Use of robust methods to determine quadratic surfaces: application to heritage M a Amparo Núñez a, * , Felipe Buill a,1 , Joaquin Regot b, 2 , Andrés de Mesa b, 2 a Department of Geotechnical Engineering and Geo-Sciences (ETCG), Universitat Politècnica de Catalunya, Dr. Marañon 44-50, 08028 Barcelona, Spain b Department of Graphic representation, Universitat Politècnica de Catalunya, Av. Diagonal, 08028 Barcelona, Spain article info Article history: Received 26 June 2012 Received in revised form 3 September 2012 Accepted 20 September 2012 Keywords: Archaeological heritage Virtual reconstruction 3D modelling Massive capture of data Robust methods abstract 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). Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The preservation of our architectural heritage is the responsi- bility of every citizen. Architectural heritage is often found in a deteriorated state as a result of natural disasters and inclement weather. The possibility of losing this heritage calls for: an exhaustive cataloguing of its elements, the creation of a detailed model of these elements (Robson et al., 2001; Blake et al., 2007), and the adoption of the necessary measures to avoid its complete destruction. A project should be devised whenever a restoration is necessary. Adequate data should therefore be provided to determine as accurately as possible the state of the works undertaken to ensure their success. Data capture should follow a study and plan of field work in order to save time on the capture and ensure sufficient data. In this way, the necessary information will be available in order to carry out an optimum reconstruction of the archaeological heritage. The methods that allow spatial data capture can be applied to many fields, from manual measuring methods using tapes, clinometers, etc. to digital mass data collection technologies using topographic techniques, photogrammetry and laser scanning (Arias et al., 2006)(Chen et al., 2000). The last technique enables us to save time and effort in field work since it gathers a large amount of data in relatively little time. Automation techniques are essential to better process and use the data to obtain models. This paper outlines a procedure and working methodology used to obtain the 3D reproduction of a column from laser scanning data. Thus a parametric model is constructed to make explicit the geometry of the object under survey. This process involves adjusting methods that detect the erroneous points obtained during data capture. Of these, the most common are the least- squares, the least-median-of-squares of the residues and the RANSAC (RANdom SAmple Consensus) method. 2. Methodology suggested Nowadays the elaboration of specific shapes from a 3D data collection using digital techniques is commonly used in cultural heritage cataloguing. In most cases, the technology and resources employed when collecting data from real objects entails not only greater accuracy but also the possibility of defining the virtual 3D models of these objects. * Corresponding author. Tel.: þ34 93 4054019. E-mail addresses: m.amparo.nunez@upc.edu (M.A. Núñez), felipe.buil@upc.edu (F. Buill), joaquim.regot@upc.edu (J. Regot), andres.de.mesa@upc.edu (A. de Mesa). 1 Tel. þ34 93 4054019. 2 Tel. þ34 93 4016382. Contents lists available at SciVerse ScienceDirect Journal of Archaeological Science journal homepage: http://www.elsevier.com/locate/jas 0305-4403/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jas.2012.09.027 Journal of Archaeological Science 40 (2013) 1289e1294