where Eg; denotes the global irradiance of the surface in
band k. This quantity again is the sum of 3 terms: of the
direct solar irradiance, of the diffuse sky irradiance due to
solar radiation scattered by the atmosphere downwards to the
earth, and of the diffuse sky irradiance due to the radiation
reflected by the terrain surface and scattered back by the
atmosphere:
1/cos
Ecri = EskTo®
cosŸ + TLadr + bp TT Lpri (7)
Es, here is the solar irradiance of a plane perpendicular to
the incident radiation at the upper edge of the atmosphere, Ÿ
is the zenit angle of the solar radiation path, L4; is the solar
radiation scattered by the atmosphere downwards, and by is
the “reflectance” of the atmosphere due to backscattering for
radiation reflected by the terrain surface.
Similar to the quantity bx describing the backscattering char-
acteristics of the atmosphere, a forward scattering coefficient
fr can be defined, yielding an expression for the quantity
Louk introduced in equation 5 :
D ous E fx : Loki (8)
Combining all these equations, one obtains the following re-
lationship between the terrain reflectance values p, and the
pixel values d; in the image:
dei = my-
1/cosŸ 1 Tok + fk
| (esca cos) 4 nL aa Phi qusc + Lauk
Tak
In this equation, some of the quantities are constant and
known, such as Es, from satellite observations of the so-
lar radiation, and 9 from the exact time of image acquisition.
The sensor parameters my and a; are known in principle from
preflight or inflight calibration procedures. These parameters
may change with time, however, so that it might be of interest
to introduce them as unknown variables in the image under-
standing problem, or at least to allow small corrections of the
given values. The atmospheric parameters Tox, Ladk, L Auk,
fx and b, are unknown. They depend mainly on a large num-
ber of parameters of aerosole properties and aerosole concen-
tration distribution and thus are interrelated in a complicated
manner described by intricate atmospheric models. It must
be noted that these atmospheric influences can be quite pro-
nounced and must not be neglected in the calculations, as
the disturbing quantities LA,; and L,,, sometimes exeed
the signal quantities L,xTox. One way to handle these at-
mospheric parameters in the image understanding procedure
is to work with a limited number (e.g. 2 to 4) “standard
atmospheres” with constant aerosole types (e.g. “rural at-
mosphere”, “urban atmosphere”) and to use one additional
continuous parameter (e.g. atmospheric extinction, or hori-
zontal visibility V3) to describe the atmospheric situation at
the time of image acquisition. The atmospheric quantities in
the physical model equation can then be reduced to the 2
unknown variables M (discrete, denoting the standard atmo-
sphere model category), and V;..
(9)
766
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Lau = Laon (M, VV),
Tor = Tor (M, Vh),
fk = fa(M, Vh),
Lauk = Laur (M, Ve},
br = bu (M, Va)
(10)
Fig. 3 illustrates the quantity L4,; as calculated with LOW-
TRAN7 for LANDSAT TM bands k=1,2,3,4,5,7, for a stan-
dard midlatitude summer atmosphere M with a standard rural
aerosole profile, and for 3 values of V, (5km, 23km, 50km).
Polynomial regression can be used to describe this depen-
dence of Laur and of the other atmospheric parameters of
equation 10 on V; for a given M.
4 APPLICATION OF THE MODEL TO REAL DATA
Data sets of LANDSAT TM data for experiments with the
physical model were obtained by manual selection of test ob-
jects on a conventional image processing system. The re-
flectance data for different surface materials such as water
of different degree of pollution, soil, forest (different tree
species) and meadow were taken from field measurements
and from the literature. Using these data, the basic validity
of the model could be proved. The reflectance data (defined a
priori) produced the observed pixel values for plausible values
of the atmospheric parameters.
Solving the image understanding problem by global optimiza-
tion techniques is being studied at present. In particular,
simulated annealing and genetic algorithms are being tested.
REFERENCES
[Schneider, 1993] SCHNEIDER, W., 1993. Land use map-
ping with subpixel accuracy from LANDSAT TM image
data. Proc. 25th Int. Symp. on Remote Sensing and Global
Environmental Change, Graz, 4-8 April 1993, p. 11-155 -
11-161.
[Schneider, Bartl, 1995] SCHNEIDER, W., BARTL, R.,
1995. Physical models in remote sensing image under-
standing: model formulation and first results. In: Visual
Modules. Proceedings of the 19th OAGM and 1st SDVR
Workshop. Schriftenreihe der Osterreichischen Computer
Gesellschaft, R.Oldenbourg Wien München, p. 59-67.
[Steinwendner, 1996] STEINWENDNER, J., 1996. Segmen-
tation of satellite images with subpixel accuracy. In: Inter-
national Archives of Photogrammetry and Remote Sens-
ing, Vienna, Austria.
