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e 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. 
6 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; 
e geometrical transformation based on local parameters. 
The main characteristics of plane global transformation can be summarized in the next few steps: 
e the source image is transformed on the base of parameters calculated before the transformation (resampling); 
* parameters are valid for each point of the image; 
e 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: 
n 
X= Y Na x y! 
i-0 j-0 
3 
Y= > Nix y 
i-0 j=0 
The procedure which utilizes this polynomial is known by the name of rubber-sheeting. In the case in which only linear 
terms are taken into consideration, we are brought back to the linear transformations commonly used in the survey 
discipline (affine, conformal, projective). 
The equations are exactly satisfied if the number of points known n = % p, and the number of the parameters are taken 
into consideration. It would seem evident therefore that if there are a great number of known points to use and if an 
exact solution is needed then elevated grade polynomials must be used. In this last case, non linear transformation 
(2second order) are applied. 
In general a larger than needed number of points is used and the value of the parameters is estimated to the least 
squares; in this way it is possible to evaluate the results of the transformation. 
The local transformations are those in which the parameters of transformation are calculated for each single point of the 
image and have a local validity. The scope is to distort only a part of the image while leaving the rest of the image 
unaltered. 
To this second kind belong finite elements transformations and that ones based on points or features (usually known as 
point based warping and feature based warping). 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 31