Use of robust methods to determine quadratic surfaces: application to heritage

3D surveys of archaeological elements and the construction of virtual models enable us to reconstruct historical sites. They provide useful data to select specific building processes. Photogrammetry and Terrestrial Laser Scanning (TLS) are the most common techniques to obtain synthetically heritage models. These techniques provide massive data which can only be managed by replacing them by primitive shapes, thereby obtaining more simple models and the explicit geometry of the element. Statistical and robust methods are used for this substitution, thereby avoiding the common errors due to measuring. Of these methods, the most widely used are the least-median-of-squares (LMedS) and the RANSAC method. Another computation method consists in recursive processes based on evolutive-type algorithms to adjust the model to the data captured. This paper describes two surface computation methodologies to determine the modelling of a column shaft located in temple G of the archaeological park of Selinunte (Sicily). ► Geometric model determination from point clouds obtained by laser scanning. ► Application of Robust method to make easier the analytic computation of the surfaces. ► Application of recursive processes to order the different elements of a model. ► Generation of theoretical 3D models to analyse the constructive processes.