the collinearity 
istinct points of 
lems should not 
olved if, instead 
t belongs on the 
creation of an 
JEM data. This 
ndence between 
tirely based on 
positions of the 
tem in spherical 
defined by the 
latitude. This 
mediary model, 
' the values in 
ition of the size 
pond to integer 
pond to integer 
id trimming the 
eased. Each cell 
n the surface of 
ection indicated 
of the matrix is 
of the cell (row, 
1d longitude are 
sed to detect all 
| degrees wide. 
" mean distance 
ralue fills the 
| are detected in 
he radius of the 
ace 1s obtained. 
it gave a very 
F 
ye 
REATION 
mages. Given a 
f an area of the 
d image on the 
ition (x, y) the 
je cartographic 
itude values are 
lel, the distance 
of the model is 
lation on the 
| coordinates of 
n the reference 
s. Finally, the 
tem, and using 
yosition on the 
rameters of the 
image is found 
ween a position 
> corresponding 
(4) 
m=f-fix(minF)+1 
p=l-fix(minL)+1 
where m,n- the size ofthe matrix of the 
intermediary model (rows, columns) 
1, f = the parameters of latitude and longitude for a 
given point 
minL, minF = the minimum values of latitude and 
longitude respectively 
After all of the developed images are created, the coordinates of 
the control points on the projection plane are also calculated. 
The outcome is an ASCII file, which is first converted to DXF 
format and then to an image, which is used for the process of 
mosaicing. In Figure (5), an example is presented. The mosaic 
illustrated consists of nine images that were created in the way 
described. 
  
  
  
  
Figure 5. Cartographic development mosaic consisting of 
nine images. 
Another issue is the research that must be done prior to the 
implementation. This process involves the selection of the most 
appropriate projection type and the way in which it shall be 
implemented so as to ensure that the product will be useful, 
reliable and suitable for the application it is designed for. In 
order for this to be possible, some kind of optimization has to 
take place so that the final products have the desired attributes 
and, most importantly, the least possible distortions. Another 
reason that makes this process obligatory is that the method is 
very time-consuming for projects that involve a large number of 
models. For example, in this case the mosaics produced would 
be used for preservation purposes. Taking this fact into account, 
it was chosen to work mainly with conformal projections. In 
Particular, the Mercator Conformal Projection was implemented 
for the four pediments that adorn the nave of the Daphni 
Monastery. In each case, the implementation of the projection 
was different depending on the position of the main theme on 
the object surface. Additionally, a mosaic was created for the 
dome of the church, but this time using the Stereographic 
  
projection and taking into account the position and the area of 
the dome that was covered by the mosaic. 
DISCUSSION 
The proposed method had very satisfactory results even for 
surfaces that could not be very well defined. It is obvious that 
on cartographic developments no measurements can be made 
and thus the accuracy of such a product is of no importance. 
However, in cases where numerous models are to be 
incorporated, all the parts of the development should be 
accurately constructed in order to be coincident in overlapping 
areas and thus proper for mosaicing. 
By implementing the proposed method, the results were 
satisfactory even for mosaics that consisted of a very large 
number of images (the largest mosaic consisted of 42 images). 
Nevertheless, the method has some disadvantages. As 
mentioned at the beginning, the application was designed and 
implemented in the MATLAB environment. Apart from the 
advantages and the numerous possibilities that MATLAB 
offers, some very significant problems were encountered. The 
most important problem is due to the relatively small speed that 
can be achieved for the creation of very large images e.g. an 
image of approximately 40MB, can take about a quarter of an 
hour. Another problem is that there is some kind of restrain on 
the size of the images that can be produced e.g. it was 
impossible to create an image of the size of 80 MB. As proved 
through experimentation, these magnitudes and the respective 
limitations depend on the platform and the resources of the 
system used. 
At this stage the method is rather time-consuming and could not 
be characterized productive. It is clear that the creation of an 
application that would be independent from MATLAB would 
be much faster and would not have such restrictions. 
REFERENCES 
Bugayevskiy, L.M. & Snyder, J.P. Map Projections. A 
Reference Manual , Taylor & Francis, London, 1995 
Georgopoulos, A., Ioannidis, C., Makris, G., Tournas, E., 
Tapinaki, E., Digitally Developing Works of Art, CIPA 
International Symposium, Potsdam, 2001 
Faber, P., /mage-Based Passenger Detection and Localization 
Inside Vehicles, International Archives of Photogrammetry and 
Remote Sensing, Vol. XXXIII, Part 5B. Amsterdam, 2000 
Miniutti D, The Cartographic Projections For The 
Representation of Double Curved Surfaces. International 
Archives of Photogrammetry and Remote Sensing. Vol. 
XXXIII, Part B5. Amsterdam 2000, p. 51-56 
Theodoropoulou, I, Single Image Photogrammetry with 
Analytical | Surfaces. CIPA TG/2 (http://www.fpk.tu- 
berlin.de/~iliana/cipa.htm), 1999 
  
Theodoropoulou, I., The Definition of Reference Surfaces For 
Architectural Photogrammetry, International Archives of 
Photogrammetry and Remote Sensing, Vol. XXXIII, Part5B. 
Amsterdam, 2000 
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