Fitting of 3D circles and ellipses using a parameter decomposition approach

Many optimization processes encounter a problem in efficiently reaching a global minimum or a near global minimum. Traditional methods such as Levenberg-Marquardt algorithm and trust-region method face the problems of dropping into local minima as well. On the other hand, some algorithms such as simulated annealing and genetic algorithm try to find a global minimum but they are mostly time-consuming. Without a good initialization, many optimization methods are unable to guarantee a global minimum result. We address a novel method in 3D circle and ellipse fitting, which alleviates the optimization problem. It can not only increase the probability of getting in global minima but also reduce the computation time. Based on our previous work, we decompose the parameters into two parts: one part of parameters can be solved by an analytic or a direct method and another part has to be solved by an iterative procedure. Via this scheme, the topography of optimization space is simplified and therefore, we reduce the number of local minima and the computation time. We experimentally compare our method with the traditional ones and show superior performance.