Direct least-squares fitting of algebraic surfaces
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This paper addresses a common problem in dealing with range images. We propose a novel method to fit surfaces of known types via a parameter decomposition approach. This approach is faithful and it strongly reduces the possibilities of dropping into local minima in the process of iterative optimization. Therefore, it increases the tolerance in selecting the initializations. Moreover, it reduces the computation time and increases the fitting accuracy compared to former approaches. We present methods for fitting cylinders, cones, and tori to 3D data points. They share the fundamental idea of decomposing the set of parameters into two parts: one part has to be solved by some traditional optimization method and another part can be solved either analytically or directly. We experimentally compare our method with a fitting algorithm recently reported in the literature. The results demonstrate that our method has superior performance in accuracy and speed.