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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXX V, Part B7. Istanbul 2004 
2.1 Block adjustment based on RPC/RPB parameters 
2.1.1 Model of block adjustment: After the ground 
coordinates (X, Y, Z) of a control point are converted to the 
geographic coordinates (Latitude, Longitude, Height), its image 
coordinates (s, /) can be computed: 
  
Ps Latitude  — LAT |. OFF 
LAT SCALE 
Ls Longitude — LONG _ OFF 
A LONG _ SCALE (1) 
yy Height - HEIGHT | OFF 
HEIGHT SCALE 
  
20 
No pF LH) 
p led 
X 
> b-p,(P,L,H) 
$=] 
y e ptP LIH) 
i=l 
20 
S d,-p,(P,L,H) 
i=l 
I-y:LINE SCALE-LINE OFF (3) 
s=xSAMP_SCALE+SAMP OFF 
  
(2) 
  
A = 
Where the parameters LINE OFF, … , dj, ... are from the RPC 
parameter file, p; are polynomials (Zhang, 2001). For each point 
following equations can be acquired: 
*, 
Cre, tested r= f,+ fi5+ Sal (4) 
S= Ey FE C+H gr, = hy + hic+ h,r 
Where (c, r) are the measured image coordinates, and the 
parameters e, f, 2, h; are unknowns corresponding 
images. 
2.1.2 Computation: For control points, the error equations are 
according to the formula (3) and (4) corresponding relative 
images. For Tie points, the approximations of their ground 
coordinates are computed based- on RPC parameters and 
measured coordinates of stereo image pair firstly "!. Then, their 
error equations are similar as control points. After the 
parameters e, f, ej h; for each image are determined, 
coordinates (s, /) can be computed by coordinates (c, r) and 
parameters g;, ^;. Finally, the ground coordinates (X, Y, Z) can 
be computed by RPC parameters, left image coordinates (s, //) 
and right image coordinates (s; 4) “1, 
2.2 New strict geometric model based on affine 
transformation 
To avoid the the relativity of the traditional parameters of 
RSIPHR, a new, simple and strict geometric model based on 
affine transformation has been proposed SI In the new model, 
the strict mathematical relationship of the image coordinates (x, 
y) and the space coordinates (.X, Y, Z) is 
Z 
— P992 (yy )sa *aX-aY aZ (5) 
f -xtga : 
(y = vo = b, + bX " b,Y A bz (6) 
2.2.1 Calculation of Parameters: Because a in the left of 
equation (5) is unknown, the equation is not linear. The 
calculation procedure is iterative based on the linearization. For 
simplifying, let x denote x — x,, y denote V — Yo, in the next part 
1097 
of this paper. The equation (5) is linearized as following error 
equation: 
da, + X da, * Y,da, + Z da ; + 
  
  
Z; sin a Xx(f-Z,/uncos a)) 
x, ——= = : da + 
mf -— x,ma)cos?^ a (f-xiga) cos^q 
Z, 
d Sud Iv. 7 
ay +X 0+ Yu, + Za, mosg. 9 (7) 
: j f -xga 
Using error equation (6) and more than 5 control points, a, a, 
a; a, and a; can be solved iteratively. From equation (6), the 
linear equation can be acquired: 
by + Xb + Yb + Zb, — y, =0 (8) 
Using equation (8), b,, b,, b; and b; can be solved directly 
without the iteration. 
2.2.2 Calculation of ground coordinates: Ground Coordinates 
(X, Y, Z) can be computed from parameters a, a;, bj, left and 
right image coordinates (x, , yi) and (x, , y): 
  
  
X fx 
An 42. UT : —  — du 
mcosa,(f - xtga,) (x F-xtga; 
b, b, [E y12 Y 7 by, C 
X, s, ©) 
a, à + 7 En 
mcosa, (f —x,(ga, ) f[-x,tga, 
b, b,, b,, E Mr T bi 
Or denote equation (9) as AX=L, and then the resolution is 
X=(A" A)" AL, 
3. IMAGE MATCHING WITH 2D RELAXATION FOR 
DEM GENERATION 
2 D relaxation matching should be used because there is quite 
large y-parallax in the approximate epipolar image pair‘! of 
some of the RSIPHR. Instead of grid point sampling, well- 
distributed feature point sampling is used in the matching 
approach. To ensure the reliability of the matching results, as 
well as fast processing, image pyramids are incorporated into 
the matching strategy. An algorithm for image matching, which 
has the ability to bridge over the poor texture areas and preserve 
the terrain features at high accuracy, is developed. Finally, a 
| Digital epipolar images | 
Y 
Pyramid images generation 
Image processing 
[... Point feature extraction m] 
Y 
[ Cross correlation = 
Y 
| Relaxation iteration «] 
Y 
Error match detection and 
elimination 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Pyramid back matching 
New point densification 
  
  
  
Figure 1: Workflow of matching