Remove and Redistribute the Control Points for Bezier Curve Approximation

The main advantage of squared distance minimization is that it does not need a parameterization of data points on the model shape. However, it is sensitive to the initial curve due to its local nature of optimization. To this end, we integrate SDM with procedures for removing the redundant control points and redistributing the rest of the control points of the active Bezier curve. It adopts a concept of reducing the number of the control points to acquire more compact representation for the resultant curves. We introduce a new type of fairness term. This leads to a approach that is more robust and applicable than SDM used alone. It plays a significant role in improving the quality and the velocity of fitting curves especially when the parameterization and the compatibility of input curves are not good enough. Experimental results demonstrate its usefulness and quality.