
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
JeanPhilippe Tarel, David B. Cooper, "The Complex Representation of Algebraic Curves and Its Simple Exploitation for Pose Estimation and Invariant Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 7, pp. 663674, July, 2000.  
BibTex  x  
@article{ 10.1109/34.865183, author = {JeanPhilippe Tarel and David B. Cooper}, title = {The Complex Representation of Algebraic Curves and Its Simple Exploitation for Pose Estimation and Invariant Recognition}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {22}, number = {7}, issn = {01628828}, year = {2000}, pages = {663674}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.865183}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  The Complex Representation of Algebraic Curves and Its Simple Exploitation for Pose Estimation and Invariant Recognition IS  7 SN  01628828 SP663 EP674 EPD  663674 A1  JeanPhilippe Tarel, A1  David B. Cooper, PY  2000 KW  Complex polynomials KW  pose estimation KW  poseindependent curve recognition KW  Euclidean invariants KW  completesets of rotation invariants KW  curve centers KW  implicit polynomial curves KW  algebraic curves KW  shape representation KW  shape recognition. VL  22 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—New representations are introduced for handling 2D algebraic curves (implicit polynomial curves) of arbitrary degree in the scope of computer vision applications. These representations permit fast, accurate poseindependent shape recognition under Euclidean transformations with a
[1] G. Taubin,“Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 11151137, Nov. 1991.
[2] Z. Huang and F.S. Cohen, “AffineInvariant BSpline Moments for Curve Matching,” IEEE Trans. Image Processing, vol. 5, no. 10, pp. 1,4731,480, Oct. 1996.
[3] 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. 131147, Feb. 1990.
[4] S. De Ma, “ConicsBased Stereo, Motion Estimation and Pose Determination,” Int'l J. Computer Vision, vol. 10, no. 1, 1993.
[5] T.H. Reiss,“Recognizing planar object using invariant image features,” Lecture Notes in Computer Science, no. 676. Berlin: SpringerVerlag, 1993.
[6] Geometric Invariance in Computer Vision, J.L. Mundy and A. Zisserman, eds., MIT Press, 1992.
[7] I. Weiss,“Noiseresistant invariants of curves,” IEEE Trans. Pattern Anal. and Machine Intelligence, vol. 15, no. 9, pp. 943948, Sept. 1993.
[8] E. Calabi, P.J. Olver, C. Shakiban, A. Tannenbaum, and S. Haker, “Differential and Numerically Invariant Signature Curves Applied to Object Recognition,” Int'l J. Computer Vision, vol. 26, no. 2, pp. 107135, Feb. 1998.
[9] A.N. Bruckstein and A.M. Netravali, “Differential Invariants of Planar Curves and Recognizing Partially Occluded Shapes,” Visual Form: Analysis and Recognition, pp. 8998, 1991.
[10] Z. Lei, T. Tasdizen, and D.B. Cooper, “PIMs and Invariant Parts for Shape Recognition,” Proc. IEEE Int'l Conf. Computer Vision, pp. 827832, Jan. 1998.
[11] F. Mokhtarian, S. Abbasi, and J. Kittler, “Robust and Efficient Shape Indexing through Curvature Scale Space,” Proc Sixth British Machine Vision Conf., BMVC '96, pp. 5362, 1996.
[12] J. Ponce, A. Hoogs, and D.J. Kriegman, “On Using CAD Models to Compute the Pose of Curved 3D Objects,” Computer Vision, Graphics, and Image Processing, vol. 55, no. 2, pp. 184197, Mar. 1992.
[13] J.P. Tarel and D.B. Cooper, “A New Complex Basis for Implicit Polynomial Curves and Its Simple Exploitation for Pose Estimation and Invariant Recognition,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 111117, June 1998.
[14] M. Unel and W. Wolovich, “Complex Representations of Algebraic Curves,” Proc. IEE Intl. Conf. Image Processing, Oct. 1998.
[15] T. Tasdizen, J.P. Tarel, and D.B. Cooper, Improving the Stability of Algebraic Curves for Applications IEEE Trans. Image Processing, vol. 9, no. 3, pp. 405416, Mar. 2000.
[16] Z. Lei, M.M. Blane, and D.B. Cooper, “3L Fitting of Higher Degree Implicit Polynomials,” Proc. Third IEEE Workshop Applications of Computer Vision, pp. 148153, Dec. 1996.
[17] M. Schwartz, Information Transmission, Modulation, and Noise, fourth ed. McGrawHill. 1990.
[18] J.P. Tarel, W.A. Wolovich, and D.B. Cooper, “Covariant Conics Decomposition of Quartics for 2D Object Recognition and Affine Alignment,” Proc. Int'l Conf. Image Processing, pp. 818822, Oct. 1998.
[19] J.P. Tarel, H. Civi, and D.B. Cooper, “Pose Estimation of FreeForm 3D Objects without Point Matching Using Algebraic Surface Models,” Proc. IEEE Workshop ModelBased 3D Image Analysis, pp. 1321, 1998.