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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