Unsupervised Classification of Complex Scenes using Polarimetric

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					      Unsupervised Classification of Complex Scenes using Polarimetric
                        Interferometric SAR Data.
                                             L. Ferro-Famil, E. Pottier
                                   IETR, UMR CNRS 6164, University of Rennes 1,
                                   Campus de Beaulieu, Bât. 11D, 35042 Rennes, France.



Abstract: This paper introduces an approach to the                   medium and high degree of randomness along the entropy
classification and interpretation of SAR data using                  axis.
complementary       polarimetric    and     interferometric
information. Polarimetric data are first classified into
canonical scattering types. The interpretation and the
segmentation of an optimized interferometric coherency
set leads to the discrimination of different natural media
that cannot be achieved with polarimetric data only. The
resulting classes show an enhanced description and
understanding of the observed scene.
Keywords: SAR, Polarimetry, Interferometry, Statistical
segmentation


                     1. Introduction
Polarimetric SAR data classification has been widely
addressed in the last decade [1-3]. Interferometric data
provide information concerning the coherence of the
scattering mechanisms and can be used to retrieve
observed media structures and complexity [4][5]. An
example of the complementary aspect of polarimetric and
interferometric information is given with polarimetric
interferometric data acquired by the DLR E-SAR sensor
at L band in repeat-pass mode with a baseline of 10m. It
can be observed in Fig. 1 that a polarimetric color-coded
image and a coherence image give different descriptions
of the observed scene.
This paper introduces an unsupervised classification
process, gathering complementary information contained
in polarimetric and interferometric data and based on
polarimetric decomposition theorems [3], multivariate
Wishart [6][7] density functions and optimal
interferometric coherence set [4][5].

2. Unsupervised Classification of POL-SAR data
2.1 Unsupervised H-α classification

This classification procedure is based on the polarimetric
decomposition introduced by Cloude and Pottier[2][3].
They propose to identify in an unsupervised way                      Figure 1 : Optical image (top), polarimetric color
polarimetric scattering mechanisms in the H- α plane sub-            coded image (middle) and interferometric coherence
                                                                     (bottom) over Oberpfaffenhofen
divided into 8 basic zones so as to discriminate surface
reflection (SR), volume diffusion (VD) and double                    Detailed explanations, examples and comments
bounce reflection (DB) along the α axis and low,                     concerning the different classes can be found in [2][3].
                                                                     This unsupervised estimation of the type of scattering

                                      RADAR 2004 - International Conference on Radar Systems
mechanisms may reach some limitations due to the
arbitrarily fixed linear decision boundaries in the H- α
plane which may not fit data distribution.

2.2    Combined     Wishart      H-A- α      Unsupervised
Classification Schemes

2.2.1 Wishart H- α Segmentation

Lee et al. [1][6] introduced an unsupervised ML
segmentation procedure based on the Wishart statistics of
multilook coherency matrix.          A k-mean iterative
clustering algorithm is used to assign, at each iteration, a
sample coherency to the nearest class according to a ML
decision rule. Cluster centers are initialized with the                         C1   C2    C3   C4   C5   C6   C7    C8
results of the unsupervised identification of a scattering
mechanism. This initialization provides 8 classes relating
to the underlying physical scattering mechanism and
giving a stable initial approximation of the segmentation.
Results obtained using Wishart H- α segmentation are
displayed in Fig. 2. The main kinds of natural media are
clearly discriminated by this segmentation scheme.

2.2.2 Wishart H-A- α Segmentation

Pottier and Lee [8] further improved the ML Wishart
unsupervised segmentation by explicitly including the
anisotropy information during the segmentation
procedure. This polarimetric indicator is particularly                          C1   C2    C3   C4   C5   C6   C7    C8
useful to discriminate scattering mechanisms with
different eigenvalue distributions but with similar                             C9   C10   C11 C12   C13 C14   C15   C16
intermediate entropy values. Segmentation results
presented in Fig. 2 show an enhanced description of the             Figure 2 : Wishart H- α segmentation results (top),
Oberpfaffenhofen scene. The introduction of the                     Wishart H-A- α segmentation results (bottom)
anisotropy in the clustering process permits to split large
segments into smaller clusters discriminating small
disparities in a refined way.

    2.3 Unsupervised Identification with Canonical
               Scattering Mechanisms
An efficient estimation of the nature of scattering                                                                    SR
mechanisms over natural scenes can be achieved by
gathering results obtained from the polarimetric
decomposition and segmentation procedures presented in
the previous paragraphs [9]. Volume diffusion and double                                                               DR
bounce scattering were found to be over-estimated during
the identification of scattering mechanisms using the H- α
segmented plane, due to perturbing secondary terms. H                                                                  VD
and A may be used to restrict the polarimetric study to the
most significant contributions. Specific identification             Figure 3 : Unsupervised identification to canonical
procedures may then be applied in the H-A plane [9]. The            scattering mechanisms
identification results are shown in Fig3. The unsupervised
classification results show a good discrimination of the
three basic scattering mechanisms over the scene under
consideration. It may be noted that the identification
assigns some buildings to the volume diffusion class.
Polarimetric properties as well as the power related
information do not permit to separate these targets from
forests.

