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A New Framework of Invariant Fitting

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Computer Analysis of Images and Patterns (CAIP 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1689))

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Abstract

This paper is an extension of the already published paper Voss/Suesse [11]. In that paper we have developed a new region-based fitting method using the method of normalization. There we have demonstrated the zero-parametric fitting of lines, triangles, parallelograms, circles and ellipses. In the present paper we discuss this normalization idea for fitting of closed regions using circular segments, elliptical segments and rectangles. As features we use the area-based low order moments. We show that we have to solve only one-dimensional optimization problems in these cases.

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References

  1. F. Bookstein, “Fitting Conic Sections to Scattered Data,” Computer Graphics and Image Processing, vol. 9, pp. 56–71, 1979

    Article  Google Scholar 

  2. A.W. Fitzgibbon, M. Pilu, and R.B. Fisher, “Direct Least Squares Fitting of Ellipses,” Proceedings 13th ICPR, Wien 1996 pp. 253–257

    Google Scholar 

  3. D. Forsyth et.al., “Invariant Descriptors for 3D-Object Recognition and Pose,” IEEE Trans. PAMI, vol. 13, pp. 971–991, 1991

    Google Scholar 

  4. R.M. Haralick, and L.G. Shapiro, “Computer and Robot Vision,”, Vol. I, Addison-Wesley, 1993

    Google Scholar 

  5. K. Kanatani, “Statistical Bias of Conic Fitting and Renormalization,” IEEE Trans. PAMI, vol. 16, pp. 320–326, 1994

    MATH  Google Scholar 

  6. Y. Kanazawa, and K. Kanatani, “Optimal Conic Fitting and Reliability Evaluation,” IEICE Trans.Inf.Syst., vol. 9, pp. 1323–1328, 1996

    Google Scholar 

  7. D. Kapur, and J.L. Mundy, “Fitting Affine Invariant Conics to Curves,” In Mundy J.L. and Zisserman A.: Geometric Invariance in Computer Vision, MIT Press 1992 pp.252–266, 1992

    Google Scholar 

  8. P. Rosin, “A Note on Least Square Fitting of Ellipses,” Pattern Recognition Letters, vol. 14, pp. 799–808, 1993

    Article  MATH  Google Scholar 

  9. I. Rothe, H. Suesse, and K. Voss, “The Method of Normalization to Determine Invariants,” IEEE Trans. PAMI, vol. 18, pp. 366–375, 1996

    Google Scholar 

  10. F. Solina, and R. Bajcsy, “Recovery of parametric models from range images: The case for superquadrics with global deformations,” IEEE Trans. PAMI, vol. 12, pp. 131–147, 1990

    Google Scholar 

  11. K. Voss., and H. Suesse, “Invariant Fitting of Planar Objects by Primitives,” IEEE Trans. PAMI, vol. 19, pp. 80–83, 1997

    Google Scholar 

  12. K. Voss., and H. Suesse, “A New One-Parametric Fitting Method for Planar Objects,” accepted for IEEE Trans. PAMI, 1999

    Google Scholar 

  13. I. Weiss, “Geometric Invariants and Object Recognition” IJCV, vol. 10, pp. 207–231, 1992

    Article  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Voss, K., Suesse, H. (1999). A New Framework of Invariant Fitting. In: Solina, F., Leonardis, A. (eds) Computer Analysis of Images and Patterns. CAIP 1999. Lecture Notes in Computer Science, vol 1689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48375-6_33

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  • DOI: https://doi.org/10.1007/3-540-48375-6_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66366-9

  • Online ISBN: 978-3-540-48375-5

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