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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
Figure 4. The Length Definition of the MGW 
4.2 The Length Measurement of the GW 
According to the MGW resource field investigate results, 
accurately measure the three-dimensional coordinate of each 
inflex point on the surface centre line of the MGW under the 
MGW stereo pairs with the 1:10k specification precision. 
The quantity of the measured inflexion point must be enough to 
guarantee to reflect the distribution characteristic of the surface 
centre line of the MGW, at the same time, in order to reduce the 
measurement mistake, the same section of the MGW need to be 
measured twice by different operators along the positive and 
negative direction, when the difference of the two times’s length 
measurement result is less than 0.001m, the average of the two 
times’s length measurement result will be the final measurement 
length. 
4.3 Value Assignment 
The MGW length includes surface length, projection length and 
categorised lengths. According to the attribute of the MGW, 
such as the wall’s building up age, building up materials, 
protection status, administrative division, etc, categorised 
lengths can be the length of the vanished MGW, the length of 
the Gansu province’s MGW etc. 
During the stereo measurement of the MGW, the attribute value 
should be assigned to the MGW section in order to count the 
different length of the MGW. The attribute include function of 
the wall (first line or second line), building up materials (stone, 
clay, etc), protection status (good, vanished, etc), administrative 
division, building age, etc. At the same time, in order to assess 
the length measurement precision, X, Y, Z direction 
aero-triangulation adjustment precision also need to be assigned 
to the MGW section respectively. 
4.4 Length Calculation Formula 
The track line of The MGW is a three-dimensional curve, the 
surface length of the MGW is the curve length of 
three-dimensional. 
Using of digital photography method to obtain inflection point 
coordination of the MGW, calculating the curve length between 
the adjacent inflection points, the surface length of the MGW is 
the cumulative length of each curve length. 
The Formula of calculating the surface length of the MGW is: 
L - T - jr Vo*».. '*.>* 4 ‘Gr... -yj’+fr.,. ■*.)" 
a (1) 
Where Pi Pi*' is inflection points, ( x * y ' z ')>(*'*> yi+1 Zi+I ) 
is Pi P«' three-dimensional coordinates, L is the curve’s 
surface length of the MGW. 
4.5 Accuracy Assessment Model 
During the stereo measurement of the MGW inflection points, 
each measuring is independent of each other, the measuring 
error of three directions should also be independent of each 
other, in the same time, in every triangulation densification 
network, the accuracy of each measuring point can be assumed 
to be equal. That is, ox=ox 1 =ox2=... =axn , 
ay=ay 1 =ay2=...=ayn, az=oz 1 -az2=... =ozn. 
According to the length calculation formula(l), respectively xi, 
yi, zi from derivatives, measuring section ’s error (o L) formula 
is as follows: 
l = é + (|^)x i 1 + (! l > 2 < 
“! dx -, 1 Sy, dz i 
(X 2 - * 1 ) : 
_i_ } 2 + (X , -X ,) 2 )<t 
+ (y.-yy^K 
L i L 2 y 
+ (' 
V ( Z i ' 2 ¡-' Z i*l ~ Z ' ) 2 + 
f/ L, ' L j 
L„, 
-)cr. 
Where ax, ay, az is three direction’s measurement accuracy 
under the stereo measuring environment, that is the 
densification precision of every triangulation densification 
network. 
Using the formula (2) to calculate the MGW each section’s 
length measurement accuracy, and using the formula (3) to 
calculate the overall length measurement accuracy of the MGW, 
the overall error (a Lall) formula is as follows:. 
crL. 
(3) 
Where i is the MGW serial number of each section’s length 
measurement, n is the total number of sections. 
5. TEST 
5.1 Measurement Method Test 
One of the main purpose of the test is to validate the method to 
obtain the surface length of the MGW. The ways, such as 
RTK-GPS, Photogrammetry, and measuring the length of the 
MGW based on the 1:50k DRG and DEM, had been tested in 
Beijing, Hebei and Gansu. The result of the test is as follow: