Guerra, Francesco 
  
The fact remains that, in general, the assignation of a correct metric support is highly important for the use of this 
cartography, not only as an archive document, having a qualitative nature but rather as real cartography from where 
quantitative information can be taken. 
An idea that must guide in this direction is that of keeping in mind that these maps have been drawn up as maps, that is, 
with an practical operational purpose, and were used for this. Perhaps the concept of metrics has changed, or more 
simply, the threshold for acceptable levels of uncertainty has changed over time. 
3. TRANSFORMATION-CORRESPONDENCE 
Can the geometric transformation of a map be avoided and can other alternative ways for its quantitative reading be 
found? 
To respond positively to this question, it is necessary to introduce a radical change in the way to use cartography which 
must change from a paper map to a digital map. 
The warping techniques can be used, not in order to transform the maps but in order to create correspondence, realising 
special software which manage and visualise these correspondences between the maps. 
The procedure of referencing-transformation, previously cited, remains valid but is combined with and in some cases 
replaced by the procedure of referencing-correspondence. 
The analytical and algorithmic part of the two procedures is the same: 
global transformations + local transformations (warping). 
The ways to apply the transformations changes as well as the support for the cartographic image which in the 
correspondence becomes numeric and no longer paper. 
It is possible to image that the relations between pixels in the source image and the destination image are resolved in a 
definitive way at the time of sampling in the final image for the transformation procedure, while in correspondence, it is 
resolved quickly and visualised in real time. 
The procedure of referencing-transformation, which has for an output a new image with geometric characteristics 
controlled and assigned through the use of features, is replaced by the procedure of referencing-correspondence, where 
the features are used for the on-flight calculation of homologous points. 
4 2WIN SOFTWARE 
What has just been described must be realised with special software that allows for the loading of digital maps and the 
identification of homologous points. 
The software implemented by the author for this purpose has the name 2WIN, inspired by the fact that the screen is 
organised into two windows. In these, on the left window, the reference cartography is visualised and on the right, the 
map to transform. The methods of functioning are quite commonplace: by identifying a point on one of the two maps, 
the program calculates the position on the other and highlights this by centring the two windows on homologous points. 
The centre of the two windows is always on two corresponding points. 
The method of calculation to use can be that of the WPP or WPF programs, developed by the author for his PhD thesis. 
This involves a software which implements the algorithms of local transformation, based on points or lines, borrowed 
from the morphing techniques of computer graphics and properly adapted to cartography. 
The definition of the features for this correspondence and their memorisation is done by two WPP and WDF software 
which therefore complement 2WIN. 2WIN is in fact a “visualiser” of numeric cartography which also implements the 
algorithm for the interactive identification of the homologous points. 
The fact that this program is interactive, meaning that it must respond in real time to the questions placed by the user, 
has made it necessary to optimise the code for a greater speed of execution. In the transformation programs such as 
WPP and WPF, the problem did not arise since the execution of the transformations occurs only once and therefore the 
problem of an extended wait is limited. 
Even though today enormously powerful calculators are used, the warping algorithms are so burdensome from a 
computer calculation standpoint that without optimisation, it was not possible to obtain acceptable response times. 
Therefore, it was decided to calculate the local transformations, not by using the complete set of the features, but only 
those closer to the point to calculate. The decision is justified from a numeric point of view if one thinks that the weight, 
in the definitions given, is always inversely proportionate to a power of the distance. Therefore a feature's influence 
diminishes in proportion to the farther away it is. 
The problem of the research into the nearby features has been resolved by implementing a “quadtree” structure for the 
memorisation of the features themselves. In this way, the research into the nearby features and the calculation of the 
homologous point have given acceptable response times. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 341