In: Paparoditis N., Pieirot-Deseilligny M.. Mallet C. Tournaire O. (Eds), LAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
r(Jt) = 
cos(« ) 
»■(tgPu+tgPu) 
[pixel / m] 
(4) 
a. e - 
Depending on this both angles the change of resolution between 
the far and close range of the image can be calculated as factor 
77 expressed by equation (5). 
r„(y)~r f (y) 
r f (y) 
(5) 
where: 
r„ - ground resolution at near range 
rj — ground resolution at far range 
Different values of p for different cameras and different viewing 
angle are presented in table 1. 
Camera: 
ФП 
0=25 0 
0=35 0 
0=45° 
0=55 ° 
7 
7 
0 
7 
PCE-TC 2 
20 
0.18 
0.28 
0.43 
0.67 
Flir A3 25 
25 
0.23 
0.37 
0.57 
0.93 
PCE-TC 2 
32 
0.31 
0.50 
0.80 
1.39 
Table 1. Changes of the resolution between near and far range 
of an orthogonally oriented surface depending on inclination 
angle and camera type (angular aperture) 
For description of planes which are seen under angle # 90° the 
equations (3) and (4) can be extended as follows: 
cos(^ + a v )-cos(^) 
r(y) = 
r(x) = 
H(tgP u + tg/3 2y ) 
cos(a x ) ■ cos(y x ) 
H-(lg/}„+tg0 u ) 
(6) 
where: 
Yv, Yv ~ angles between normal of the plane and the viewing 
direction of the camera on the respectively xc-plane and yz- 
plane in camera coordinate system 
Using equations (5) and (6) the changes of resolution of a 
differential surface which is seen in far range from angle y f —> 
90° can be calculated. Then in the near range y„-yf-(p. 
Camera: 
ФП 
0=25 0 
0=35 ° 
и 
СЛ 
0 
0=55 ° 
0 
7 
7 
7 
PCE-TC 2 
20 
4.72 
5.22 
5.93 
7.11 
Flir A325 
25 
6.06 
6.85 
8.01 
10.05 
PCE-TC 2 
32 
8.04 
9.37 
11.46 
15.48 
Table 2. Changes of the resolution between near and far range 
of a surface seen from angle y close to 90° 
Comparing Tables 1 and 2 can be assessed that for surfaces seen 
from an angle close to 90° the change of the distance is not 
significant, while for surfaces seen from an extremely 
unfavourable angle the difference between far and near range is 
meaningful. 
Due to rasterisation each texture is an image which has an 
equal-distance sampling. The gray values of the texture need to 
be calculated from the original IR image. For preserving the 
original resolution the grid for the texture has to be designed 
with maximal resolution which can occur. 
For definition of the best possible resolution two strategies can 
be considered: 
• Every plane in the model gets the same ground resolution. 
The advantage of this strategy is that already at the 
beginning of the texturing process all texture matrixes can 
be predefined and the memory necessary to store the 
textures can be planed. A homogeneous ground resolution 
of the textures is also advantageous during image analysis, 
such as feature extraction, because the scale of the detected 
features is the same for all textures. On the other hand, in 
this method many textures synthetically get much higher 
resolution then it was in the original image. Consequently, 
more memory is consumed as necessary. 
• The best possible resolution is determined separately for 
every plane. Specifically, for every plane in every image the 
point with the best resolution is found and the resolution of 
this point is applied for the texture creation. 
The best possible resolution can be calculated assuming that it 
occurs at orthogonally oriented differential surface placed in 
one of the points of the 3D model. Based on ExtOri parameters 
for first frame of the sequence and the resolution in all visible 
points can be calculated with the equation (3). The best 
resolution is stored. Then the same procedure can be applied for 
other frames. If a higher resolution was found, the value is 
overwritten. 
3.3 Texture quality 
For optimal texture selection a quality measure g, of every 
texture should be calculated as follows: 
я, • О - о- ) + a 2 -d ij +a 3 - cos y xij • cos y 
Чц = 
a { +a 2 + a 3 
a i +a 2 + a 3 Ф 0 
(7) 
where: 
y x , y, - angles between normal of a model polygon and viewing 
angle of the camera, 
aj, a 2 , a 3 - coefficients, 
o, - occlusion factor, 
d ( - distance factor - calculated by equation (8). 
D -D. 
d max ij 
Z) mH - D- 
max min 
(8) 
where: 
D ma x ~ maximal possible distance from the projection centre to 
model points, 
D min - minimal possible distance from the projection centre to 
model points, 
Dj- distance from the projection centre to the centre of a model 
polygon. 
In general textures with high occlusion shouldn’t be considered 
in texturing process. In case of small occlusion, the occluded 
part can be replaced by parts of textures with lower resolution. 
The balance between occlusion factor and other factors can be 
set using coefficients a,, a 2 and a 3 . In case of object 
recognition, for instance windows, from textures a higher 
resolution is preferred. Thus the coefficient a/ should be smaller