deforma- 
1e motion 
ted. This 
p in linear 
1s have to 
1997). 
5 with sig- 
ns whose 
Using rib- 
optimizing 
er to rep- 
t) can be 
d Leclerc, 
1, (13) 
he ribbon 
0, to) and 
All center 
. Figure 2 
on snake, 
he advan- 
13) is that 
nt Can be 
dth of rib- 
the same 
'nal forces 
hand con- 
ie. On the 
on the rib- 
mation for 
the center 
t and right 
the ribbon 
so, to) COr- 
Adapting 
on (10) to 
n (11) has 
0 be large 
an be de- 
les on the 
(14) 
which are 
idings, the 
irection of 
ribbon will 
he extrac- 
age inten- 
k to bright 
at its right 
anding the 
to be neg- 
itive along 
ie function 
s,t). (15) 
  
      
  
U(s,t) 
0°" 
— 
D (s.t) 
L'*0?'0 
= 
Ü, (s, > t) 
  
  
  
  
(b) 
(a) Parametric representation of the rib- 
Each slice v(so,to) is identified by center 
(z(so, to), y(so, to)) and width 2w(so,to). (b) Image gradi- 
ents for the two sides of the ribbon and their projection onto 
the ribbon's unit normal vector (so, to). 
Figure 2: 
bon snake. 
3.3 Ziplock Principle 
A problem often encountered is the following: to make in- 
teraction as efficient as possible only the end points of the 
snake are given manually. The direct straight connection of 
these end points can — especially close to the center — be 
far off from the linear object to be extracted by the snake. 
When optimizing the whole snake at a time this is not only 
ineffective, but the snake can also get stuck in local min- 
ima. To overcome this, the “ziplock” method was introduced 
in (Neuenschwander et al., 1995). There, the information 
is gradually propagated from the ribbon's ends towards its 
center by optimizing only parts of the snake at a time while 
approaching the center. The curvature of the snake is con- 
strained to be low. By this means the "active" parts of the 
snake remain close to the linear feature during the whole 
optimization. The whole snake and the linear feature be- 
have like a ziplock which is closed from both ends. 
4 RESULTS 
A part of an ERS tandem data set from the Siberian low- 
lands is used to demonstrate the new method. It contains 
straight pipelines and roads. Figure 3 shows the magni- 
tude and Figure 4 the coherence. Figures 5 and 6 display 
the line pixels extracted with the MRF method. The result 
shown in Figure 5 is based on intensity data only. It can 
be seen that it does not contain the pipelines in the lower 
half of the image where they cross a river. This is different 
when the extraction is based on a combination of intensity 
and coherence data as displayed in Figure 6. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
  
Figure 3: Multitemporal histogram-equalized magnitude of 
an ERS-SAR scene. 
  
Figure 4: Multitemporal histogram-equalized coherence of 
an ERS-SAR tandem interferogram. 
The posterior odds of the most probable line states versus 
the no-line states are shown in Figure 7. They combine the 
basic line information of intensity and coherence data, and 
are, therefore, input of the interactive ziplock snake-based 
pipeline extraction. Figures 8 and 9 show five extracted 
pipelines and roads superimposed to the magnitude and 
the coherence image. A careful visual inspection reveals 
that a correct extraction of the pipelines would not have 
been possible with one of the data sources alone. The 
magnitude does not contain any line information in the flu- 
vial plain of the river, and the coherence does not show 
sufficient line information in the upper part of the image. 
The ziplock method was of major importance for the suc- 
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