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Figure 1: Information flow in the proposed image understand- 
ing system: Subdivision of the problem into segmentation and 
physical model application 
[Schneider, Bartl, 1995]. 
Starting from the image, image objects are identified by seg- 
mentation according to homogeneity criteria. The advantage 
of this approach is twofold: 
1. The amount of information to be processed in the fol- 
lowing analysis is reduced so that it becomes man- 
agable, and 
2. the mixed-pixel-problem can be brought under con- 
trol: A high percentage of the pixels of a satellite 
image are mixed pixels containing radiometric infor- 
mation of more than one surface category at an un- 
known mixing ratio. If the segmentation is performed 
employing spatial subpixel analysis [Schneider, 1993, 
Steinwendner, 1996], objects with pure spectral signa- 
tures can be obtained even in the case of a very high 
percentage of mixed pixels in the original image. 
The physical model of image acquisition transforms the re- 
flectance characteristics px; of objects à (regions on the ter- 
rain surface) in spectral bands k, to pixel values di; in the 
image. This transformation is influenced by global parame- 
ters pA, describing the various absorption and scattering pro- 
cesses in the atmosphere, and by sensor parameters pr. The 
parameters pa usually are unknown. 
The image understanding problem is to assign every region 
object à to one surface category C;. The set of possible sur- 
face categories is defined a priori by the (mean) reflectance 
values pic of the categories C in the spectral bands k. For 
certain categories C, other properties (geometrical parame- 
ters such as shape or size descriptors of the regions belonging 
to these categories) may be characteristic. The mean values 
of these geometrical parameters for categoty C are denoted 
gio where j is an index defining the parameter. gj; is the 
geometrical parameter j for object i as determined from the 
image. The image understanding problem can now be for- 
mulated in the following way: Given are 
e the physical model 
dpi = du (Phi, PA,PI) (1) 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
the sensor parameters pr, 
e the (mean) pixel values dx; of the objects, 
e the (mean) reflectance values pc of the surface cate- 
gories to be identified, and 
e the (mean) geometrical parameter gc of the surface 
categories to be identified. 
The problem is to find the global parameters DA and the 
category C; of every object in such a way that 
3a : (pri — Pk). N° b; - (gji — 9;c;). — Min. (2) 
ki ji 
The quantities a; and b; here are the weights of the different 
spectral bands and geometrical parameters. These weights 
also determine the relative importance of the geometrical pa- 
rameters as compared to the spectral characteristics. 
Reference information ("ground truth data") can be used 
in this image understanding scheme: "Radiometric control 
points" (reference surfaces on the terrain with given re- 
flectance data) may provide input values for px;, and "the- 
matic control points” (regions with known land use) may 
provide input values for C;. 
3 PHYSICAL MODEL 
Object reflectance, radiance and irradiance quantities as well 
as atmospheric absorption and scattering are expressed as in- 
tegral quantities for the individual discrete spectral bands of 
the sensor. Assuming a sensor with linear radiometric re- 
sponse, the pixel value dg; is related to the radiance Lj; 
incident on the sensor instrument I by 
dri = myLik; 0; (3) 
mx and a, are the multiplicative factor and the additive term, 
respectively, characterizing the response of the sensor to in- 
cident radiation in the spectral band k. 
Lik; can be traced back to pk; with the use of a computer- 
coded numeric model such as LOWTRANT: 
Li Lm. pi) (4) 
This method is very general and fairly accurate, but compu- 
tationally expensive. One has to bear in mind that numerous 
evaluations of (4) are necessary to solve (2). 
In an attempt to formulate the problem analytically to facili- 
tate computation, Lj; can be regarded as a sum of 3 terms 
(Fig. 2): of the radiance reflected by the terrain surface, Lj; 
(i.e. the signal proper), attenuated by the transmission of 
the atmosphere for a vertical path 4 = 0, 70x, the radiance 
of solar radiation scattered by the atmosphere directly to the 
sensor, LA, (u stands for upwards), and the radiance re- 
flected by the terrain surface and scattered afterwards by the 
atmosphere to the sensor, Lpuki: 
Liki — LokiTok - LAuk + Lpuki (5) 
Assuming a terrain surface with Lambertian reflectance char- 
acteristics, the reflected radiance is 
1 
Loi ; PEG + Pri (6)