(3.2) 
e change in 
|. and 0 and 
ariables with 
certain frac- 
1 
ayis./—e * 
'ge for strong 
figs. 3.2 and 
At each grid 
by state ac- 
on the curva- 
ing count for 
propriate di- 
of the count. 
V 
  
=0.02, 
  
  
  
1 1 1 1 L 1 1 L 1 1 
e 1 g 3 4 5 6 7 8 9 
Fig.3.3. Random walk simulation with K,=0, t=15, op=0.5, 6, =0.01. 
  
For the computation of the energies H (eo) a neighbor- 
hood system of two-site cliques is defined (Koch & Schmidt, 
1994). Each site has neighbors of varying order forming a 
clique with each of those neighbors. Fig 3.4 shows the neigh- 
borhood system of site s up to order 5. For an element e, of the 
state space Eg, the counts of the random walk model are 
summed clique by clique. Each count depends on the parame- 
ter values £r and €, i.e. on direction and curvature in the 
neighboring site f and the direction and curvature proposed at 
site s, as well as on the location of / with respect to s. If Er is 
"no line", the counts at s are 0 independent of £,. High counts 
for £, indicate a high probability of £,, as the presence of a 
neighboring line site supports the presence of a line with a 
certain direction and curvature. 
  
514130 475 
  
4121112 
  
  
4 
3 1 S 1 3 
d | 2/31 | 2, 4 
  
S4 4/3144 $5 
Fig. 3.4. Neighborhood system for a two-site clique Gibbs field. Site s and 
another site form a two-site clique of neighborhood order n shown in 
the graph. 
  
  
  
  
  
  
  
We now extend our two-site clique neighborhood model, as a 
line should also make certain neighboring lines improbable. 
This is because line sites parallel to a directly neighboring line 
site do not conform with the elongatedness of lines. It can be 
modeled with the same type of random walks. We only 
imagine a different type of particles, called inhibiting particles, 
diffusing perpendicularly to the direction of a line site. The 
particles inhibit the presence of lines perpendicular to the 
direction of propagation in the same way the particles used 
before supported the presence of lines in the direction of 
propagation. Therefore, the corresponding counts make the 
presence of those lines improbable and are subtracted from the 
supporting counts. 
Introducing a one-site clique containing only s, we can control 
the overall probability of a line independent from the state of 
neighboring sites. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
Hence, in agreement with (2.8), H,Íe,|àe;) is computed from 
a o -In(c)-» i£c2z1 (2 
AENOE = : 
SNESIENST Vd In(1) if C<1 
C= Cy, (e,) SY Ca, (eles: sie A;) 
A, 
where C, ] is the count-equivalent of the one-pixel clique: 
C if €, ="line(6,, K;}" 
C. (e,) 4 l 5 ( 3 J i 
1 " : " ; " 
à if €, ="no-line 
cj and c,, are empirically chosen "basic currents" which control 
the overall probability of line and no-line sites. »,C 4, is the 
A» 
sum of the counts of the two-site cliques containing s. 
3.2 Specific Knowledge from GIS Data 
The intention is to use GIS data to support the extraction of 
linear structures. It may for instance be known that a road is 
crossing the imaged area, and an approximate registration of 
the SAR scene and the GIS data may be given. Around the 
projection of the road center line into the SAR scene the prob- 
ability to detect a line with the direction and curvature of the 
road center line should be increased. These facts have to be 
used to compute the energy of the prior PDF. 
It is known that the registration of SAR and GIS data can only 
be accurate to a limited degree. What is more, the decision 
about the exact location of the linear structure in the results of 
the algorithm has to depend on the SAR data and not on the 
given geographic information. Therefore, a corridor symmetri- 
cal around the object center line is defined inside of which the 
probability of the object class e, = line(0;,x;) is uniformly 
increased. 0;, K; are the direction and curvature of the object 
center line at the point i closest to site s (Fig. 3.5). 
Center ] ine 
    
a | corridor 
Fig. 3.5. Corridor around an object center line in which the detection of 
lines with direction and curvature of the object center line is 
increased. 
The parameters of the algorithm are the width of the corridor 
which depends on the accuracy of the registration, and the 
amount by which the probability of line detection is increased. 
The increase in probability is taken into account by changing 
the computation of Ca; in (3.3) to 
315