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FITTING, PORTAYAL AND MAPPING 
FOR THE PRODUCTION OF 2" ORDER SURFACES PHOTOMOSAICS 
Artemis Valanis 
School of Rural and Surveying Engineering — Laboratory of Photogrammetry 
National Technical University of Athens, Greece 
9, Heroon Polytechniou Str., Zographos, GR-157 80 
e-mail: rs97053@central.ntua.gr 
KEY WORDS: Photogrammetry, Architecture, Map Projections, Surface Reconstruction, Mosaicing 
ABSTRACT 
The Daphni Monastery is known worldwide for its famous Byzantine mosaics. After the earthquake of 1999, the monastery suffered 
serious damage and the Greek Ministry of Culture took action for the conservation of the monument. Within the frame of the 
requested tasks, the laboratory of photogrammetry was assigned the task of creating very large-scale (1:5) cartographic developments 
of the Domes. 
Although hitherto encountered in literature, the creation of cartographic developments is not a standardized and automated process. 
In addition, the demanded large-scale products called for the development of a very innovative and rather complicated approach. 
In this paper a complete approach is described in order to create cartographic developments of 2"-order surfaces. The proposed 
process was successfully applied in this case. 
INTRODUCTION 
The Daphni Monastery is considered to be one of the most 
important specimens of Byzantine art and architecture and it is 
known worldwide for its famous Byzantine mosaics. The 
monastery was built in the 11” century and is situated in the 
southeastern part of Attica near Athens. After the earthquake of 
1999, the monastery suffered serious damage and the Greek 
Ministry of Culture took action for the conservation of the 
monument. For that reason the Laboratory of Photogrammetry 
of NTUA was assigned with the thorough survey and recording 
of the monument. In particular, the project involved the creation 
of a variety of products such as: horizontal plans at five 
different levels (1:25, 1:50), 26 elevations (1:25, 1:50) — 6 
exterior and 20 interior- both in photomosaics and line 
drawings, upper views (1:25, 1:50) both in photomosaics and 
line drawings, photomosaics (1:5) of all Mosaics on planar or 
developable surfaces photomosaics (1:5) of all Mosaics on non- 
developable surfaces and a data base (GIS) with detailed 
architectural information. 
The problem of producing photomosaics of the various details 
on developable surfaces (i.e. cylinders, cones etc) has been dealt 
with elsewhere (Georgopoulos et al., 2001). 
This paper mainly deals with the creation of large-scale 
developments of 2™-order surfaces. Although there has been 
significant research on this area, it mainly involved grayscale 
Images or single image applications. The demand for large-scale 
products led to the proposed approach, which is able to 
Incorporate a significant number of images. 
The application involves: 
® data collection for interior work 
e the fitting of a mathematically defined surface (in this 
case a sphere) to a 3D point cloud 
e the procedure followed for the definition of a system 
suitable for the projection processes 
e the creation of an intermediary model for the one-to- 
one correspondence between the points of the surface 
of the object and the points of the model surface 
e the procedure for the production of the cartographic 
developments 
The process followed for the fitting of a mathematically defined 
surface was based on the relevant articles presented by Faber, 
(2000) and Theodoropoulou, (2000). 
With respect to the creation of cartographic development, the 
application was based on the relevant articles presented by 
Theodoropoulou, (1999) and Miniutti, (2000). 
However, the core of the process lies within the intermediary 
model, which is created with utilization of the DEM. This 
model is used during the projection process in order for the 
mosaicing of the numerous images of the object to be possible. 
Another very significant aspect of the process is the procedure 
followed for the selection of a reference system suitable for the 
projection. 
It should be noted that the whole process was designed and 
implemented in the MATLAB environment and it utilizes data 
that are always collected within the frame of such applications 
i.e. geodetically collected control point coordinates, digital 
images and the respective orientations, DEM data etc. 
DATA COLLECTION 
Considering the demand in large detail, and the high quality of 
the final products, the data collection methods were properly 
adjusted. All photographs were taken with a Hasselblad camera 
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