The ability to produce architectural models from edge and range data is of fundamental importance to describe the data in a compact form. While the problem of model fitting has been successful addressed, the problem of a high accuracy and stability of the fitting is still an open problem. It is obvious that the quality of the fitting results has a substantive impact on the quality of reverse engineering where we work with a constrained reconstruction of 3D geometric shapes. Thus it is important to get good fits to the data.
We revisited the Euclidean Fitting of curves and surface to 3D data to investigate if it is worth considering Euclidean Fitting again. We can summarize that robustness and accuracy increases sufficiently compared to other often used methods and Euclidean Fitting is more stable with increased noise. The main disadvantage of the Euclidean Fitting, computational cost, has become less important due to rising computing speed and is becoming an insignificant deterrent to usage, especially if high accuracy is required. We improved the known fitting methods by an (iterative) estimation of the real Euclidean distances and compared the performance of our method with several methods proposed in the literature. We can conclude that the Euclidean fitting guarantees a better accuracy with acceptable computational cost.
P. Faber, R. B. Fisher "Euclidean Fitting Revisited", Proc. 4th Int. Workshop on Visual Form, 28-30 May 2001, Capri, Italy.