An additional branch free algebraic B-spline curve fitting method

Algebraic curve fitting based on the algebraic distance is simple, but it has the disadvantage of inclining to a trivial solution. Researchers therefore introduce some constraints into the objective function in order to avoid the trivial solution. However, this often causes additional branches. Fitting based on geometric distance can avoid additional branches, but it does not offer sufficient fitting precision. In this paper we present a novel algebraic B-spline curve fitting method which combines both geometric distance and algebraic distance. The method first generates an initial curve by a distance field fitting that takes geometric distance as the objective function. Then local topology-preserving calibrations based on algebraic distance are performed so that each calibration does not produce any additional branches. In this way, we obtain an additional branch free fitting result whose precision is close to or even better than that produced by purely algebraic distance based methods. The adopted precision criterion is the geometric distance error rather than the algebraic one. In addition, we find a calibration fatigue phenomenon about calibrating strategy and propose a hybrid mode to solve it.