(4) 
Method 
Number 
of 
ground 
control 
points 
Xrms 
Yrms 
Trmas 
Affine 
28 
0.2626 
0.2990 
0.3980 
2nd order affine 
28 
0.2309 
0.2781 
0.3615 
3rd order affine 
28 
0.2310 
0.2772 
0.3608 
4th order affine 
28 
0.2309 
0.2771 
0.3607 
5 th order affine 
28 
0.2308 
0.2763 
0.3601 
6th order affine 
28 
0.2309 
0.2772 
0.3607 
Table 3. Total RMS errors by using different method 
Y r 
Trma *\j X rms + Y r 
(5) 
where X RMS is the root mean square error of X, Y RMS the root 
mean square error of Y, T RMAS the root mean square error, n the 
number of ground control points, XR i the residual error of 
one ground control point on the direction of X, and YR t the 
residual error of one ground control point on the direction of Y. 
It is obvious from the Table 4, the RMS errors of geometric 
correction gradually reduce along with the increasing of 
polynomial order number, and the RMS error is smallest when 
the polynomial order number is 5. If the order increases, the 
RMS error will increase, too. RMS errors of the second order 
polynomial are smaller than 0.5 pixels, which satisfies the 
requirement of the remote sensing images. 
Where X RMS , Yrms and Trmas are the units of pixel, and 
XrmS~ 
(3) 
3.3.2 RMS errors of checking points: 15 checking points 
are selected uniformly on the corrected images to inspect the 
correcting situation and the errors of checking points are shown 
in Table.4. 
Point 
number 
Position of point 
after correction 
Actual coordinate of 
checking point 
Position errors of 
checking point 
RMS of 
simple- point 
Notes 
X(m) 
Y(m) 
X(m) 
Y(m) 
AX 
AY 
2 
513037.07828 
654965.98000 
513037.264 
654966.274 
-0.186 
-0.294 
0.348 
3 
513043.66497 
654680.98932 
513043.990 
654681.072 
-0.325 
-0.083 
0.335 
4 
513392.58553 
655043.75214 
513392.375 
655043.483 
0.211 
0.269 
0.342 
5 
513528.14427 
654788.86352 
513528.105 
654788.748 
0.039 
0.116 
0.122 
6 
513043.89808 
654159.42341 
513043.674 
654159.180 
0.224 
0.243 
0.331 
7 
512912.76734 
654784.41835 
512912.791 
654784.256 
-0.024 
0.162 
0.164 
8 
513087.59714 
654566.23453 
513087.801 
654566.552 
-0.204 
-0.317 
0.377 
9 
513880.31298 
654107.97735 
513880.067 
654107.837 
0.246 
0.140 
0.283 
RMS 6 = ±j-RMSf 
V n 
= ±0.350/w 
10 
513259.60275 
655028.67721 
513259.780 
655028.585 
-0.177 
0.092 
0.200 
11 
513101.07165 
654059.19855 
513101.634 
654059.462 
-0.562 
-0.263 
0.621 
12 
513508.37463 
654478.69624 
513508.741 
654478.865 
-0.366 
-0.169 
0.403 
13 
513130.33893 
653667.74868 
513130.263 
653667.400 
0.076 
0.349 
0.357 
14 
513266.91957 
654262.85005 
513266.556 
654262.573 
0.364 
0.277 
0.457 
15 
513603.45999 
653996.68264 
513603.349 
653996.299 
0.111 
0.384 
0.399 
Table 4. Errors of checking points after geometries correction 
The total RMS error of control points is 0.35m. The control 
point of geometric correction and checking points are rooted in 
the digital topographic maps of 1:500 scaled, so that 
RMS Toatal — 
Real ^Control (6) 
"W =±>M4„,- m L mi =±Vo.35 2 -O.l 2 =±0.335«