A comparison of machine learning, spherical harmonic functions, and geometric error model in improving the accuracy of terrestrial laser scanners

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Abstract
Terrestrial laser scanners (TLSs) are portable dimensional measurement instruments that produce a three-dimensional point cloud by measuring the range, the horizontal angle, and the vertical angle of points in a scene. To ensure they perform according to specifications, manufacturers might require periodic onsite compensation to update parameters of an internal geometric error model. This model, however, is generally not available to the user and is therefore not applicable if the user wishes to correct the data offline. In this paper, we discuss two alternative approaches to improving the accuracy of TLSs, both of which involve black-box error models, i.e., they do not rely on an understanding of the geometric and optical errors of a TLS. The first approach uses artificial neural networks (ANNs) and the second uses spherical harmonic functions (SHFs) to model point coordinate errors. We compare the performance of these approaches against our geometric error model through an experiment involving a TLS as the instrument under test and a laser tracker as the reference instrument. We calculated 15 parameters on the raw data (before fitting any model) and on the data after fitting the geometric error model, the ANN-based, and SHF-based models, to assess their performance. We observed a reduction in mean distance errors of at least 80% (from 0.08 mm to 0.016 mm) and mean two-face errors of about 60% (from 0.15 mm to 0.06 mm) after application of the geometric error model on both the training and testing data sets. ANNs generally performed better on the training data set by about 5%–10% when compared to the geometric error model but performed somewhat poorly on the testing data set by about 5%. All SHFs considered in this paper performed better than the geometric error model on the training data set by about 5%–20%. Low order SHFs performed better than the geometric error model on the testing data by about 5%.

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