Prof. Pierfrancesco Lombardo ^{(1)}, Tiziana Macrì Pellizzeri^{(1)}
, Marco Meloni^{(1)}
, and Massimo Sciotti^{(1)}

A new technique, named DPOL MUM, is proposed for
the segmentation of multifrequency polarimetric SAR images,
that exploits the characteristic block diagonal structure
of their covariance matrix. This technique is based on the
newly introduced split-merge test, that has a reduced
fluctuation error than the straight extension of the
polarimetric test (POL MUM) and is shown to yield a more
accurate segmentation on simulated SAR images. DPOL-MUM is
especially useful in the extraction of information from
urban areas that are characterised by the presence of
different spectral and polarimetric characteristics. Its
effectiveness is demonstrated by applying it to segment a
set of polarimetric SIR-C images of the town of Pavia. The
classification of the image segmented with DPOL MUM shows
higher probability of correct classification compared to
POL MUM and to a similar technique that does not use the
correlation properties (MT MUM).

Extended summary

It is
well known that multifrequency polarimetric SAR images
carry appreciably more information about the observed scene
than the single-channel SAR images. In particular, the
specific reflectivity at the different frequencies and both
the reflectivity and the phase relationships between the
different polarimetric channels provide useful indications
on the characteristics of the different observed objects,
allowing a more accurate classification [1-4].

Many
examples of both segmentation and terrain classification
using polarimetric SAR data can be easily found in
literature, with application to very different monitoring
and surveillance applications [5-10]. Many proposed
techniques operating with polarimetric SAR images are
suited to pixel-by- pixel classification on the basis of
the polarimetric properties, whereas it has been clearly
demonstrated (see [11], [1]) that large performance
improvement can be achieved by first segmenting the image
into regions with homogeneous characteristics, and then
classifying the resulting global regions. It is therefore
of interest to define optimal segmentation techniques for
the multifrequency polarimetric SAR images. Moreover, it
has been shown that the use of multifrequency polarimetric
SAR images yields a further improvement in the possibility
to identify and classify homogeneous regions with slightly
different terrain characteristics. An effective approach
for the segmentation of polarimetric SAR images has been
proposed in [12], [13], which can easily been extended to
perform the joint segmentation of any set of complex
correlated SAR images and therefore also to the case of
multifrequency polarimetric images. However, the
corresponding large increase of dimensionality implies also
an increased level of uncertainty in the underlying test,
that is a potential source of performance degradation.
However, it is usual to model the images acquired at
different frequencies as uncorrelated. This is also the
case for many other situations, as the case of
multitemporal set of images collected with long revisit
time, [14]. The exploitation of this model, that
corresponds to a block diagonal covariance matrix for the
multifrequency polarimetric images can largely reduce the
uncertainty in the segmentation test and yield much better
performance than the simple extension of the polarimetric
segmentation scheme. Therefore, the aim of this paper is to
derive optimal segmentation techniques that fully exploit
the statistical model of the multifrequency polarimetric
SAR images, and to evaluate their performance both
theoretically and on simulated data. The application to a
set of SAR images of urban areas shows the practical
results obtained with the proposed technique. The proposed
techniques use a generalised Maximum Likelihood (ML)
approach, based on the joint Probability Density Function
(PDF) of the pixels in each homogeneous region. In
particular, we adopt a multivariate Gaussian model to
describe the statistical behaviour of the single channels
(and therefore a complex Wishart model for the distribution
of the corresponding multilook complex data), thus the
statistical characteristics of the different regions are
encoded in the covariance matrix. The proposed segmentation
techniques are based on the use of an optimal split-merge
test to merge regions with similar characteristics (region
fusion), and they are totally unsupervised. The generalized
likelihood ratio test is used to derive the optimal test to
decide whether two adjacent regions should be split or
merged. The likelihood function is also the basis of the
proposed supervised classification technique. Based on the
results in [15], we extend to the general multifrequency
case the derivation of the ML segmentation technique
presented in [12], [13], which makes no assumption on the
structure of the covariance matrix and is particularly
suited for monofrequency, monotemporal polarimetric images.
Thereafter, we consider the special case of a covariance
matrix with a special, known structure that can be used as
a priori information to reduce the losses introduced by its
local estimation performed inside the algorithm. In
particular, we consider the case of a block diagonal
structure for the covariance matrix, that is usually the
case for multifrequency or multitemporal polarimetric SAR
data. Thus, we derive a ML segmentation technique
specifically designed for this case. A theoretical
performance analysis of the optimum model based Split-Merge
Test is presented. The analysis is used to set the
appropriate thresholds for the test as a function of the
desired false alarm probability and the regions size.
Simulation is then adopted to confirm these predictions.
Moreover, the two proposed approaches are compared, showing
that the use of the a priori information about the
covariance matrix structure results in an increased
capability to discriminate regions with different
characteristics. Finally, the proposed segmentation
techniques are applied to a set of polarimetric and
multifrequency (C and L band ) SIR-C images of the town of
Pavia, in Northern Italy.

References:

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[11] T. Macrì Pellizzeri, C. J. Oliver, P.
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and Optical Images", in print IEE Proceedings on Radar
Sonar and Navigation, 2002.

[12] P. Lombardo, C.J. Oliver,
"Optimal Classification of Polarimetric SAR images Using
Segmentation", IEEE Radar Conference 2002, Long Beach (CA),
April 2002.

[13] P. Lombardo, C.J. Oliver, "Optimal
Polarimetric Segmentation for the Classification of
Agricultural Areas", EUSAR 2002, Koeln, Germany, June 2002.

[14]P. Lombardo, T. Macrì Pellizzeri, "Maximum Likelihood
Signal Processing Techniques to Detect a Step Pattern of
Change in Multitemporal SAR Images", IEEE Transactions on
Geoscience and Remote Sensing, Vol. 40, No. 4, April 2002,
pp. 853-870.

[15] Lombardo P., Oliver C.J., "Optimum
Detection and Segmentation of oil-slicks using polarimetric
SAR data", IEE Proceedings on Radar, Sonar and Navigation,
Vol. 147, No. 6, December 2000.