On Bias correction for geometric parameter estimation in computer vision

Takayuki Okatani, Koichiro Deguchi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

Maximum likelihood (ML) estimation is widely used in many computer vision problems involving the estimation of geometric parameters, from conic fitting to bundle adjust- ment for structure and motion. This paper presents a de- tailed discussion on the bias of ML estimates derived for these problems. Statistical theory states that although ML estimates attain maximum accuracy in the limit as the sam- ple size goes to infinity, they can have non-negligible bias with small sample sizes. In the case of computer vision problems, the ML optimality holds when regarding variance in observation errors as the sample size. A natural question is how large the bias will be for a given strength of observa- tion errors. To answer this for a general class of problems, we analyze the mechanism of how the bias of ML estimates emerges, and show that the differential geometric properties of geometric constraints used in the problems determines the magnitude of bias. Based on this result, we present a numerical method of computing bias-corrected estimates.

Original languageEnglish
Title of host publication2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009
PublisherIEEE Computer Society
Pages959-966
Number of pages8
ISBN (Print)9781424439935
DOIs
Publication statusPublished - 2009 Jan 1
Event2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Miami, FL, United States
Duration: 2009 Jun 202009 Jun 25

Publication series

Name2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009
Volume2009 IEEE Computer Society Conference on Computer Vision and ...

Other

Other2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
CountryUnited States
CityMiami, FL
Period09/6/2009/6/25

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Biomedical Engineering

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  • Cite this

    Okatani, T., & Deguchi, K. (2009). On Bias correction for geometric parameter estimation in computer vision. In 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009 (pp. 959-966). [5206722] (2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009; Vol. 2009 IEEE Computer Society Conference on Computer Vision and ...). IEEE Computer Society. https://doi.org/10.1109/CVPRW.2009.5206722