Practical Error Analysis of Cross-Ratio-Based Planar Localization

  • Jen-Hui Chuang
  • Jau-Hong Kao
  • Horng-Horng Lin
  • Yu-Ting Chiu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4872)


Recently, more and more computer vision researchers are paying attention to error analysis so as to fulfill various accuracy requirements arising from different applications. As a geometric invariant under projective transformations, cross-ratio is the basis of many recognition and reconstruction algorithms which are based on projective geometry. We propose an efficient way of analyzing localization error for computer vision systems which use cross-ratios in planar localization. By studying the inaccuracy associated with cross-ratio-based computations, we inspect the possibility of using linear transformation to approximate localization error due to 2-D noises of image extraction for reference points. Based on such a computationally efficient analysis, a practical way of choosing point features in an image so as to establish the probabilistically most accurate planar location system using cross-ratios is developed.


cross-ratio error analysis error ellipse robot localization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jen-Hui Chuang
    • 1
  • Jau-Hong Kao
    • 1
  • Horng-Horng Lin
    • 1
  • Yu-Ting Chiu
    • 1
  1. 1.Deptartment of Computer Science, National Chiao-Tung University, No. 1001, Ta-Hseuh Rd., HsinchuTaiwan

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