This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A New One-Parametric Fitting Method for Planar Objects
July 1999 (vol. 21 no. 7)
pp. 646-651

Abstract—This paper is an extension of the already published paper by Voss and Suesse [11]. In that paper, we developed a new region-based fitting method using the method of normalization. There we 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 super-ellipses. 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.

[1] F. Brookstein, “Fitting Conic Sections to Scattered Data,” Computer Graphics and Image Processing, vol. 9, pp. 56-71, 1979.
[2] A.W. Fitzgibbon, M. Pilu, and R.B. Fisher, “Direct Least-Square Fitting of Ellipses,” Proc. 13th Int'l Conf' Pattern Recognition, Aug. 1996.
[3] D.A. Forsyth,J.L. Mundy,A. Zisserman,C. Coelho,A. Heller,, and C. Rothwell,“Invariant descriptors for 3D object recognition and pose,” Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 971-992, Oct. 1992.
[4] R.M. Haralick and L.G. Shapiro, Computer and Robot Vision. New York: Addison-Wesley, 1993.
[5] K. Kanatani, “Statistical Bias of Conic Fitting and Renormalization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 3, pp. 320-326, Mar. 1994.
[6] Y. Kanazawa and K. Kanatani, “Optimal Conic Fitting and Reliability Evaluation,” IEICE Trans. Information and Systems, vol. 9, pp. 1,323-1,328, 1996.
[7] D. Kapur and J.L. Mundy, “Fitting Affine Invariant Conics to Curves,” J.L. Mundy and A. Zisserman, eds. Geometric Invariance in Computer Vision, pp. 252-266. MIT Press: 1992.
[8] P.L. Rosin, “A Note on the Least Square Fitting of Ellipses,” Pattern Recognition Letters, vol. 14, no. 10, pp. 799-808, 1993.
[9] I. Rothe, H. Suesse, and K. Voss, “The Method of Normalization of Determine Invariants,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 4, pp. 366-376, Apr. 1996.
[10] F. Solina and R. Bajcsy,“Recovery of parametric models from range images: The case for superquadrics with global deformations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 131-147, Feb. 1990.
[11] K. Voss and H. Suesse, “Invariant Fitting of Planar Objects by Primitives,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, pp. 80-83, 1997.
[12] I. Weiss, “Geometric Invariants and Object Recognition,” Int'l J. Computer Vision, vol. 10, no. 3, pp. 201-231, June 1993.

Index Terms:
Fitting, canonical frame, moments, ellipses, normalization.
Citation:
Klaus Voss, Herbert Suesse, "A New One-Parametric Fitting Method for Planar Objects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 646-651, July 1999, doi:10.1109/34.777376
Usage of this product signifies your acceptance of the Terms of Use.