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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Bookstein, “Fitting Conic Sections to Scattered Data,” Computer Graphics and Image Processing, vol. 9, pp. 56–71, 1979
A.W. Fitzgibbon, M. Pilu, and R.B. Fisher, “Direct Least Squares Fitting of Ellipses,” Proceedings 13th ICPR, Wien 1996 pp. 253–257
D. Forsyth et.al., “Invariant Descriptors for 3D-Object Recognition and Pose,” IEEE Trans. PAMI, vol. 13, pp. 971–991, 1991
R.M. Haralick, and L.G. Shapiro, “Computer and Robot Vision,”, Vol. I, Addison-Wesley, 1993
K. Kanatani, “Statistical Bias of Conic Fitting and Renormalization,” IEEE Trans. PAMI, vol. 16, pp. 320–326, 1994
Y. Kanazawa, and K. Kanatani, “Optimal Conic Fitting and Reliability Evaluation,” IEICE Trans.Inf.Syst., vol. 9, pp. 1323–1328, 1996
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
P. Rosin, “A Note on Least Square Fitting of Ellipses,” Pattern Recognition Letters, vol. 14, pp. 799–808, 1993
I. Rothe, H. Suesse, and K. Voss, “The Method of Normalization to Determine Invariants,” IEEE Trans. PAMI, vol. 18, pp. 366–375, 1996
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
K. Voss., and H. Suesse, “Invariant Fitting of Planar Objects by Primitives,” IEEE Trans. PAMI, vol. 19, pp. 80–83, 1997
K. Voss., and H. Suesse, “A New One-Parametric Fitting Method for Planar Objects,” accepted for IEEE Trans. PAMI, 1999
I. Weiss, “Geometric Invariants and Object Recognition” IJCV, vol. 10, pp. 207–231, 1992
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-48375-6_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66366-9
Online ISBN: 978-3-540-48375-5
eBook Packages: Springer Book Archive