The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
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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.