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

•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.

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.