Hybrid curve fitting

Computing (Vienna/New York)

Volumn 79, Issue 2-4, 2007, Pages 237-247

  Aigner, M ^a,b   Juttler B ^a,b  

^a Johannes Kepler University ^*

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Active curve; Curve fitting; Evolution process; Normal distance minimization

Indexed keywords

ACTIVE CURVES; EVOLUTION PROCESSES; NORMAL DISTANCE MINIMIZATION;

APPROXIMATION THEORY; COMPUTER SIMULATION; OPTIMIZATION; PARAMETER ESTIMATION; VECTORS;

CURVE FITTING;

EID: 34147106543     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-006-0201-3     Document Type: Article

References (20)

1. Aigner, M., Jüttler, B.: Robust computation of foot points on implicitly defined curves. In: Mathematical Methods for Curves and Surfaces: Tromsø 2004 (M. Dæhlen et al., eds.). Nashboro Press 2005, pp. 1-10.
2. Alhanaty, M., Bercovier, M.: Curve and surface fitting and design by optimal control methods. Computer Aided Design 33, 167-182 (2001).
3. Blake, A., Isard, M.: Active contours. Springer 2000.
4. Hagen, H., Brunnett, G., Santarelli, P.: Variational principles in curve and surface design. Surv. Math. Ind. 3, 1-27 (1993).
5. Hoff K. E. et al.: Fast computation of generalized Voronoi diagrams using graphics hardware. SIGGRAPH '99 Proc. pp. 277-286.
6. Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. A.K. Peters/Wellesley, Mass. 1996.
7. Hu, S.-M., Wallner, J.: A second-order algorithm for orthogonal projection onto curves and surfaces. Comp. Aided Geom. Des. 22, 251-260 (2005).
8. Engl, H. W., Hanke, M., Neubauer, A.: Regularization of inverse problems. Dordrecht: Kluwer Academic Publishers 1996.
9. Osher, S., Sethian, J.: Fronts propagating with curvature dependent speed, algorithms based on a Hamilton-Jacobi formulation. J. Comp. Phys. 79, 12-49 (1988).
10. Osher, S., Fedkiw, R. P.: Level set methods and dynamic implicit surfaces. Springer 2003.
11. Rogers, D. F., Fog, N. G.: Constrained B-spline curve and surface fitting. Comp. Aided Design 21, 641-648 (1989).
12. Sarkar, B., Menq, C.-H.: Parameter optimization in approximating curves and surfaces to measurement data. Comp. Aided Geom. Design 8, 267-280 (1991).
13. Pottmann, H., Leopoldseder, S.: A concept for parametric surface fitting which avoids the parametrization problem. Comp. Aided Geom. Design 20, 343-362 (2003).
14. Pottmann, H., Leopoldseder, S., Hofer, M.: Approximation with active B-spline curves and surfaces. Proc. Pacific Graphics 2002, IEEE Press, pp. 8-25.
15. Pottmann, H. et al.: Industrial geometry: recent advances and applications in CAD. Comp. Aided Design 37, 751-766 (2005).
16. Redding, N. J.: Implicit polynomials, orthogonal distance regression and the closest point on a curve. IEEE Trans. on Pattern Analy Machine Intelligence 22, 191-199 (2000).
17. Speer, T., Kuppe, M., Hoschek, J.: Global reparametrization for curve approximation. Comp. Aided Geom. Design 15, 869-877 (1998).
18. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comp. Vision 1.4, 321-331 (1987).
19. Wang, W., Pottmann, H., Liu, Y.: Fitting B-spline curves to point clouds by squared distance minimization. ACM Trans. on Graphics 25.2 (2006).
20. Yang, H. et al.: Evolution of T-spline level sets with distance field constraints for geometry reconstruction and image segmentation (submitted). FSP report no. 1 (2005), available at www.ig.jku.at.