The sites are visited once per iteration in a random sequence.
For simulated annealing the object parameters of the sites are
randomly initialized with the proportions between line and no-
line sites given by cj and c, according to (3.3). The computa-
tion of probability densities from energies is conducted as
p(x,px, e exp ee (5.1)
(cf. (2.8)) where T is a temperature variable. It is decreasing
according to a cooling schedule
1
C-lni
where C is a cooling constant and i is the index of the current
iteration. A theoretical value for C which ensures that the
simulated annealing procedure finally leads to a global opti-
mum exists, but it would require prohibitorily many iterations
until stability and the optimum were reached. Therefore, fast
cooling with an empirical value of C close to 1 was used.
Tz (5.2)
For the ICM algorithm € is initially set to the maximum likeli-
hood interpretation of the image which is the result when each
site is visited once and E, is set to the object parameter €
which gives the minimum energy H, (ysl£s). i.e. the maximum
conditional density py ( »,le.) of the observations given the
object parameter. During ICM estimation the discrete condi-
tional PDF is computed in the same way as for the Gibbs
sampler. In each site E, is set to the value € with the maximum
conditional posterior probability p(es]ys 08s). The algorithm
stops when p(ely) reaches a maximum, i.e. when no sites
change their states any more.
6. RESULTS
The model of continuous curvilinear structures based on
random walk simulations was tested by Gibbs sampling from
the prior PDF p(e). For a 128 by 128 pixels image we obtain
results such as the one shown in Fig. 6.1. The picture shows
thin curvilinear features some of which are connected starting
to form a network. This is not quite what would be expected of
a road network. But consider that the model is based on
comparatively small neighborhoods. What is more, Gibbs
sampling means drawing random samples from the complete
configuration space where transitions between the most prob-
able states can only occur by changing the state of single sites,
i.e. by obtaining less probable states. Therefore, this result is
acceptable.
A TOPSAR airborne data set consisting of intensity (Fig. 6.2)
and coherence (Fig. 6.3) was evaluated. Fig. 6.4 shows the
response of the intensity-ratio operator based on detector
masks for 3 pixel wide dark lines aiming at the detection of
narrow roads. This is the information contained in the data
which is handed over to the Bayesian inference procedure. Fig.
6.5 shows the result of a maximum likelihood classification of
the intensity data which is equivalent to thresholding the
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
intensity-ratio response of Fig. 6.4. The result is noisy, lines
vary strongly in width and direction, and have several gaps.
Note that this is a result obtained without using prior
knowledge about the continuity of linear structures. Fig. 6.6
shows the result of 25 iterations of simulated annealing. Many
of the gaps have been closed even in locations where the ratio
image does not show a significant response of the ratio line
detector, the width of the lines usually is small and does not
vary much, and the detected directions are stably following the
directions of the lines. This demonstrates the usefulness of the
line model.
Fig. 6.7 results from 25 iterations of simulated annealing
evaluating both intensity and coherence data. In comparison to
Fig. 6.6 an improvement of the line extraction can be realized.
Fig. 6.8 shows the corridor generated from a road center line
given in a GIS. Once this data is included into the estimation
procedure this road can be detected more easily (see Fig. 6.9).
7. CONCLUSIONS AND RECOMMENDATIONS
We proposed a new approach for the extraction of linear struc-
tures from SAR intensity and coherence data in a Bayesian
framework using an MRF to model continuous curvilinearity.
Test results demonstrate the plausibility of the MRF line
model as well as the usefulness of combining SAR intensity
with coherence and given GIS data when extracting linear
objects.
Further tests of the approach are necessary. Presently, we con-
sider improvements regarding speed and scale space integra-
tion. Computational speed could be gained by using local
highest confidence first (LHCF) estimation (Chou et al., 1993)
which would implicitly relate the algorithm to line following
algorithms. Scale space requirements can presently be met by
using different line widths in the detector masks. A more
effective way would be the use of an image pyramid or a multi-
resolution MRF model (Lakshmanan & Derin, 1993; Bouman
& Shapiro, 1994). We intend to make these topics subjects of
future publications.
ACKNOWLEDGMENTS
We thank Vexcel Corporation, Boulder, for providing the test
data set.
REFERENCES
Adair M., Guindon B. [1990]: Statistical Edge Detection Operators for
Linear Feature Extraction in SAR Images, Canadian Journal of
Remote Sensing, Vol. 16, No. 2, pp. 10-19.
Arduini F., Dambra C., Regazzoni C. S. [1992]: A Coupled MFR Model
for SAR Image Restoration and Edge-Extraction, IGARSS '92,
Houston, Vol. 2, pp. 1120-1122.
Bellavia G., Elgy J. [1986]: Spatial Feature Extraction from Radar
Imagery, Symposium on Remote Sensing for Resources Develop-
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