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To visualize the surface of an object, laser scanners determine the rectangular coordinates of points of a grid on the surface of the object in a local coordinate system. Vertical angles, horizontal angles and distances of a polar coordinate system are measured with the scanning. Outliers generally occur as gross errors in the distances. It is therefore investigated here whether rectangular or polar coordinates are better suited for the detection of outliers. The parameters of a surface represented by a polynomial are estimated in the nonlinear Gauss Helmert (GH) model and in a linear model. Rectangular and polar coordinates are used, and it is shown that the results for both coordinate systems are identical. It turns out that the linear model is sufficient to estimate the parameters of the polynomial surface. Outliers are therefore identified in the linear model by the expectation maximization (EM) algorithm for the variance-inflation model and are confirmed by the EM algorithm for the mean-shift model. Again, rectangular and polar coordinates are used. The same outliers are identified in both coordinate systems.

Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems