Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

3 Scopus Citations
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Author(s)

  • Junli Liang
  • Guoyang Yu
  • Pengliang Li
  • Liansheng Sui
  • Yuntao Wu
  • Weiren Kong
  • Ding Liu

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)49-75
Journal / PublicationMultidimensional Systems and Signal Processing
Volume29
Issue number1
Online published16 Sep 2016
Publication statusPublished - Jan 2018

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.

Research Area(s)

  • Alternating direction method of multiplier (ADMM), Ellipse fitting algorithm, Generalized multidimensional scaling matrix, Givens transform, Low rank, Nuclear norm minimization, Unknown auxiliary parameter (UAP)

Citation Format(s)

Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery. / Liang, Junli; Yu, Guoyang; Li, Pengliang; Sui, Liansheng; Wu, Yuntao; Kong, Weiren; Liu, Ding; So, H. C.

In: Multidimensional Systems and Signal Processing, Vol. 29, No. 1, 01.2018, p. 49-75.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review