|
| This Article | ||
| ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
| | ||
| Search | ||
| ||
| ASCII Text | x | ||
| Zhibin Lei, David B. Cooper, "Linear Programming Fitting of Implicit Polynomials," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 212-217, February, 1998. | |||
| BibTex | x | ||
| @article{ 10.1109/34.659942, author = {Zhibin Lei and David B. Cooper}, title = {Linear Programming Fitting of Implicit Polynomials}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {20}, number = {2}, issn = {0162-8828}, year = {1998}, pages = {212-217}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.659942}, 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 - Linear Programming Fitting of Implicit Polynomials IS - 2 SN - 0162-8828 SP212 EP217 EPD - 212-217 A1 - Zhibin Lei, A1 - David B. Cooper, PY - 1998 KW - Implicit polynomials KW - shape representations KW - linear programming KW - distance approximation KW - fitting algorithms KW - user interface. VL - 20 JA - IEEE Transactions on Pattern Analysis and Machine Intelligence ER - | |||
Abstract—A new implicit polynomial (IP) fitting method is presented. It provides a different way of viewing the IP fitting problem from those of the nonlinear optimization approaches. It requires less computation, and can be done automatically or interactively. Linear Programming (LP) is used to do the fitting. The approach can incorporate a variety of distance measures and global geometric constraints.
[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. 1115-1137, Nov. 1991.
[2] G. Taubin, "An improved algorithm for algebraic curve and surface fitting," Proc. Fourth Int'l Conf. Computer Vision, pp. 658-665,Berlin, Germany, May 1993.
[3] S. Sullivan, L. Sandford, and J. Ponce, "Using Geometric Distance Fits for 3D Object Modeling and Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 12, pp. 1,183-1,196, 1994.
[4] Z. Lei, D. Keren, and D.B. Cooper, “Computationally Fast Bayesian Recognition of Complex Objects Based on Mutual Algebraic Invariants,” Proc. IEEE Int'l Conf. Image Processing, Oct. 1995.
[5] J. Mundy and A. Zisserman, eds. Geometric Invariance in Computer Vision.Cambridge, Mass.: MIT Press, 1992.
[6] D. Keren,D. Cooper,, and J. Subrahmonia,“Describing complicated objects by implicit polynomials,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 1, pp. 38-53, 1994.
[7] R.J. Vanderbei, LOQO User's Manual. Program in Statistics and Operations Research, Princeton Univ., Nov. 1992.
[8] G.B. Dantzig, Linear Programming and Its Extensions.Princeton, N.J.: Princeton Univ. Press, 1963.
[9] J. Subrahmonia, D.B. Cooper, and D. Keren, “Practical, Reliable, Bayesian Recognition of 2D and 3D Objects Using Implicit Polynomials and Algebraic Invariants,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 5, pp. 505-519, May 1996.
[10] Z. Lei and D.B. Cooper, New, Faster, More Controlled Fitting of Implicit Polynomial 2D Curves and 3D Surfaces to Data Proc. IEEE Conf. Computer Vision and Pattern Recognition, June 1996.
[11] Z. Lei and D.B. Cooper, "Linear Programming Fitting of Implicit Polynomials With Applications in Object Recognition and Interactive Computer Graphics," LEMS Tech. Report 146, Brown Univ., Oct. 1995.

