International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
  
DEKAN EN ATZE Ze AZ OÖ) 
where D = distance from exposure station to pseudo-GCP 
X, Y, Z = pseudo-GCP object coordinates 
Xo, Yo, Zy = perspective center 
AX, AY, AZ = differences between the laser scanner irradiation 
point and perspective center 
The trifocal tensor is a geometric relation of three images 
containing the same objects from different perspectives (Hartley, 
1993). The trifocal tensor is expressed by three square matrixes 
(3x3), which are T,, T,, and T,, the components of these 
matrixes are t;, t;, and ft, and the image coordinates of 
matched points for these three images are (xi, yi, Z1), (X2, V2, 22), 
and (x, ys, z3). Thus, the following equations are obtained by 
the geometric relation. 
—-ZjZ,83 *tZ1y38m + Va75En — Yiy8s 70 
ZiZ8g 7 Z3338 s 7 V2738n + V1 X85 =0 
ZZ,gy 72,y48p 7 X2738n + X%, 7385, =0 
—ZZgutz1X85 *X,2,84 7 XaX3En =0 
(4) 
where Ey = Xılu + Yılzy + Zit 
It is understood that image coordinate (x,, y?) is the spatial 
intersection of two epipolar lines on the second image (centre 
image) and is calculated by Equation (5), derived from Equation 
(4). Therefore, the geometric constraint condition uses Equation 
(5). 
zs +8, )- g(r; ty) 
z(gas*22)- £s * v.) G) 
- £n * £5)* 25(5, ty) 
EAT +81 )+ 83 (x; *yi) 
  
= 
I 
N 
3 
Camera calibration is performed by calculating these unknown 
parameters, which can be calculated as values by minimizing 
the following function, H (Equation (6)), under the least squares 
method. 
ab 
H = + p,(Axc? + Ayc}) — min 
7 p (ANT HAUT AZE) 
(6) 
n 
iz 
where Ax, 
AD; = residuals for distance 
Axe, Ayc = residuals for the centre image of the geometric 
constraint condition 
AX;, AY;, AZ; = residuals for pseudo-GCP object coordinates 
m = number of pseudo-GCPs 
n = number of images 
P 1, P 2» P 3, P4 = weight for each condition 
Ay; = residuals for image coordinates 
3. OBJECT EXTRACTION PROCEDURES 
Object extraction was performed in the ALS data phase and 
image phase. Detail procedures are as follows. 
3.1 Visualization of normal vectors 
There have been many approaches to building extractions from 
ALS data since the late 1990s, such as using height data and 
normalized DSMs, subtracting DTM from DSM, region 
growing, slope maps, and normal vectors. In particular, normal 
vectors are used for terrain or road surface information, rooftops, 
trees, and so on. Normal vectors are calculated from a TIN 
54 
generated from random point clouds. A normal vector is 
managed by the grid for efficiency. Gridding is normalized 
using a whole value by combining the normal vectors in the grid 
range. A normal vector map was produced in the X, Y, Z 
direction assigned to the R, G, B channels. The normal vector 
map is shown in Figure 3. It seems that normal vector maps 
indicate the shapes of houses as well as the slope of the roof by 
color gradation. The X, Y, and Z directions indicate each 
characteristic, e.g., the X and Y directions show North and East 
lighting on the map (Figure 4) and the Z direction shows object 
shapes (Figure 5). 
  
Figure 3. Normal vector map 
  
23 
Figure 4. The X direction of the normal vector map 
  
ge — 
  
Figure 5. The Z direction of the normal vector map 
3.2 
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