: 265-268.
[4] XU Wenfu, XUE Qiang, LIU Houde, et al. A pose measurement method of a non-cooperative GEO spacecraft based on stereo vision [C]// International Conference on Control Automation Robotics & Vision (ICARCV). Guangzhou, 2012: 966-971.
[5] JIA Wenyan, YUE Yaofeng, Fernstrom J D, et al. 3D localization of circular feature in 2D image and application to food volume estimation [C]// Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). San Diego, CA, 2012: 4545-4548.
[6] Galamhos C, Matas J, Kittler J. Progressive probabilistic Hough transform for line detection [C]// IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Fort Collins, CO, 1999: 560-561.
[7] Chia A Y S, Leung M K H, How-Lung E, et al. Ellipse detection with Hough transform in one dimensional parametric space [C]// IEEE International Conference on Image Processing (ICIP). San Antonio, TX, 2007: 333-336.
[8] 李良福, 冯祖仁, 贺凯良. 一种基于随机Hough变换的椭圆检测算法研究 [J]. 模式识别与人工智能, 2005, 18(4): 459-464. LI Liangfu, FENG Zuren, HE Kailiang. An improved algorithm for ellipses detection based on randomized Hough transform [J]. Pattern Recognition and Artificial Intelligence, 2005, 18(4): 459-464. (in Chinese)
[9] 屈稳太. 基于弦中点Hough变换的椭圆检测方法 [J]. 浙江大学学报: 工学版, 2005, 39(8): 1132-1135.QU Wentai. Chord midpoint Hough transform based ellipse detection method [J]. Journal of Zhejiang University: Engineering Science, 2005, 39(8): 1132-1135. (in Chinese)
[10] 范怡, 傅继武. 基于中点提取的椭圆检测算法 [J]. 计算机应用, 2011, 31(10): 2705-2707.FAN Yi, FU Jiwu. Ellipse detection algorithm based on center extraction [J]. Journal of Computer Applications, 2011, 31(10): 2705-2707. (in Chinese)
[11] SONG Ge, WANG Hong. A fast and robust ellipse detection algorithm based on pseudo-random sample consensus [C]// Kropatsch W, Kampel M, Hanbury A, eds. Proceedings of 12th International Conference on Computer Analysis of Images and Patterns. Vienna, Austria: Springer, 2007: 669-676.
[12] XIE Yingdi, Ohya J. Efficient detection of ellipses from an image by a guided modified RANSAC [C]// Image Processing: Algorithms and Systems VII. San Jose, CA: SPIE, 2009, 72450W.
[13] Martelli S, Marzotto R, Colombari A, et al. FPGA-based robust ellipse estimation for circular road sign detection [C]// IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW). San Francisco, CA, 2010: 53-60.
[14] Guerrero J, Salcudean S E, McEwen J A, et al. Real-time vessel segmentation and tracking for ultrasound imaging applications [J]. IEEE Transactions on Medical Imaging, 2007, 26(8): 1079-1090.
[15] Thévenaz P, Delgado-Gonzalo R, Unser M. The ovuscule [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(2): 382-393.
[16] Taubin G. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(11): 1115-1138.
[17] 陈宝林. 最优化理论与算法 [M]. 北京: 清华大学出版社, 2005.CHEN Baolin. Optimization Theory and Algorithm [M]. Beijing: Tsinghua University Press, 2005. (in Chinese)
[18] 杨向东, 芮晓飞, 谢颖. 基于高效Hough变换的圆柱特征检测方法 [J]. 清华大学学报: 自然科学版, 2015, 55(8): 921-926. YANG Xiangdong, RUI Xiaofei, XIE Ying. Efficient Hough transform based cylinder feature detection algorithm [J]. J Tsinghua Univ: Sci and Tech, 2015, 55(8): 921-926. (in Chinese)
[19] 付生鹏, 赵吉宾, 夏仁波, 等. 基于环形镜面的相机外部参数自动标定方法[J]. 机器人, 2015, 37(3): 277-285.FU Shengpeng, ZHAO Jibin, XIA Renbo, et al. Annular mirror based extrinsic camera automatic calibration [J]. Robot, 2015, 37(3): 277-285. (in Chinese)