Digital Representations and Analysis of Deformations Induced in Map Supporting Materials

Historical maps often suffer significant deformations of their supporting material of any type. These deformations make it difficult to make an accurate reading of maps in its geometric and semantic context. As invaluable materials of cultural heritage, historical maps, in very many cases (rolled parchments, maps in old books and atlases etc.) cannot be put through a scanning process requiring a plane positioning of the map supporting surface, which is usually undulated. Digital photography is then an alternative if certain technical details are fulfilled. In order to capture the undulated map surfaces due to the curvilinear deformation of their supporting material, the research group proposed use of three dimensional (3D) laser scanning. With this new digital technology, capturing such map surfaces gives a cloud of points with an uncertainty of about 0.1 mm, which forms the initial 3D model of the surface. From the point cloud we can pass to deformation analyses using processing based on proper types of finite element models. In some simpler cases it is enough to define a parametric interpolated surface which is easier to manipulate as far as the memorization and the transmission is concerned. One problem in this approach is setting up an external reference system for the 3D scanning and the associated photogrammetric survey of the map surface, giving the necessary imagery to the point cloud. Since it is not possible to attach control points on the map surface, the referencing is assured by non contact control mechanisms. The next step is the digital photogrammetric survey using high-resolution calibrated cameras. The external control is common with the reference system of the laser scanning in a way to preserve the uniformity of both the geometric and the radiometric data. For the latter, special samples of colour standards are taken during the capturing session. The procedure described here gives a metrically accurate model of high precision with the same time high image fidelity. All types of deformation analyses are then possible, applying the strain tensor approach in order to depict, via invariants, the deviations of the map supporting material from well fitted regular surfaces. Given that the map supporting material has physical properties, a stressstrain analysis is then suitable.