Analytical and Quantitative Methods for the Analysis of the Geometrical Content of Historical Cartography

The preliminary remark to the research described in the paper is the utilization of GIS for the management and the analysis of geographical-territorial data in their historic-temporal evolution, or rather to arrange historical information according to a key of spatial reading. In the development of a territory the historical cartography has had a deciding role. This means the necessity of getting data and informations from maps not only temporally arranged but even spatially referenced. The historical maps, however, for their metrical and semantic characteristics, are rather difficult to reference with the commonly used procedure. Often times in fact, they contain topographical and not metrical information and their insertion into a GIS is actually impossible. The aim of the research is to recover the metrical content in historical maps (particularly portolan charts, Isolari, perspective views of towns of XV-XVI century) using analyses which lead to a definition of a methodology for the quantitative analysis of historical cartography. This implies to use procedures that treat of: • global transformations: such as projective, affine, Helmert, polynomial transformation; • local transformation: such as finite element transformation, point based or feature based warping. Historic cartography has been, for long time, a subject of study by the historians and therefore, it has been considered as an archive document, a testimony of a certain period in the history of a territory, of a city. The study initiated and proposed in this paper faces, rather, the historic cartography according to an approach which is typical of the current cartography: extract territorial information which has been spatially referenced. The historic cartography, within the problems of using the GIS, is surely a field in which the questions relating to the referencing assume great interest. But how is it possible to geo-reference ancient charts? Often times they present some common characteristics such as: • an uncertain metrical content • a non definite system of reference • representational scale • unknown unit of measure • an approximate projected system, • non definite surface of reference • not recognizable projective system: • semantic content difficult to interpret. Such characteristics in the maps and charts from varying eras are found in greater or lesser measures, and consequently, it is necessary to make specific considerations when faced with each and every individual map. A map has different levels of accuracy, planimetrical, topographical, proportional, conventional, hierarchical, which are to be distinguished and to which the reader has to adapt according to the function that the map assumes: in a sea chart, distances, lands and bearings are characterized by a high accuracy. Harbors and mouths are positioned correctly and, often, magnified as regard the graphical scale of the chart. Instead, coasts are represented in a conventional way, such as the topography of the hinterland (such as mountains or representative architectures of a place). So there are two different categories: Balletti, Caterina International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 30 • maps and plans of cartographic interest: executed for technical and public purposes, they represent geographical outlines, respecting proportional relations between parts. In this case, the geographical configuration is in orthogonal projection, while topographical characteristics are seen in perspective or in a front view, according to a schematic conventional look. Wordings offer practical knowledge. • maps and plans executed for didactic purposes: their aim were not to give geographical informations, but to illustrate. The fact remains that, in general, the assigning of a correct metric support is very important for the use in cartography, not only as a document for the archives, that is, of a qualitative nature, but a true cartography from which to extract quantitative information. An idea that must guide and propel in this direction is that it is important to keep in mind that these charts have been created as charts, that is, with an operative and practical purpose, and that they were used as such. Perhaps the concept of metrics has changed, or more simply, the acceptable accuracy threshold has changed over the years. They are, however, representations of the territory and therefore are informational. How can a piece of information that is arranged on the territory but non metrical be transferred onto a metrical support (GIS)? The preliminary remark is to recover the metrical content in historical maps using analyses which lead to a definition of a methodology for the quantitative analysis of historical cartography. This means to use procedures of referring that treat of: • geometrical transformation based on global parameters which are calculated using a high number of control points; • geometrical transformation based on local parameters. The main characteristics of plane global transformation can be summarized in the next few steps: • the source image is transformed on the base of parameters calculated before the transformation (resampling); • parameters are valid for each point of the image; • a larger than needed number of points is used to estimate to the least squares the parameters; • an estimate of the results of transformation is given by usual statistic parameters. These transformations are used in the referenced procedure as a global transformation. In the same time they are used to evaluate the presence and the distribution of deformation in the residual analyses. In practice, it has to do with the traditional plane transformations that allow for the passage from system (o,x,y) to system (O,X,Y); the general equation which regulates such a passage is represented by a polynomial of the nth order like so: