Two error functions used for nonlinear Least Squares (LS) fitting of spheres to range data from 3D imaging systems are discussed: orthogonal error function and directional error function. Both of the functions allow unrestricted gradient-based minimization and they were tested on more than 40 datasets collected under different experimental conditions (e.g., different sphere diameters, instruments, data density, and data noise). It was found that the orthogonal error function results in two local minima, and the outcome of the optimization depends on the choice of starting point. The centroid of the data points is commonly used as the starting point for the nonlinear LS solution. The choice of starting point is sensitive to data segmentation, and for some sparse and noisy datasets can lead to a wrong minimum. The directional error function has only one minimum. Therefore, it is not sensitive to the starting point and this makes it more suitable for applications which require fully automated sphere fitting. Such situations arise when 3D imaging systems are used in a fully automated environment where sphere targets are used for data registration.
Citation: IEEE Transactions on Instrumentation and Measurement
Pub Type: Journals
sphere fitting, orthogonal error function, directional error function, 3D imaging systems, target-based registration