'd out mov- 
ns contour 
concerned, 
ormal situ- 
ction. 
f the point 
ned by its 
(2.1) 
olynomial 
(2.2) 
(2.3) 
(2.4) 
"MQ.3) i 
mine the 
using the 
XYZ lit 0 
ctions for 
TM. The 
2.3) 
a 
b Zu M 
X Culp, V=iy, 
d 
e z, v. 
f 
2.2.3 Weighing factors of observation Contribution of 
each observation point around À should depend on the distance 
between the point and À. Weight of each observation must be 
larger when the point is closer to À. Thus, the following 
function (2.6) giving a proper weight value at every position of 
distance is introduced, as Fig 3. 
p, = exp{-(d/d,)’} (2.6) 
where d,:standard distance 
d, = (71 y 90 
Fig 3 Weighing function for observation 
2.2.4 Normal equations The normal equation of the least 
square method is set up from (2.5),(2.6) :'s: 
SX=K (2.7) 
where: S = L'PL 
K= L'PC 
P, 0 
P= p, 
0 
Pp. 
The coefficients of the local DTM are obtained as the solution 
of (2.7) as follow: 
X = S'K (2.8) 
2.3 New coordinates of the point A 
After the DTM is determined, the point A is moved hori- 
zontally, until it is dropped on the DTM surface, and accord- 
863 
ingly, the contour line which A belongs to are renewed. To cal- 
culate correction for coordinates of A, a condition that "the new 
position of A should be on the DTM surface" is used. In this 
step, the coordinates of A are considered as observation data on 
the DTM surface. Each of x,y and z coordinates is an observa- 
tion, and correction for each will be calculated setting approxi- 
mate weight to each of three coordinates. Then the planimetry 
of point A will be changed by adding those calculated correc- 
tions to x and y. 
The accuracy of calculated DTM is also important. In case 
the DTM is not accurate enough, it is not a proper way that to 
move the point A perfectly onto the DTM surface. Therefore the 
accuracy of local DTM generation should be concerned when 
the corrections are calculated(Fig 4). 
obtained DTM 
  
  
  
Fig 4 Movement of point A 
2.3.1 Observing accuracy of point A and calculating 
accuracy of the local DTM Surmising from study, 
observation of elevation using 1/40,000 scale aerial 
photographs has about ¢ =2m (s.d.) accuracy, and that of 
planimetry has about ¢ =5m. However, they are like!’ 
influenced by the quality of the photographs and operator's skill. 
Also it is difficult to estimate reliable accuracy of generated 
DTM. In this study, the standard deviation of residuals among 
observed elevations and generated local DTM surface at all of 
the collected points are taken into account in determining a 
weighing factor. 
2.3.2 Condition equations The local DTM generated 
for point À is described as: 
z = f(x,y) = a+bx+cy+dx2+exy+f;? (2.9) 
If the point A locates right upon the DTM surface, z,-f(x,,y,) = 0 
should have been satisfied. It is not satisfied in general, there- 
fore, coordinates of point A and the coefficients of the DTM are 
to be corrected by solving the condition equations. Actually, the 
coefficients except 'a' can be ignored because of their little ef-