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is maximum or at least very high. In MRF this can be 
achieved with the help of various methods manipulating 
local probability densities. In this work, the local highest 
confidence first (LHCF) algorithm (Chou et al., 1993) has 
shown the best performance with respect to detection qual- 
ity and computational speed. 
Using the equivalence of MRF and neighbour Gibbs fields 
(Geman and Geman, 1984, Winkler, 1995), Bayes' theorem 
(1) can be formulated for the local probability density in a 
single pixel s: 
P(Es|OEs, Ys) X P(Ys|Es) - P(Es|OEs). (3) 
In neighbour Gibbs fields probabilities are expressed as a 
function of energies H: 
pla) = 5 exp {-H(z)} (4) 
where Z is a normalizing constant. With (4), instead of 
probabilities energies can be used: 
H,(e;|0¢s,y,) = H,(ysles) + H,(e5|0¢,). (5) 
In the following the computation of the different energy 
terms will be treated. A complete description of the method 
can be found in (Hellwich, 1997). 
2.1 Data Evaluation 
Line extraction is conducted using a template which con- 
sists of a line zone and two neighbouring side zones (Lopes 
et al., 1993). The simple line model assumes that the 
backscatter properties are homogenous in the line zone 
as well as in the side zones. To evaluate the image data 
the template is centered at each pixel. The likelihood that 
the center pixel of the template has the line state rises if 
the contrast between the line zone and both side zones in- 
creases. A contrast between the side zones is permitted. 
By rotating the line zone different line directions are treated. 
The data evaluation for each pixel results in the energy term 
Hs(ys|es) where y, is not a grey value of a pixel but a mea- 
sure of the contrast between line and side zones, i.e. a de- 
rived observation. H, is computed for both intensity and 
coherence. 
2.1.1 Intensity SAR intensity has a multiplicative noise 
model (Goodman, 1975, Caves, 1993). Therefore, the nor- 
malized intensity ratio r as a measure of contrast between 
two homogeneous regions has a constant false alarm rate. 
It is given by 
(IL I 
= =, = 6 
r = min (3 T, ) (6) 
where I, and I, are the mean intensities of both regions. 
The result of the evaluation of a template for a specific line 
direction is the maximum of the two normalized intensity 
ratios between the line zone and the side zones. This is 
a derived observation r, in pixel s. Hence, the energy is 
given by 
2 
z^ fe €L 
H, (rsles) = 2; . (7) 
241 ic, —N 
Where c, is a constant, and t, is a threshold balancing the 
no-line state versus the line states. L is the set of line states 
with different line directions, and N is the no-line state. 
  
Figure 1: Model of the influence of a line pixel with horizon- 
tal direction. In the light irradiated field it supports, in the 
dark field it inhibits line pixels. 
Eq. (7) was inspired by normally distributed observations. 
Empirical investigations (Hellwich, 1997) have shown that it 
sufficiently agrees with the theoretically derived probability 
density of the normalized intensity ratio between homoge- 
neous regions with a known contrast (Lopes et al., 1993, 
Caves, 1993). 
2.1.2 Coherence For coherence an additive noise 
model is considered appropriate (cf. (Tough et al., 1994)). 
Therefore, the difference d of the mean coherence values 
having a constant false alarm rate was used as a measure 
of contrast between the regions. The derived observation 
d, for a pixel s is the minimum of the coherence differences 
between the line zone and both side zones. Corresponding 
with (7) the energy for differences d, is computed from 
(ds —n4)? feel 
a 207 S 8 
Hs(ds|€s) — (t zh )9? if = N ( ) 
d 
where pq is a very large coherence difference occurring in 
the evaluated data. It can be set relatively arbitrarily. t, is a 
threshold balancing the no-line state versus the line states. 
c4 is used for weighting the coherence data with regard to 
the intensity data. 
2.2 Markov Random Field Model 
As the MRF model is not essential for the fusion of the two 
data sources, it is described very briefly only. The purpose 
of the model is the detection of continuous, thin lines. It is 
designed to bridge speckle-related (short) gaps interrupting 
the lines. 
According to the model, each pixel with line state influences 
pixels in its neighbourhood. In a line pixels direction it 
supports the presence of line pixels with a corresponding 
line direction. The effect of this influence is a stronger line 
continuity, i.e. a closing of gaps. Perpendicularly to its di- 
rection a line pixel inhibits the presence of line pixels with 
the same direction, thus preventing the occurance of thick 
lines. These two types of influences a line pixel puts on 
its neighbourhood are modelled with the help of completion 
fields (Williams and Jacobs, 1995) which the pixel "radiates" 
(cf. Fig. 1). The two parameters of the model control the 
strengths of the line supporting and the line inhibiting fields. 
They are also used to weight the influence of the MRF prior 
with respect to the data. 
Summarizing, line extraction is controlled by the parame- 
ters t., t4, and c, for data evaluation, and the line sup- 
porting and the line inhibiting parameter of the MRF model. 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 533