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where n(x,y) is a noise and a, through a, are 
unknown coefficients. The unknown parameters are 
determined so as to minimize X n(x,y)*. Eq. 1) 
does not include the correction to intensity level 
difference between L(x,y) and R(X, YD. Its 
removed before correlation by local averaging the 
pixel values over the correlation area. Sub-pixe] 
values of R(X,Y) are interpolated for differentia- 
tion by the 1-D bi-linear spline (Press,1992). 
We judged the precision by residual y-parallaxes. 
A pair of aerial film (1:10,000 scale) was scanned 
with a scanner, VEXCEL VX3000PLUS, with the pixel 
size of 25um*x25um. This scanner was also used for 
measurement of ground displacement (see Section 
4). The film distortion was assumed negligible. We 
picked up 53 orientation points at strong edges 
on flat places like traffic marks on roads 
uniformly over the overlapped area. With eye 
observation on the original scale images, the 
residual y-parallax(rms) was 0.68 pixel, and on 
the four times enlarged images it was 0.40 pixel. 
This was assumed the best, because on more 
enlarged images, y-parallaxes got large. Table 2 
shows the residual y-parallaxes for some 
measurement conditions. 
5x5 and  11*11 
precision). 
Tested pixel sizes were 
(larger ones gave the same 
Besides eq.(1) also tested the form 
xta, 
X 
Pra e 
  
  
The best result was obtained for eq.(1) with the 
window size of 11 pixels. According to the error 
propagation theorem, 0.4 pixel y-parallax(rms) 
corresponds to 0.4/1.414=1/3 pixel error in image 
coordinates. It should be noted this best 
precision is the same as the best obtained by the 
eye observation. 
3.2 Modified LSC 
The convergence domain with the LSC is usually one 
pixel. GOKUU extends it by the following way. 
(1) Edges are extracted from the left image by LoG 
filtering. The LoG filter is defined as 
Véexp(-(x?*«y?)/20) (3) 
where c is a scale parameter. It is set to 2, 
which scales the filter with an influence area of 
t5pixels. The filtering produces countless small 
edges. Then corners are extracted by the following 
algorithm (see Fig.6): 
1f( not less than 3 edges are found in 8 pixels 
around pixel 0) O is a corner; /*Fig.(a)x/ 
else if ( the edge passing through O is a straight 
line) /*Fig.(b) */ 
else ( 
O is not a corner; 
if( not less than 3 edges in 8 pixels around A or 
B) O is a corner; /*Flg.(c) */ 
149 
else if ( /COD «z135c ) O is a corner;/*Fig.(d)x/ 
else O is not a corner; 
) 
Then the Sobel filter (Iannino,1979), a differen- 
tiation filter with a light smoothing, is applied 
to the area. This filter produces the intensity 
gradient at every pixel. In 11x11 pixels around 
the approximated corner point, the corner with the 
maximum intensity is picked up as an orientation 
point. By conventional correlation this 
orientation point is matched to the right image up 
to one pixel, then the LSC is applied. If the 
terrain is flat in a 21x21 pixel area, convergency 
is almost assured in a 11x11 pixel area. 
4. THE MEASUREMENT OF GROUND DISPLACEMENT IN THE 
KOBE EARTHQUAKE 
4.1 Aerial Photographs and Control Surveys 
We selected Ashiya-city as a pilot area, which is 
as wide as 2-3 km east to west and 8-9km north to 
south. It faces the Seto Inland Sea in the south 
where reclaimed land spreads. 
Table 2 shows the data on the aerial photographs, 
GCPs and the result of aerial triangulation used 
for the measurement work. One set of the 
photographs were taken before the earthquake ( 
hereafter pre-photos) and the other taken after 
that ( post-photos). The city is covered with 
about 50 models for each set of photographs. The 
scales of the photographs are 1:40,000 and Y: 
40,000-1:50,000 respectively. There is a gap of 
three years in two flights, and the flight 
directions differ by 90 degrees. These make the 
identification of the same points less easy. 
The flight for pre-photos was for a map production 
for the sewerage management. The ground control 
survey was done by triangular and traverse 
surveying, with the estimated precision of 3cm (in 
planimetry) and 1cm (in height). The direct 
levelling was also conducted, with the-estimated 
precision of 1cm. 
The control survey for the post-photos was 
conducted in September, 1995 by GPS surveying. The 
measurements were adjusted with Trimnet (Trimble 
Corp.). The precision is estimated to be 3cm (in 
planimetry) and 1cm (in height). 
4.2 Aerial Triangulation 
Aerial triangulation was executed by GOKUU. Table 
3 includes the results. The standard deviations of 
errors image points 
were assumed 7um for both pre- and post-photos. 
in observed coordinates of 
The horizontal error of supplementary GCPs was 5cm 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996