Robust Ellipse Fitting via Half-Quadratic and Semidefinite Relaxation Optimization

Junli Liang, Yunlong Wang, Xianju Zeng

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

Abstract

Ellipse fitting is widely applied in the fields of computer vision and automatic manufacture. However, the introduced edge point errors (especially outliers) from image edge detection will cause severe performance degradation of the subsequent ellipse fitting procedure. To alleviate the influence of outliers, we develop a robust ellipse fitting method in this paper. The main contributions of this paper are as follows. First, to be robust against the outliers, we introduce the maximum correntropy criterion into the constrained least-square (CLS) ellipse fitting method, and apply the half-quadratic optimization algorithm to solve the nonlinear and nonconvex problem in an alternate manner. Second, to ensure that the obtained solution is related to an ellipse, we introduce a special quadratic equality constraint into the aforementioned CLS model, which results in the nonconvex quadratically constrained quadratic programming problem. Finally, we derive the semidefinite relaxation version of the aforementioned problem in terms of the trace operator and thus determine the ellipse parameters using semidefinite programming. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.

Original languageEnglish
Article number7165614
Pages (from-to)4276-4286
Number of pages11
JournalIEEE Transactions on Image Processing
Volume24
Issue number11
DOIs
StatePublished - 1 Nov 2015

Keywords

  • constrained least-square (CLS)
  • Ellipse fitting
  • half-quadratic optimization
  • iris localization
  • maximum correntropy criterion (MCC)
  • outliers
  • quadratically constrained quadratic programming (QCQP)
  • semidefinite programming (SDP)
  • semidefinite relaxation (SDR)
  • spacecraft pose determination

Fingerprint

Dive into the research topics of 'Robust Ellipse Fitting via Half-Quadratic and Semidefinite Relaxation Optimization'. Together they form a unique fingerprint.

Cite this