                                     RADAR 2004 - International Conference on Radar Systems
  3. Polarimetric Interferometric SAR data analysis                         the projection vectors, w1 and w 2 , to maximize the
3.1 Polarimetric interferometric representations                            modulus of the coherences [4][5]. The results of the
                                                                            optimization procedure show an enhanced contrast
The polarimetric interferometric behavior of a target is                    between the different optimal coherences.
fully described a six element complex target vector, k 6 ,
                                                                                 4. Unsupervised Classification of Polarimetric
obtained by stacking target vectors from each
                                                                                          Interferometric SAR data
interferometric image. The corresponding (6×6)
interferometric coherency matrix is given by [3]:                           The color-coded image presented in Fig. 4 represents the
                                                                            joint information associated to the optimal coherencies
       1              T             T12          k 1 
T6 =     ∑ k 6 k †6 = T †1
       n n                           T2  , k 6 = k            (1)       and reveals particular behaviors of different types of
                       12                          2                     natural medium under examination.
T1 and T2 are the standard n-look (3×3) hermitian sample                    White areas indicate targets showing high coherence
                                                                            independently of the polarization. Such a behavior is
covariance matrices for separate images. T12 is a (3×3)                     characteristic of point scatterers and bare soils. Green
complex matrix which contains information about the                         zones reveal the presence of a single dominant coherent
interferometric correlation between k 1 and k 2 .                           mechanism within the resolution cell. Such zones
                                                                            correspond to surfaces with low SNR responses and some
3.2 Polarimetric interferometric coherence set                              particular fields. Forested areas, characterized by a dark
                                                                            green color have scattering features dominated by a single
The sample interferometric correlation matrix, T12 , has                    mechanism but with a very low coherence.
                                                                            Coherence related information permits to discriminate
complex diagonal elements, from which is computed a
                                                                            particular buildings that cannot be separated from forested
three polarimetric complex coherence set (γ 1, γ 2 , γ 3 ) , as             areas using only polarimetric data. Over forested areas,
follows:                                                                    the polarimetric color-coded image shows homogeneous
                                                                            zones, while interferometric data indicate that there exist
                                      *
                                 k1i k2i                                    large variations of the coherent scattering properties
                 γi =                                             (2)       corresponding to clear-cuts and low-density forest.
                                           *
                             k1i k1*i k2i k2i
                                                                                                                                     | γopt 1 |
where the operator < > stands for the sum over n samples
represented in (1). Standard real coherence values are
                                                                                                                                     | γopt 2 |
obtained from the modulus of γ i , while its arguments
correspond to the interferometric phase difference. It may
be noted that the coherence defined in (2) is not invariant
                                                                                                                                     | γopt 3 |
under a change of polarimetric basis. In general,
coherence may be decomposed into multiplicative
contributions as :

             γ = γ SNR .γ spatial .γ temporal .γ polar            (3)

where the different terms indicate decorrelations related
respectively to the back-scattered wave signal to noise
ration, the spatial distribution of the illuminated scatterers,             Figure 4 : Color-coded image of the optimal
temporal variations between the acquisitions and finally                    coherence set (top), segmentation results over the
the polarization state. Cloude and Papathanassiou [4][5]                    Volume Diffusion class (center), and all three
introduced the following original formulation of the                        canonical scattering mechanisms (bottom)
interferometric coherence:
                     †                                                      4.1 Optimal coherence set analysis
                   w 1 T12 w 2
    γi =                                                       (4)
               †                                                            In order to analyze the polarization related part of the
             w 1 T1w 1      w † T2 w 2
                              2                                             optimal coherence set, two parameters are built from
where w1 and w 2 are three elements complex vectors                         relative coherence quantities.
permiting to compute the interferometric coherence of a                                  γ opt 1 − γ opt 2            γ opt 1 − γ opt 3
polarization channel in any emitting-receiving                                    A1 =                       , A2 =                               (2)
polarization basis. Papathanassiou and Cloude further                                         γ opt 1                      γ opt 1
developed this concept to define an optimal coherence set
                                                                            These parameters indicate relative amplitude variations
(γ opt 1, γ opt 2 , γ opt 3 ) , with γ opt 1 ≥ γ opt 2 ≥ γ opt 3 . The      between the different optimized channels. The indicators
optimal coherence set is obtained by analytically tuning                    A1 and A2 may be used to estimate the number of
                                                                            independent coherent scattering mechanisms from the
                                             RADAR 2004 - International Conference on Radar Systems
optimization results. The different optimal coherence set              The classification algorithm processes the different
configurations are represented and identified in Figure 5.             canonical scattering mechanisms separately. Pixels
 A2                                                                    belonging to one of the typical scattering type shown in
                                                                       Fig. 3 are segmented using the optimized coherence set
                                                                       and statistical metrics [9]. Results for the Volume
                                                                       Diffusion and Surface Reflection classes are shown in
                                                                       Fig. 7.
                                N/A


