Reconstruction of free-form space curves using NURBS-snakes and a quadratic programming approach

In this study, we propose a robust algorithm for reconstructing free-form space curves in space using a Non-Uniform Rational B-Spline (NURBS)-snake model. Two perspective images of the required free-form curve are used as the input and a nonlinear optimization process is used to fit a NURBS-snake on the projected data in these images. Control points and weights are treated as decision variables in the optimization process. The Levenberg-Marquardt optimization algorithm is used to optimize the parameters of the NURBS-snake, where the initial solution is obtained using a two-step procedure. This makes the convergence faster and it stabilizes the optimization procedure. The curve reconstruction problem is reduced to a problem that comprises stereo reconstruction of the control points and computation of the corresponding weights. Several experiments were conducted to evaluate the performance of the proposed algorithm and comparisons were made with other existing approaches. A novel approach for the reconstruction of free-form space curves is presented.The proposed approach is based on NURBS-snake model and quadratic programming.An energy minimization method which is analogous to snake model "NURBS-snake model" is used.Levenberg-Marquardt algorithm is used for optimizing the parameters of the energy function.The initial parameters of the NURBS-snake are obtained using a two step procedure in which firstly weights are obtained by solving a quadratic programming problem and then control points are evolved by solving a system of linear equation.The proposed method has been tested using various synthetic and real data.The proposed scheme is also applicable when the samplings of image curves vary.The method is easy to implement and can be used to reconstruct complex free-form shape curves.

[1]  Cui Hanguo,et al.  Optimized NURBS Curve and Surface Fitting Using Simulated Annealing , 2009, 2009 Second International Symposium on Computational Intelligence and Design.

[2]  Fernand S. Cohen,et al.  Part II: 3-D Object Recognition and Shape Estimation from Image Contours Using B-splines, Shape Invariant Matching, and Neural Network , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Wei-Cheng Xie,et al.  Iteration and optimization scheme for the reconstruction of 3D surfaces based on non-uniform rational B-splines , 2012, Comput. Aided Des..

[4]  Gang Xu,et al.  Robust active contours with insensitive parameters , 1994, Pattern Recognit..

[5]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[6]  Mubarak Shah,et al.  A Fast algorithm for active contours and curvature estimation , 1992, CVGIP Image Underst..

[7]  Gerald E. Farin,et al.  From conics to NURBS: A tutorial and survey , 1992, IEEE Computer Graphics and Applications.

[8]  Yi Jun Xiao,et al.  Optimized stereo reconstruction of free-form space curves based on a nonuniform rational B-spline model. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Ramesh C. Jain,et al.  Using Dynamic Programming for Solving Variational Problems in Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  K. Lam,et al.  Fast greedy algorithm for active contours , 1994 .

[11]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[12]  Balasubramanian Raman,et al.  Error estimation in reconstruction of quadratic curves in 3D space , 2007, Int. J. Comput. Math..

[13]  Richard I. Hartley,et al.  Projective reconstruction from line correspondences , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[14]  Ravinda G. N. Meegama,et al.  NURBS snakes , 2003, Image Vis. Comput..

[15]  Takeo Kanade,et al.  Shape and motion from image streams under orthography: a factorization method , 1992, International Journal of Computer Vision.

[16]  Weiyin Ma,et al.  Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces , 1995, Comput. Aided Des..

[17]  J. Kruth,et al.  NURBS curve and surface fitting for reverse engineering , 1998 .

[18]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[19]  Les A. Piegl,et al.  On NURBS: A Survey , 2004 .

[20]  Balasubramanian Raman,et al.  RECONSTRUCTION OF CUBIC CURVES FROM TWO OR MORE IMAGES USING GEOMETRIC INTERSECTION , 2009 .

[21]  H. S. Sawhney,et al.  Intelligent interactive image outlining using spline snakes , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[22]  Yuandi Zhao,et al.  Two-view curve reconstruction based on the snake model , 2011, J. Comput. Appl. Math..

[23]  Simon Flöry,et al.  Fitting curves and surfaces to point clouds in the presence of obstacles , 2009, Comput. Aided Geom. Des..

[24]  Hong Qin,et al.  Dynamic NURBS with geometric constraints for interactive sculpting , 1994, TOGS.

[25]  Laurence G. Hassebrook,et al.  A multistage, optimal active contour model , 1996, IEEE Trans. Image Process..