The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
1386 
Ag(*,, y j, z k ) + v(x, ,y Jt z k ) = 
g* (*, > y j »+ X >gx ( x ,. T, »(*, » 7, > ** )ifa 2 
+ 2 k g x (x,, y j, z k )da, + g v (x,, >>,., z* )d& 0 + x,g v (x,., y } , z k )db, 
+ (*/, T;.)^2 + Z k S y (*■ . y j,)<®3 + (*J. J'y. Z * )^0 
+ (*,, y j. ** VG + ^g z (x,, ^, z* )</c 2 + z* g 2 (x,, , z* )dc 3 
+ dh 0 +g l (x i ,y j ,z k )dh t 
where a 0 , a/, a 2 , a 3 , b 0 , b/, b 2 , b 3 , c 0 , c/, c 2 and c 3 are unknown 
parameters for affine transformation; h 0 and h h are unknown 
coefficients for radiometric correction. 
However, there is a need to give initial value to the matcher. 
The values are acquired by transforming PRISM stereo images 
to ground coordinates using geometric model (equation 7). This 
process is called ortho-rectification. In the ortho-rectification 
conversion process, geometric corrected low resolution DEM 
data provided by geographical survey institute (GSI) are used 
for both of backward and nadir look images. When the same 
place of both images is located to same coordinate, the selected 
pixels can be input to matching model. 
4.2 DSM Generation 
In the general DLT model (equation 6), when the image 
coordinates (u, v) of the correspondence point of the stereo pair 
are know, the ground object coordinates (X, Y, Z) can be solved 
by least squares method. 
hX + b 2 Y + bfZ + b. 
u - — L — — ± 
b 9 X + b^ 0 Y + b u Z +1 (6) 
b 5 X + bj + b 7 Z + ¿> 8 
V ~ b 9 X + b l0 Y + b u Z + \ 
For two stereo images, the DLT model can be demonstrated by 
equation (7). 
jj _ a n\ X + a n2 Y + Q n3 Z + a nA 
n b n ,X + b n2 Y + b„,Z + \ 
v ^a n s X + a n6 Y + a ni Z + a n^ 
” b Kl X + b K2 Y + b m3 Z + \ 
JJ _ a b\ X + a bl Y + a b3 Z + a b4 
b b bl X + b b2 Y + b b3 Z +1 
y _ a bS X + a bb Y + a bl Z + a bi 
b b M X + b b2 Y + b b ,Z + \ 
(7) 
where U w V„ are image coordinates of nadir image and U h , V b 
are image coordinates of backward image. 
4.3 Verification of 3D Measurement 
5. RESULTS AND DISCUSSION 
When the model generated less error occurrence along with x 
direction in the image, the big errors are occurred in y direction. 
As of look, Nadir has more consistency then other oblique 
looks (forward and backward) table 2. 
GCP 
CP 
U(pixel) 
V(pixel) 
U(pixel) 
V(pixel) 
Forward 
1.56 
1.3 
2.13 
1.53 
Nadir 
0.54 
8.48 
1.28 
8.26 
Backward 
1.65 
7.15 
2.01 
7.03 
Table 2: RPC model residual error around GCP and CP 
In other hand, when the 3D projective function is used as 
transformation model, all three looks have less than one pixel 
accuracy around GCP. However, the errors are grown around 
check point (CP) (table 3). 
GCP 
CP 
U(pixel) 
V(pixel) 
U(pixel) 
V(pixel) 
Forward 
0.29 
0.26 
1.25 
0.95 
Nadir 
0.25 
0.21 
1.59 
1.28 
Backward 
0.27 
0.26 
1.91 
0.89 
Table 3: 3D Projective residual error around GCP and CP 
Comparison results of height (Z) values are shown in table 4. 
The maximum error around check points is 3.5 meters with root 
mean squares error of 2.4 meters. 
GCP 
Z (GPS) 
Z (ALOS-PRISM) 
Error 
1 
297.956 
299.493 
-1.537 
2 
291.025 
291.398 
-0.373 
3 
290.097 
287.595 
2.502 
4 
327.953 
324.479 
3.474 
5 
325.426 
323.69 
1.736 
6 
312.236 
309.774 
2.462 
7 
306.098 
307.069 
-0.971 
8 
309.322 
312.575 
-3.253 
9 
309.049 
311.938 
-2.889 
10 
315.088 
311.91 
3.178 
11 
319.438 
317.35 
2.088 
12 
324.52 
322.466 
2.054 
13 
289.559 
291.716 
-2.157 
14 
317.969 
315.71 
2.259 
RMSE 
2.364 
The required coefficients for 3D projective transformation are 
calculated from well-distributed 14 GCPs. Over 90% of 
corresponding points from the selected area are matched when 
we generate stereo image matching. 3D coordinates were 
calculated using those matched points. Finally, DSM is 
generated from 3D coordinates. As of accuracy evaluation, 
calculated 3D coordinates are validated with GPS-VRS data. 
Differential errors are calculated based on Z values 14 GCPs of 
both data (table 4). 
Table 4: 3D Mesurement errors by DLT method 
We can found some noises in the generated DSM data when the 
place has low contrast such as forests or flat area. The miss- 
matching errors could be occurred in such area (figure 4). 
Therefore, the accuracy of check points will be growing with 
the advanced of high contract area.