set 1 set 2 set 3 set 4
total* | 89.42 [90.12 | 90.01 96.05
No. 40569 | 40825 40749 | 40507
tier3* | 119.92 | 130.03 | 122.96 | 124 26
No.** 1101 1104 1104 1102
tier4* 80.04 78.57. 1:79:05 80.44
No.** 6871 6873 6871 6875
tier5* 83.58 | 84.62 84.52 82.90
No.** | 31488 | 31638 | 31576 | 31166
tier6* | 146.56 | 131.44 | 136.44| 212.11
No.** 11082 1092 1077 1239
Table 1: Total DEM accuracy and each tier DEM
accuracy
* DEM accuracy (meters)
**matching number
4.3 Average of disparity sum and DEM accuracies
In CHEOPS, the seed points are produced randomly in the
first tier of image. Accuracy might be improved if we
can find a way of selecting the seed points that will have
the best final results. An unique object function should
be used and many sets of seed points created and the set
which gives the best result retained. From table 1 it is
concluded that the highest DEM accuracy can be
achieved only if the fifth tier DEM accuracy is good.
Certainly, it is impractical and meaningless, if we chose
the seed points based on the fifth tier DEM accuracy.
Dowman et al., (1993) stated that the disparity of the
matching results have great impact on the DEM
accuracies. And in this research, this conclusion is used
as the object function to decide the best seed points.
This algorithm is implemented on the third tier, for the
seed points are produced in great number (more than
1000) and the calculation time can be accepted. Four
different sets of seed points were produced iteratively
1000 times, separately for each set, and those seed
points in each set with the smallest Average of Sum
Disparity (ASD) were retained. The resulting ASD values
on the third tier for the original and smallest one are
listed in the table 2 and their DEM accuracies are shown
in table 3 for easy comparison.
set 1 set 2 set 3 set 4
original tier3 * -0.504 | -0.502 | -0.501 | -0.508
minimum * -0.486 | -0.486 | -0.486 | -0.486
Table 2: Average and minimum sum disparity for
original and smallestone on tier3 for four sets
of seed points
* Average of sum disparity (pixels)
set 1 set 2 set 3 set 4
original 89.42 |90.12 |90.04 |96.05
smallest ADS 87:30' 1:97.67 88.67 | 88.77
Table 3: DEM accuracy (m) for original and smallest
ADS seed points
In the table 3 the smallest ASD value, the DEM accuracy
just increased a little, but it provides another feasible
approach to choose the seed points.
5. GEOMETRIC CONSTRAINTS ON ERS-1
SAR INTERSECTION
The equations (1)-(4) give the intersection condition of
the ERS-1 SAR. That is, for a single terrain point, it
must satisfy these four equations- two Doppler equations
and two range equations. And the purpose of this section
is to find an unique function to search for the bad terrain
points caused by the matching errors based on these four
equations. Unfortunately, the two Doppler equations are
not useful for most of the matching points satisfy this
condition, that is - the velocity vectors of the orbit are
perpendicular to the vectors connecting the terrain
points and orbit position. In figure 2, this condition is
represented by the SIRIP1LVIR and S2R2P21V2R. As
with the range equations, they are very effective in
removing the matching blunders. In this research, the
sum of the residuals of two range equations is defined as
the range error which is also shown in figure 2. In
theory, the smaller the range errors, the higher the DEM
accuracy but it is not the case in practic. To more
accurately estimate the DEM height errors caused by the
range errors, this paper calculates the height errors and
range errors for four different data sets. The results are
listed in table 4
where P1 and P2 are the any two terrain points from
intersection
P1 is the intersection of PISIL and P1SIR
P2 is the intersection of P2S2L and P2S2R
let SIL: the orbit position for point P1 (left image)
SIR: the orbit position for point Pl(right image)
R11: the range distance for point P1(left image)
RIR: the range distance for point P2(right image)
P1S1L: slant range for P1 (left image)
P1S1R: slant range for P1(right image)
Range error for P1=(P1S1L-R1L)+(PISIR-RIR)
Same notation for P2
Range error for P2=(P2S2L-R2L)+(P2S2R-R2R)
Figure 2: Geometric condition for ERS-1 SAR
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
