ion and x.y, 
1d y in the 
illumination, 
imeters o, p 
nder some 
n. For many 
ition can be 
(2) 
(3) 
can also be 
the Fourier 
he following 
(4) 
(S) 
ier transform 
Xf the Fourier 
m of |(x,y) to 
: a and b can 
he surface is 
" transform of 
over direct 
a consistent 
d, with no 
gth features. 
le a low pass 
inaffected by 
IS crevasses. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
control in this half 
of the strip 
  
1001 
op 1108 1101 Numbers of TEST 4 
1107 1103 / the points 
2006 E To \ used = = 
+ ® 5$ —L-112 + © o> 
2005 T e — 1104 * + © 
S à E o? 
A = Xyz . : 
2004 2002 m No height control in 
2003 1106 2001 71105 hey this half of the strip 
TEST 1 TEST 5 
e xm —! 
9 
$ $ $ 
+ o eo 
[d 9 
L-—L | = 9 
: 2 No planimetric or S 
No planimetric or height control in this 
height control in this corner of the strip 
corner of the strip 
TEST2 TEST 6 
AT 
® © 
+ © 
+ + + e o ® + $ 
® 
E] da eg 
There is no height Although the across-strip 
control in the bottom distribution is better, the 
of the strip centre is unsupported 
TEST 3 TEST 7 
EIER. es 
© ® © 
e 9 ® 
o9 ; e o 9 
9 ® 
® 
L| © a? 
No height or planimetric 
  
  
  
  
  
  
  
  
  
The distribution remains 
similar to test 6, but 
there is more control 
  
  
Figure 2: The distribution of control points used in various tests 
This makes the technique insensitive to image noise and 
speckle. À final advantage is that the process is efficient, 
taking only a few minutes of computer time. 
The elevation model created by this technique is arbitrarily 
scaled and may have a regional tilt. To provide surface 
elevations, it is necessary to calibrate the elevation model 
using measured surface heights. In this study, the model 
was calibrated using the airborne altimetric data, which 
allowed height values to be generated for regions of the 
snow-field where there was sufficient surface detail for 
successful stereo-matching. 
CONTROL POINTS 
The techniques and sources described above produced 15 
control points, of which 9 had known elevation values. 
These control points are of three types: surveyed points (1 
point), planimetric points from the TM scene (6 points) and 
heighted points from the shape-from-shading algorithm (8 
points); the accuracy of the positions depends on their 
source. The surveyed points have a nominal accuracy of 
x11 m (Knight, 1986), but the local geometry of the survey 
network greatly affects the accuracy of particular points. 
Because the image is tied to the same survey network as 
the surveyed points, the correspondence between the 
image and surveyed points is within one pixel (i.e. within 
30 m) and the nominal accuracy with which points on the 
image can be located is x30 m. As the TM scene covers 
a much larger extent than the study area, it was possible 
to verify the co-location of the image with survey points not 
used in this study. However, difficulties of identifying 
corresponding points on the TM image and the aerial 
photographs caused larger errors. Points on the edges of 
rock outcrops were located more reliably than those at the 
centre because of the high contrast between snow and 
rock. Errors may also arise from the different dates of the 
TM scene and the aerial photography. The extent of thin 
snow patches may alter substantially from season to 
season, and there is no means of quantifying this variation. 
423