Implicit polynomial representation through a fast fitting error estimation

IEEE Transactions on Image Processing

Volumn 21, Issue 4, 2012, Pages 2089-2098

  Rouhani, Mohammad ^a   Sappa, Angel Domingo ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Curve surface fitting; geometric distance estimation; implicit polynomial (IP); residual error minimization

Indexed keywords

CURVE/SURFACE FITTING; DATA SETS; DISTANCE ESTIMATION; FITTING ERROR; GEOMETRIC DISTANCE ESTIMATION; GRADIENT BASED; GRADIENT-BASED OPTIMIZATION; IMPLICIT POLYNOMIAL REPRESENTATION; IMPLICIT POLYNOMIALS; LEVENBERG-MARQUARDT; NONLINEAR LEAST SQUARES PROBLEMS; RESIDUAL ERROR;

POLYNOMIALS; THREE DIMENSIONAL; TWO DIMENSIONAL;

ESTIMATION;

ALGORITHM; ARTICLE; ARTIFACT; COMPUTER ASSISTED DIAGNOSIS; IMAGE ENHANCEMENT; MATHEMATICAL COMPUTING; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFACTS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 84859064833     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2011.2170080     Document Type: Article

References (27)

1. M. Sarkis and K. Diepold, "Content adaptive mesh representation of images using binary space partitions," IEEE Trans. Image Process., vol. 18, no. 5, pp. 1069-1079, May 2009.
2. A. Jalba and J. Roerdink, "Efficient surface reconstruction from noisy data using regularized membrane potentials," IEEE Trans. Image Process., vol. 18, no. 5, pp. 1119-1134, May 2009.
3. C. Darolti, A. Mertins, C. Bodensteiner, and U. Hofmann, "Local region descriptors for active contours evolution," IEEE Trans. Image Process., vol. 17, no. 12, pp. 2275-2288, Dec. 2008.
4. V. Srikrishnan and S. Chaudhuri, "Stabilization of parametric active contours using a tangential redistribution term," IEEE Trans. Image Process., vol. 18, no. 8, pp. 1859-1872, Aug. 2009.
5. H. Ben-Yaacov, D. Malah, and M. Barzohar, "Recognition of 3-D objects based on implicit polynomials," IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 5, pp. 954-960, May 2010.
6. B. Zheng, J. Takamatsu, and K. Ikeuchi, "An adaptive and stable method for fitting implicit polynomial curves and surface," IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 3, pp. 561-568, Mar. 2010.
7. R. Xu and M. Kemp, "Fitting multiple connected ellipses to an image silhouette hierarchically," IEEE Trans. Image Process., vol. 19, no. 7, pp. 1673-1682, Jul. 2010.
8. M. Rouhani and A. D. Sappa, "A novel approach to geometric fitting of implicit quadrics," in Proc. 11th Int. Conf. Adv. Concepts Intell. Vis. Syst., Bordeaux, France, Sep. 28-Oct., 2 2009, pp. 121-132.
9. A. Sappa andM. Rouhani, "Efficient distance estimation for fitting implicit quadric surfaces," in Proc. IEEE Int. Conf. Image Process., Cairo, Egypt, Nov. 2009, pp. 3521-3524.
10. 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 Anal. Mach. Intell., vol. 13, no. 11, pp. 1115-1138, Nov. 1991.
11. A. Helzer, M. Barzohar, and D. Malah, "Stable fitting of 2-D curves and 3-D surfaces by implicit polynomials," IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 10, pp. 1283-1294, Oct. 2004.
12. D. Keren and C. Gotsman, "Fitting curves and surfaces with constrained implicit polynomials," IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 1, pp. 476-480, Jan. 1999.
13. T. Tasdizen, J. Tarel, and D. Cooper, "Improving the stability of algebraic curves for applications," IEEE Trans. Image Process., vol. 9, no. 3, pp. 405-416, Mar. 2000. (Pubitemid 30572359)
14. M. Blane, Z. Lei, H. Civil, and D. Cooper, "The 3L algorithm for fitting implicit polynomials curves and surface to data," IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 3, pp. 298-313, Mar. 2000.
15. M. Rouhani and A. D. Sappa, "Relaxing the 3L algorithm for an accurate implicit polynomial fitting," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recog., San Francisco, CA, Jun. 2010, pp. 3066-3072.
16. S. Ahn, W. Rauh, H. Cho, and H. Warnecke, "Orthogonal distance fitting of implicit curves and surfaces," IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 5, pp. 620-638, May 2002. (Pubitemid 34550430)
17. M. Aigner and B. Jütler, "Gauss-Newton-type technique for robustly fitting implicit defined curves and surfaces to unorganized data points," in Proc. IEEE Int. Conf. Shape Model. Appl., New York, Jun. 2009, pp. 121-130.
18. Y. Chen and C. Liu, "Quadric surface extraction using genetic algorithms," Comput.-Aided Des., vol. 31, no. 2, pp. 101-110, Feb. 1999.
19. P. Gotardo, O. Bellon, K. Boyer, and L. Silva, "Range image segmentation into planar and quadric surfaces using an improved robust estimator and genetic algorithm," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 6, pp. 2303-2316, Dec. 2004.
20. P. D. Sampson, "Fitting conic sections to very scattered data: An iterative refinement of the Bookstein algorithm," Comput. Graph. Image Process., vol. 18, no. 1, pp. 97-108, Jan. 1982.
21. H. Hoppe, T. DeRose, T. Duchamp, J. A. McDonald, and W. Stuetzle, "Surface reconstruction from unorganized points," in Proc. 19th Annu. Conf. Comput. Graph. Interactive Techn., SIGGRAPH, Chicago, IL, Jul. 1992, pp. 71-78. (Pubitemid 23614139)
22. H. Helfrich and D. Zwick, "A trust region algorithm for parametric curve and surface fitting," J. Comput. Appl. Math., vol. 73, no. 1/2, pp. 119-134, Oct. 1996. (Pubitemid 126407305)
23. W. Wang, H. Pottmann, and Y. Liu, "Fitting B-spline curves to point clouds by curvature-based squared distance minimization," ACM Trans. Graph., vol. 25, no. 2, pp. 214-238, Apr. 2006. (Pubitemid 44023257)
24. D. Adi, S. Shamsuddin, and A. Ali, "Particle swarm optimization for nurbs curve fitting," in Proc. IEEE Int. Conf. Comput. Graph., Imag. Vis., Tianjin, China, Aug. 2009, pp. 259-263.
25. R. Fletcher, Practical Methods of Optimization, 2nd ed. New York: Wiley, 1990.
26. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed. New York: Springer-Verlag, 2002.
27. A. Fitzgibbon, M. Pilu, and R. Fisher, "Direct least square fitting of ellipses," IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 5, pp. 476-480, May 1999.