The International Archives of the Photogrammetry. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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Where d is the day and the fraction of the year’s day. 
(Kq, P©) are the ecliptic coordinates of the sun. 
£ is the obliquity of the ecliptic. 
These are transformed to the horizontal coordinate system 
(A,h) through the Time Equation and easy spherical 
trigonometry formulation. 
This way, in the same orthorectification process, it is 
possible to identify those pixels that stay under the 
influence of a shadow, which can be contrasted with the 
digital level assigned to that pixel. 
• In second place, the local enhancement of digital levels 
from the image in those zones, using all the radiometric 
advantages from digital photogrammetric cameras that do 
the capture in 12bits. 
This opens the possibility to increase the possible window of 
flight for this kind of tasks, which is nowadays very limited to 
the time of the year (and central hours of the day) when the 
solar inclination is appropriate. 
4. PROPOSAL METHODS FOR TRUE ORTHOPHOTO 
The method adopted in the DATOS project, consists in an 
analysis of the radial angular visibility from the terrain point, in 
the nadiral direction of each image in which this point appears 
(Figure 4). 
This development, named “Multi-Visibility Analysis of from 
the object” presents the advantages of angular methods that 
resolve problems from methods based on Z-Buffer algorithms 
of DSM's cell size and the availability of additional information 
from buildings, and simplifies the true ortho production 
process, eliminating the need to do mosaiking afterwards and 
the analysis of occluded areas within images, as both stages are 
included within the algorithm. 
Figure 3. Example of the use of various photographs depending 
on the best incidence angle, (solution Most Right). 
3.3 Right True Orthophoto Module: RTO+. 
RTO+ is a true orthorectification module that uses an algorithm 
of intersection of the perspective ray with the DSM to search 
imagery with occluded areas due to leaning objects. In this 
module, an own algorithm was developed to generate true 
orthophotos using a combined analysis of the optimal incidence 
angle and the intersections of the ray with defined obstacles 
within the digital surface model in the nadiral direction. The 
analysis of visibility is done for each pixel of the orthophoto 
and for all the photographs in which it will be represented, in 
increasing order of distance to the corresponding nadiral points, 
starting by the solution MOST RIGHT. In this way the 
orthorectification and mosaiking is resolved in one step, just 
like in the latter module. A height profile is considered from the 
digital surface model with its origin in the corresponding terrain 
point, and the longitude that is determined by the maximum 
possible leaning (Figure 5). 
3.4 Light RTO+ Module: LRTO+. 
It is a module developed to determine shadow areas within the 
orthoimage and to enhance them, using the DSM and the 
information of the true position of the sun. This last module 
pretends to deal with one of the principal problems of working 
with orthophotos in urban areas, the presence of shadows that 
make difficult to interpret final imagery and that arise important 
problems of radiometry adjustment of orthorectify imagery. 
Therefore, within this line it was introduced an algorithm of 
shadow attenuation, based on the precise calculation of the 
position of the sun for each photograph, from the exposure data 
from GPS systems, and the digital surface model, combined 
with the radiometry analysis of digital imagery (intersecting the 
geometrical model of shadows and the empirical model of 
shadows represented in the image). 
The process was planned in two stages: Detection and 
Enhancement (lighting). • 
• In the first place the determination of shadows, based on 
the same Profiles Method for detection of occluded areas 
in the sun direction. The position of the sun is estimated in 
ecliptic coordinates through this formula (data obtained 
from the Yearbook of the Observatorio Astronómico de 
Madrid of 2005 (IGN España): 
/¡o s 219°:77 + 0°.98563x d +1°.915 x sen(0 o .986x d - 3°.2) + 0°.02x sen(2°xd -12°) 
Pe =0° 
£ = 23°.438641 -0°.00000036 xd 
Figure 4,- Multi-Visibility Analysis from the object Method 
The main characteristics of the Multi-Visibility Analysis from 
the object Method used in True Ortho to detect shadows and 
occlusions are: 
• It is a radial method that analyses the visibility of each 
terrain point in the principal nadiral direction, 
considering it as the one that defines the closest Nadiral 
point, and secondly, in increasing order of nadiral 
distances of photographs where the point can be 
represented. 
• It is an angular method that compares visibility angles 
of each point from the DSM from the terrain point with 
respect to the visibility angle of the Perspective Centre. 
The identification of occlusions method is named 
“Nadiral Profiles Method” (Figure 5).