Surface properties of the material are well-known, the
illumination sources and the vantage point are also
known with respect to the object. Under those
constraints the surface can be reconstructed. However,
in principle shape-from-shading is an underdeter-
mined problem. The brightness of a surface cell can be
obtained from an infinity of surface orientations. To
overcome the ambiguity one needs to impose con-
straints on the surface. Those are boundary constraints
in combination with integrability.
The extension of traditional shape-from-shading as it
is known in industrial inspection and robot guidance
to the mapping of planetary surfaces was motivated
NASA's Magellan mission to planet Venus. Tradi-
tionally radar images have been converted to geomor-
phological products also on planet Earth by exploit-
ing the variations and brightness and darkness in a
radar image. ,,Landforms“ have thus been recon-
structed by simply exploiting grey values. This can be
mechanized by changing the traditional shape-from-
shading ideas to be applicable to radar images.
Frankot and Chellappa (1987), Kirk (1987), Thomas et
al. (1991), Wildey (1986) are the pioneers of this
approach. Almost without exception previous work
has addressed single images. Thus a geocoded radar
image is the starting point from which variations in
brightness are inverted into variations of surface
slope.
Most recently the ambiguities introduced by unknown
surface reflectivity properties in radar images have
been tackled by exploiting redundancy in the image
coverage. Images taken with different illumination
directions are combined and an attempt is made to
simultaneously solve for surface slope as well as
surface reflective properties. The accuracy of the result
is currently not well understood.
5.2 An Application
In NASA’s Magellan mission to planet Venus an
individual single image coverage was originally
planned to be obtained of at least 70% of the planet.
The surface shape was essentially only measured by
means of an altimeter. The spacing of altimeter
observations was to be about 13 km. The size of the
radar image pixels was 75 m. Clearly the topographic
relief from altimetry will not properly model that
which is evident visually from the radar images.
Therefore the idea was to apply shape-from-shading to
the radar images. When Magellan’s satellite survived
the initial period of obtaining a complete image
coverage of the planet, a second set of images, and
later on even a third one, were produced from different
illumination angles. As a result many of the areas on
the planet are covered by three images. No techniques
exist at this point to actually combine the three
images.
One needs to begin by removing the geometric
disparities so that then a multiple image shape-from-
shading approach can solve for detailed surface slopes
as well as surface radiometry. This work is currently
being pursued but conclusions are still pending.
Shape-from-shading from individual coverages or
from stereo images that are very similar exist.
However, in a viewable stereo pair the angles of
illumation are similar so that the surface properties are
not sufficiently determined and an ambiguity con-
tinues to exist since the surface property is unknown.
424
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
6 INTERFEROMETRY
6.1 Background
Radar interferometry has two historical roots. The first
one is from radio astronomy using Earth-based
antennas to bounce radar signals off the surface of
Mars or Venus and receiving the echoes on two
antennas that are spaced apart on Earth. This work
started in 1964 (Goldstein, 1965). The second histori-
cal root is airborne radar imaging for military
applications. As described by Graham (1974) this has
become originally a technique based on analogue
electronic processing. Both the radio astronomic and
the airborne imaging developments converted into a
digital signal processing domain by the early 1980s.
Satellite radar interferometry was first attempted from
two images taken with Seasat (1978). This opened an
entirely new field of study: the reconstruction of
topographic relief from repeat passes of a satellite over
the terrain with orbits only a few 100 meters apart.
Independently the military has developed enormous
skills in processing echoes received at multiple
antennas on an aircraft. This may involve 4 to 8
antennas, all feeding echoes into a signal processing
device, mostly attempting to differentiate moving
from stationary objects as an aircraft passes over an
area of interest. This has lateley been expanded into
single pass interferometry for the detailed reconstruc-
tion of surface shape from an airborne sensor.
Currently commercial ventures may be positioning
themselves to exploit this technology aboard low-cost
aircrafts to serve as an all-weather alternative to stereo-
scopic aerial photography. Success of this single pass
interferometry with multiple antennas (a minimum of
two spaced apart in the direction of an aircraft’s wings)
depends on the simultaneous availability of an accu-
rate positioning system for the aircraft. The major
limitation of this airborne approach is the need to
have a precise measure of the direction of the interfero-
metric base, which is the vector in 3-D space extended
by the two antennas. There are currently no good
solutions available for the determination of the direc-
tion of that base, while the position is being deter-
mined by GPS.
6.2 ERS-1 and ERS-2 in Tandem, SIR-C
The European Space Agency’s remote sensing
satellites 1 and 2 (to be followed by Envisat from
1998 forward) have stimulated an enormous interest in
exploiting repeat pass interferometry from satellites.
Because of the stability of orbits, the need for
complicated motion compensation (that is needed
from aircraft sensors) and the difficulties of precisely
knowing the interferometric base vector are greatly
reduced. This makes repeat-pass interferometry from
satellites a very attractive and inexpensive technique
that essentially uses nothing but signal processing
with the regular radar image pixels to obtain an
accurate measure of topographic relief.
The difficulty that the terrain changes between two
passes of a satellite are overcome by having ERS-1 and
ERS-2 operate in tandem i.e. they traverse over an area
of interest within minutes of one another rather than
within days or weeks of one another. The entire globe
has now been covered multiple times only subject to
receiving antennas on the ground actually collecting
the data as they are being transmitted from the
sate
cen
this
no
ares
are:
ver
bac
coh
whi
Sca
Ho
eve
hig
she
plo
oth
The
satt
giv
low
anc
typ
or ;
Thi
int
ref
hig
itie
the
Th
Shi
int
in
unt
7.1
rad
sat
rar
mc
gre
OC
slo
inc
ste
OC(
Th
noi
res
loc
7.2
To
to
im
