elevation data from the Antarctic Digital Database
(Thomson and Cooper, 1993).
3) A line of barometric surface elevations from a
survey flight over an adjacent glacier were
obtained in 1975 by BAS. These were measured
by simultaneously recording the terrain clearance
of the aircraft using a radar system and elevation
from a pressure sensor. The pressure sensor
readings were adjusted to height above sea-level
by observing the terrain clearance when crossing
features of known elevation, such as open sea or
ice-shelf.
4) A block of aerial photographs. These were
acquired on 1 January 1991, using a Zeiss
RMKA15/23 camera mounted in a deHavilland
Twin Otter. The flying height was 3800 m,
resulting in a nominal plate scale of 1:25,000.
Additionally, satellite radar altimeter data were
investigated. Measurements from the Geosat mission were
available for the region, but none were found in the study
area. If such data had been available, they would have
been of great use, superseding the barometric surface
elevations. Satellite altimeter data are only likely to be
available for very smooth, flat regions such as snow-fields,
because of limitations in the surface tracking systems on
board the satellite (Rapley and others, 1983; Mcintyre,
1991).
METHODS
To carry out the block adjustment of the aerial
photography, it was necessary to provide both planimetric
and vertical control. The survey point provides both but
one point is inadequate to control the block. Two data
sources were used to create extra control. In the first case,
additional planimetric control was generated by using the
georeferenced TM image. Points on the aerial photographs
were identified on the satellite image, and their positions
were determined using routines which were created within
a GIS system.
Vertical control was more difficult to provide. The only
additional source of height control was from the line of
altimetric data from an airborne survey. Unfortunately, this
was entirely over snow-fields, which presented insufficient
detail on the aerial photographs for stereo-matching. A
shape-from-shading technique was used to generate a
digital elevation model of the snow fields from the satellite
image. This shape-from-shading technique was developed
by APRC, and only brief details are presented here.
Further details are available on application to the senior
author.
Shape-from-shading studies are based on numerical
algorithms to solve (1), which describes the formation of an
image from a surface with Lambertian scattering properties
(Rouy and Tourin, 1992).
c
WA (1)
"() (5)
Ox) \oy
where l(x,y) is the image, o, B and y are the components
of the unit vector in the direction of illumination and x,y,
and z are Cartesian coordinates with x and y in the
horizontal plane and z vertical. For solar illumination,
where the light source is very distant, the parameters o, p
and y are constant.
Equation 1 is difficult to solve, and under some
circumstances may not have a unique solution. For many
topographic surfaces, an important simplification can be
made, i.e. for small slopes:
EE von
ox) \oy
Substituting (2) into (1) gives:
oz oz
=0 — + {} — + 3
Kx) ps Bs Y (3)
As I(x,y) is arbitrarily scaled, the constant y can also be
ignored.
A solution to (3) can be found by taking the Fourier
transform of the image. This results in the following
relationships:
-2nD ks + 2 4
Poo, ve[ 2 e
e Th 4 n, 5
Qnin, baje 23 ( )
where p and q are the coefficients of the Fourier transform
of the image and a and b are the coefficients of the Fourier
transform of corresponding elevations.
Thus, by taking the discrete Fourier transform of l(x,y) to
obtain the coefficients p and q, the coefficients a and b can
be obtained by applying equations 4 and 5. The surface is
then constructed by taking the inverse Fourier transform of
the resulting set of coefficients.
This technique has several advantages over direct
integration of the image. The solution is a consistent
surface for the entire area considered, with no
discontinuities introduced by short wavelength features.
Because the functions in (4) and (5) constitute a low pass
filter in the frequency domain, the result is unaffected by
high frequency features in the image, such as crevasses.
Test No. Xy ony Errors
No. of
points Xy z Xyz
1 6 0 37.6 153 30.9
2 14 5 176.4 30.4 140.0
3 8 0 60.5 13.6 475
4 13 5 259.2 201.8 193.0
5 9 0 59.6 14.6 47.
6 7 2 178.1 30.1 140.0
7 10 1 1707 30.8 1367
Table | Summary of test results
422
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