DIGITAL REPRESENTATIONS AND ANALYSIS OF DEFORMATIONS INDUCED IN MAP SUPPORTING MATERIALS

F. Guerra¹, A. Adami², E. Livieratos³, L. Fregonese⁴

1 - CIRCE – Universitet IUAV di Venezia

2 - CIRCE – Università IUAV di Venezia

3 - Aristotle University of Thessaloniki, Greece

4 - DIIAR – Politecnico di Milano

guerra2@iuav.it

The antique maps often suffer significant deformations of their supporting material of any type. These deformations make poor the accurate reading of maps in its geometric and semantic context. As precious goods of cultural heritage, antique maps, in very many cases (rolled parchments, maps in old books and atlases etc.) are improper to put into a scanning process requiring a plane positioning of the map supporting surface, which is usually undulated. Digital photography is then an alternative if certain technicalities are fulfilled.

In order to capture the undulated map surfaces due to the curvilinear deformation of their supporting material, the use of three dimensional (3D) laser scanning was proposed. With this new digital technology the capturing of 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 memorisation and the transmission is concerned.

A major problem in this approach is the establishment of 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 homogeneity 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 rigorous model of high precision enjoying at the same time high image fidelity. All types of deformation analysis are then possible, applying the strain tensor approach in order to depict, via invariants, the deviations of the map supporting material form best fitted regular surfaces. Given that the map supporting material has physical properties, a stress-strain analysis is then suitable.

In this paper the flow of the proposed approach is analyzed and commented accompanied by actual tests performed on material data kindly offered by the Correr Museum and the National Marciana Library of Venice.