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Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery

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Abstract

This paper develops a novel ellipse fitting algorithm by recovering a low-rank generalized multidimensional scaling (GMDS) matrix. The main contributions of this paper are: i) Based on the derived Givens transform-like ellipse equation, we construct a GMDS matrix characterized by three unknown auxiliary parameters (UAPs), which are functions of several ellipse parameters; ii) Since the GMDS matrix will have low rank when the UAPs are correctly determined, its recovery and the estimation of UAPs are formulated as a rank minimization problem. We then apply the alternating direction method of multipliers as the solver; iii) By utilizing the fact that the noise subspace of the GMDS matrix is orthogonal to the corresponding manifold, we determine the remaining ellipse parameters by solving a specially designed least squares problem. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed algorithm.

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Acknowledgments

This work was supported by NSFC (Grants 61533014 and 61471295), 973 Project (Grant 2014CB360508), Henry Fok Fund (Grant 141119), and the Fundamental Research Funds for the Central Universities (Grants 3102016BJY03 and 3102016QD065).

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Authors and Affiliations

  1. School of Electronics and Information, Northwestern Polytechnical University, Xi’an, China

    Junli Liang, Guoyang Yu, Pengliang Li & Weiren Kong

  2. Xi’an University of Technology, Xi’an, China

    Liansheng Sui & Ding Liu

  3. School of Computer, Wuhan Institute of Technology, Wuhan, China

    Yuntao Wu

  4. Department of Electronic Engineering, City University of Hong Kong, Kowloon Tong, China

    H. C. So

Authors
  1. Junli Liang
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  2. Guoyang Yu
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  3. Pengliang Li
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  4. Liansheng Sui
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  5. Yuntao Wu
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  6. Weiren Kong
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  7. Ding Liu
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  8. H. C. So
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Correspondence to Junli Liang.

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Liang, J., Yu, G., Li, P. et al. Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery. Multidim Syst Sign Process 29, 49–75 (2018). https://doi.org/10.1007/s11045-016-0452-x

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  • DOI: https://doi.org/10.1007/s11045-016-0452-x

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