ul 2004 
> points 
, which 
nt 
e of the 
ent by 
x. Their 
'ojected 
is now 
column 
sformed 
eyed on 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 
The orthorectification process has two phases : 
- the first consists in drawing, on the original shot, the edges 
of the column's shaft (generatrix), and in obtaining their 
equivalent on the development, so as to finally have the 
limits of the orthophotograph to be produced 
- the second carries out the transfer of the grey values of the 
pixels from the original photograph to the development 
A new picture will thus be created by assembling these pixels 
inside the previously drawn limits. 
The limits of the eight orthophotographs have been obtained by 
means of a « re-wrapping » procedure that transfers points from 
the development to the original shots. 
The steps are as such : 
- on the development, creation of a point and the cone's 
generatrix going through this point 
- positioning of this point and its generatrix on the vertical 
cone (change of reference based on the development's 
polylines and the cone's) 
- transfer of the point and the two end's points of the 
generatrix from the 3D model to the photograph, by means 
of a Direct Linear Transformation (DLT) 
The DLT is applied « from 3D to photo », that is to say the 
calculation of the photo-coordinates of the points from their 
object-coordinates on the vertical cone. The DLT is a non- 
iterative method consisting in the linearization of the equations 
of the central projection. It is based on 11 coefficients — named 
L1 to L11 — calculated (for each shot) from the control points 
that are known in both coordinates’ systems (photo and object). 
In a matrix form, the computation of the photo-coordinates (e, 
n) from the object-coordinates (X, Y, Z) can be written as 
following (Karara, 1989) : 
LiL5019 | Li*X-L2*Y v13*Z«1A 
[XY Zi] * Z2 160L10 7 L5* X« L6* Y «L7* Z« L8 (6) 
23170711 LO*Y +L10*Y +L11*Z +1 
The two first lines are thus divided by the last one, in order to 
obtain the photo-coordinates (e, n) : 
— L1*X+L2*Y+L3*Z+LA 
L9*X+L10*Y+L11#Z+1 
nek X{LO*Y +LI* 2 +1R 
y LO*X -LIO* Y -LII*Z 1 
The « re-wrapping » procedure is programmed as to see "live", 
simultaneously with the cursor movements, the motion of the 
chosen point and of its generatrix, at the same time on the 
development, on the vertical 3D cone and on the photograph. 
So, the limits of the orthophotograph to be produced have been 
drawn, by moving the cursor on the development surface while 
controlling the position on the original shot. 
(Figure 6) 
Vol XXXV, Part B5. Istanbul 2004 
  
Figure 6. Layout of the limits of the orthophotographs 
to be produced in the development 
The orthorectified photographs are generated in the same way, 
by applying the « re-wrapping » procedure to all the pixels' 
positions of the picture to be created in the previous limits. 
The pixels corresponding to these positions have been taken 
from the original photos and their colour values have been 
transferred to the development. The orthophotograph is the 
result of the assembling of the pixels thus defined. (Figure 7) 
  
1 
| 
co 
Figure 7. Front view of the development with one 
orthorectified photograph (the projected object points enable to 
verify the position of the orthophotograph in the development) 
—À X 
3.3 Montage of the orthophotographs and drawing of the 
epigraphy 
After orthorectifying all the shots, a single photomontage is 
made, on which the hieroglyphic inscriptions are drawn. 
The montage of the orthophotographs is not easy to realize, 
because the exact positions of the different pictures must be 
strictly respected, and their scales likewise. Moreover, there are 
differences in light exposure from one original shot to the other 
(see Figure 3), which requires image processing to obtain a 
homogeneous picture of the entire surface of the column's shaft. 
This problem can be avoided by taking the photographs in good 
light exposure conditions. 
Despite all this, once the photomontage is done, we obtain a « 
photograph » of the developed surface of the column's shaft. 
This picture represents a plane surface, on which the 
hieroglyphs can be drawn. (Figure. 8)