WEIGHTED PYRAMID LINKING FOR SEGMENTATION OF FULLY-POLARIMETRIC
SAR DATA
Ronny Hansch, Olaf Hellwich
Berlin Institute of Technology, Computer Vision and Remote Sensing
Franklinstrasse 28/29, Office FR3-1, 10587 Berlin, Germany.
Tel. +49 30-314 73 107, Fax. +49 30-314 21 104, E-mail: rhaensch@fpk.tu-berlin.de
KEY WORDS: SAR, Segmentation, Polarization, Algorithms, Multiresolution, Spatial
ABSTRACT:
Image segmentation has the general goal to define regions within an image, in which all pixels have similiar properties. For fully-
polarimetric SAR data this is often done by spectral classification without any use of spatial information. On the contrary the proposed
method aims to find homogenous segments in the image, which should be compact and connected if possible. A multiresolution
image pyramid allows to calculate information based on regions of different size instead of single pixels or small neighbourhoods.
Furthermore, a relaxation approach is used to defer the segmentation decisions until more accurate information is available.
1 INTRODUCTION
Image segmentation is an important preprocessing step in many
applications. Numerous tasks such as classification, object de
tection and so forth can be achieved much more easily and accu
rately given an appropriate segmentation.
Due to the coherent nature of SAR sensors homogeneous ar
eas are no longer homogeneous in the image, but contain strong
multiplicative distortions. This speckle effect poses severe prob
lems to spatial segmentation algorithms. A lot of work is done
for radiometric classification without using any spatial informa
tion, e.g. (Lee et al., 1997, Ferro-Famil et al., 2001, Anfinsen et
al„ 2007, Hansch et al., 2008) and there are very few approches
that try to combine spatial context and radiometric evidence as in
(Reigber et al., 2007).
I
In this paper, the segmentation algorithm proposed in (Hong and
Rosenfeld, 1984) is used to automatically derive the hierachical
structure of an image of fully-polarimetric SAR data. It is based
on a multiresolution image pyramid with the original image at
the base. Each higher level of the pyramid contains the image in
a lower resolution. The different resolutions are obtained by sim
ply averaging pixels in overlapping windows of certain size dur
ing the initialisation. Due to the overlap and window size each
element in the pyramid has several parents (at the next higher
level) and descendents (at the lower level).
Most algorithms for segmentation work with hard decisions: that
means, each pixel is uniquely assigned to a certain cluster or seg
ment. Other methods, which merge or split regions, have to de
cide for each region whether to split or to merge it. Because the
true segments or clusters are apriori unknown, such hard deci
sions will be erroneous for some pixels. That is why the forced-
choice aspect of segmentation has, in practice, a negative influ
ence on the final segmentation result. Particulary, if it is difficult
to undo wrong decisions made at the beginning. The algorithm
presented avoids this by labelling links between each element and
its parents with a certain link strength, representing the degree of
association between node and parent. This association is based on
a distance measure between the value of this pixel and the values
of its parents. As this algorithm is applied to fully-polarimetric
SAR data a distance measure is chosen, which respects the statis
tical properties of such data and is based on the Wishart distribu
tion. Having established a set of weights, pixels at higher levels
can be updated by the weighted average of the values of their de
scendents.
The entire process is then iterativly repeated until convergence,
at which point a segmentation can be extracted. Some pixels in
the pyramid will have small link strengths to all of their parents.
They form independent subtrees in the pyramid and represent the
searched segments.
2 THEORETICAL BACKGROUND
2.1 Fully-polarimetric SAR data
Fully-polaritmetric SAR data measure amplitude and phase of the
backscattered signal in four different transmit and receive polari
sation combinations. However, a common assumption is that the
cross polarisations are the same due to the reciprocity of natural
targets. Therefore each data point is a three dimensional vector s:
s = (Shh , V2S hv,Svv) (1)
where Srt is a complex component of the scattering matrix and
R £ {H, V} is the receive and T £ {H, V} is the transmit po
larisation.
Often the data is represented as spatially averaged sample covari
ance matrix in order to reduce speckle and get more statistical
information:
n
c = - V Sisf (2)
n z '
¿=i
where H denotes the conjugate transpose and n is the number
of samples used for averaging. If the distribution of s is a mul
tivariate complex Gaussian with zero mean, which is a standard
assumption when dealing with fully-polarimetric SAR data, the
sample covariance matrix C of s is complex Wishart distributed.
s ~ ZV(0,£) C ~ W(n,£)
(3)
