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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
specular reflection position, and consists of a bright, shadow-
free circular zone. For nadir images it appears always, when the
solar zenith angle (= 90° - solar elevation) is smaller than the
FOV of the camera.
For the ADS40 line scanner, the hot spot appears only in the
case that both the solar zenith and azimuth angle match one of
the CCD line viewing directions. Then the hot spot appears as a
bright linear strip along the flight line. As with aerial images,
the FOV of the ADS40 is an upper boundary for the solar zenith
angle where a hot spot can occur, and even then it can easily be
bypassed by avoiding certain times or flight directions.
Apart from the hot spot, the BRDF-effect will cause circular
brightness gradients in aerial images and across-track gradients
in line scanner images.
The origin of the bidirectional effects is mainly microscopic
shadow casting (cf. Figure 3): Each image pixel consists of a
mixture of pure or mixed material and cast shadow. This mixing
goes from the scale of the pixel size down to the wavelength of
light. Hence we will call it microscopic shadow here, because it
is not visible at this resolution. The amount of cast shadow
increases with increasing solar zenith angle (i.e. at dusk and
dawn). The amount of microscopic cast shadow contributing to
the pixel also depends on the viewers position: In the case of
the hot spot, with the Sun in the back of the viewer, the cast
shadow is hidden by the object itself, while with the Sun in the
opposite direction the shadow is darkening the pixel (assuming
no specular reflection). This shadow casting effect is often
referred to as “geometric” or “surface” scattering.
A second source of bidirectional effects is multiple scattering
between the structure elements of the target area, the so-called
“volume scattering”. This is especially occurring in vegetation
canopies.
Since the amount and the angular distribution of the
bidirectional effect depends on the microscopic shape and
structure of the target, it is possible to extract structural
information of the ground from BRDF affected images.
o
x
N
Rough water surface
"Specular reflectance Coherent backscatter with hot spot — ; }
p P " "
with "sunglint" relectance
vA
X 7» ©
Av
"Geometric scattering", "surface scattering":
shadow-driven reflectance with "hot spot"
"Volume scattering": vegetation
Figure 3. Sources of anisotropic reflectance from natural
surfaces.
Many models, empirical and physically based, have been
developed during the past forty years. Again, the inversion of
physical models tends to be slow and may be unstable. But
unless the bidirectional information itself is the goal, then the
accuracy of empirical models is sufficient.
Linear semi-empirical models are fast and easy to invert
(Chopping, 2000). They are a sum of so-called kernels, each of
which is multiplied by a parameter. A widely used linear semi-
empirical model is the Walthall model (Walthall, 1985), which
contains 4 parameters in its extended version (Nilson and
Kuusk, 1989), cf. Eqn 1.
p (6,0,,9) 2 a070? & b(07 -0:) -c80,cosp* d. (I)
where p = reflectance factor
0; = incident illumination zenith angle
0,— reflection view zenith angle
9 = relative azimuth angle
a, b, c, d = free parameters
Unfortunately the Walthall model does not include a hot spot
term. But by introducing an additional parameter, a hot spot
term can be included. For simplicity we will use as an
additional kernel the hot spot distance function of the Li-kernels
from the AMBRALS model (Wanner et al., 1995), cf. Eqn 2.
t3
D = Jan ? 0, +tan” 0, - 2 tan 6, tan 0, cos 9 (
The samples for model inversion can be retrieved by calculating
column averages of the total image as described in (Beisl,
2001), since a column in a line scanner image represents a line
of constant view angle (cf. Figure 4). The relative shape of the
modelling in then used for a multiplicative correction.
For a more accurate correction this statistics can be calculated
for separate classes within the image. For a good inversion
quality, i.e. for all images matching together in the mosaic, it is
recommended to merge the statistics from each image together
and perform a simultaneous correction (Beisl, 2002).
Column average =
mean reflectance
for constant view
zenith angle 6, and
constant relative
azimuth angle ©.
7
Figure 4. View and illumination geometry for a line scanner.
4. DATA AND RESULTS
As an example, data from a flight campaign in 2003 in Hinwil,
Switzerland are shown (cf. Figure 5, Figure 6). Each image is a
mosaic of an image strip merged with the image strip flown in
the opposite direction. The merge is done by taking one square
from one image and the subsequent square from the other
image, in order to obtain a chessboard like mosaic. So wherever
there is a difference between the images, a chessboard pattern
will appear.
