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Mathematical Problems in Engineering
Volume 2015, Article ID 606948, 14 pages
Research Article

A Quadratic Model with Nonpolynomial Terms for Remote Colorimetric Calibration of 3D Laser Scanner Data Based on Piecewise Cubic Hermite Polynomials

1Department of Electronic Engineering, “Tor Vergata” University of Rome, Via del Politecnico 1, 00133 Rome, Italy
2ENEA, National Agency for New Technologies, Energy and Sustainable Economic Development, Via E. Fermi 45, Frascati, 00044 Rome, Italy

Received 2 June 2015; Revised 21 July 2015; Accepted 27 July 2015

Academic Editor: Erik Cuevas

Copyright © 2015 Alessandro Danielis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The processing of intensity data from terrestrial laser scanners has attracted considerable attention in recent years. Accurate calibrated intensity could give added value for laser scanning campaigns, for example, in producing faithful 3D colour models of real targets and classifying easier and more reliable automatic tools. In cultural heritage area, the purely geometric information provided by the vast majority of currently available scanners is not enough for most applications, where indeed accurate colorimetric data is needed. This paper presents a remote calibration method for self-registered RGB colour data provided by a 3D tristimulus laser scanner prototype. Such distinguishing colour information opens new scenarios and problems for remote colorimetry. Using piecewise cubic Hermite polynomials, a quadratic model with nonpolynomial terms for reducing inaccuracies occurring in remote colour measurement is implemented. Colorimetric data recorded by the prototype on certified diffusive targets is processed for generating a remote Lambertian model used for assessing the accuracy of the proposed algorithm. Results concerning laser scanner digitizations of artworks are reported to confirm the effectiveness of the method.