Simulated Annealing Algorithm for Bezier Curve Approximation

Curve approximation is a very important topic in many industrial and applied fields. The typical input in real-world applications is a set of sampled data points for which a fitting curve is to be obtained. This paper addresses this problem by using Bezier curves as the approximating functions. This formulation leads to a continuous multivariate nonlinear optimization problem. Unfortunately, this is very difficult problem that cannot be solved with classical mathematical optimization techniques. In this paper, we solve the problem through a hybrid strategy combining classical methods (linear least-squares minimization), modern stochastic methods (simulated annealing) and information science metrics. For a given degree n, our method computes a near-to-optimal parameterization of data points by using simulated annealing for global search and a local search optimizer for further refinement of the global solution. Then, we compute the control points by least-squares minimization. Finally, we determine the best value for the degree of the curve by using two information science metrics that represent an adequate compromise between data-fidelity and model-complexity. Our method is applied to four illustrative examples of mathematical curves and noisy scanned data and different configurations. Our experimental results show that the method performs well for all examples.