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Robust Ellipse Fitting with an Auxiliary Normal

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Image and Graphics (ICIG 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12888))

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Abstract

Ellipse fitting is a critical part of various applications. Recovering the ellipse from noisy or incomplete arcs remains challenging. In this paper, we propose an optimization method for ellipse fitting with an auxiliary normal to improve the performance. Firstly, ellipse fitting using an unerring normal is derived according to the projection from a circle in the world frame to an ellipse in the image frame. It can recover an accurate one directly from a short arc without iterative steps. Then, owing to the measurement error, an ellipse can be fitted iteratively within a tolerance range centered on the measured faulty normal. Finally, the calculation of requisite fitting matrices is simplified to speedup optimization. Each matrix can be constructed directly from a general 6-by-6 ellipse fitting matrix. Experimental results show that our method performs better than 4 state-of-the-art methods with limited tolerance.

This work is supported by the National Natural Science Foundation of China under Grant 9174820.

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Author information

Authors and Affiliations

  1. Image Processing Center, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Zhaoxi Li, Cai Meng & Dingzhe Li

  2. Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, 100191, China

    Cai Meng

  3. Beijing Key Laboratory of Digital Media, Beihang University, Beijing, China

    Cai Meng

  4. School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou, 510000, China

    Limin Liu

Authors
  1. Zhaoxi Li
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  2. Cai Meng
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  3. Dingzhe Li
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  4. Limin Liu
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Corresponding author

Correspondence to Cai Meng .

Editor information

Editors and Affiliations

  1. Peking University, Beijing, China

    Yuxin Peng

  2. Tsinghua University, Beijing, China

    Shi-Min Hu

  3. Tampere University, Tampere, Finland

    Moncef Gabbouj

  4. Zhejiang University, Hangzhou, China

    Kun Zhou

  5. Technion – Israel Institute of Technology, Haifa, Israel

    Michael Elad

  6. Tsinghua University, Beijing, China

    Kun Xu

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Li, Z., Meng, C., Li, D., Liu, L. (2021). Robust Ellipse Fitting with an Auxiliary Normal. In: Peng, Y., Hu, SM., Gabbouj, M., Zhou, K., Elad, M., Xu, K. (eds) Image and Graphics. ICIG 2021. Lecture Notes in Computer Science(), vol 12888. Springer, Cham. https://doi.org/10.1007/978-3-030-87355-4_50

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  • DOI: https://doi.org/10.1007/978-3-030-87355-4_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-87354-7

  • Online ISBN: 978-3-030-87355-4

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