                     N/A        N/A

                                              A1

       A2
            1




        0.5
                                                                                                                    VD   SR   DR




            0         0.5       0.9 1
                                         A1

Figure 5 : Discrimination of different optimal
coherence set using A1 and A2 (top). Selection in the
A1-A2 plane (bottom).
The schematic on the left hand side of Figure separates
the different optimal coherence set configurations in five
classes. The real segmentation from A1 and A2 is realized
over nine classes in order to improve the resulting clusters
descriptivity and accuracy. Results of the normalized
optimal coherence set classification are shown in Fig. 6.
                                                                       Figure 7 : Color-coded image of the optimal
Approximately four major classes arise from the
                                                                       coherence set (top), segmentation results over the
identification of the optimal coherence set distribution.
                                                                       Volume Diffusion class (center), and all three
This unsupervised segmentation was also found to
                                                                       canonical scattering mechanisms (bottom)
achieve a high degree of descriptivity on other scenes
observed with different baselines. This is a consequence
of both the coherence optimization and the definition of               Clusters resulting from the segmentation are assigned a
relative coherence indicators.                                         color indicating their average coherence, ranging from
                                                                       dark for low coherence to light for high coherence.
                                                                       Globally, polarimetric interferometric characteristics are
                                                                       efficiently segmented into compact clusters corresponding
                                                                       to scatterers with similar polarimetric and interferometric
                                                                       characteristics. The segmentation of the Volume
                                                                       Diffusion class successfully discriminates buildings,
                                                                       dense forest, sparse forest and clear-cuts. Details of the
                                                                       classification are displayed in Fig. 8 for two particular
                                                                       zones corresponding to the DLR buildings and forest
                                                                       parcels.




Figure 6 : Unsupervised identification of the number
of coherent scattering mechanisms.



                                        RADAR 2004 - International Conference on Radar Systems
a)                                                                                        5. Conclusion
                                                                 Data acquired in polarimetric and interferometric modes
                                                                have complementary characteristics; their joint use in a
                                                                classification process provides significantly higher
                                                                performance. The classification approach resides on
                                                                separate     polarimetric    and     interferometric    data
                                                                classification and interpretation. Each scatterer is
                                                                accurately identified to a basic scattering mechanism
b)                                                              using efficient polarimetric indicators. A parameterization
                                                                of an optimal interferometric coherence spectrum is used
                                                                to segment data according to their interferometric
                                                                properties. Finally, an unsupervised classification process,
                                                                gathering polarimetric and interferometric results, is
                                                                applied to each canonical scattering mechanism. The
                                                                resulting images show significant improvements
                                                                compared to the strictly polarimetric case.
c)
                                                                                          6. References
                                                                  [1] J.S. Lee, M.R. Grunes, R. Kwok, " Classification of multi-
                                                                      look polarimetric SAR imagery based on the complex
                                                                      Wishart distribution ", International Journal of Remote
                                                                      Sensing, vol. 15, No. 11, pp 2299-2311, 1994.
                                                                  [2]     L. Ferro-Famil, E. Pottier, J. S. Lee, "Unsupervised
                                                                      classification of multifrequency and fully polarimetric
d)                                                                    SAR images based on the H/A/Alpha-Wishart classifier",
                                                                      IEEE Trans. GRS, vol. 39, n°11, pp 2332-2342,
                                                                      November 2001.
                                                                  [3] S. R. Cloude, E. Pottier " A Review of Target
                                                                      Decomposition Theorems in Radar Polarimetry ", IEEE
                                                                      Trans. GRS, vol. 34, n°2, pp 498-518, September 1995.
                                                                  [4]     S. R. Cloude, E. Pottier " An Entropy Based
                                                                      Classification Scheme for Land Applications of Polari-
                                                                      metric SAR ", IEEE Trans. GRS, vol. 35, n°1, pp 68-78,
e)                                                                    January 1997.
                                                                  [5] Cloude, S. and K. Papathanassiou, “Polarimetric SAR
                                                                      Interferometry”, IEEE Trans. GRS, vol. 36 (4), pp. 1551-
                                                                      1565.
                                                                  [6] Papathanassiou, K. P. and S. Cloude, “Single-baseline
                                                                      polarimetric SAR interferometry”, IEEE Trans. GRS. 39
                                                                      (6), 2352-2363, November 2001
                                                                  [7] J.S. Lee, M.R. Grunes, T.L. Ainsworth, L. Du, D.L.
                                                                      Schuler and S.R. Cloude "Unsupervized Classification of
                                                                      Polarimetric SAR Images by Applying Target
Figure 8 : Polarimetric Interferometric                               Decomposition and Complex Wishart Distribution ", IEEE
classification results over two areas. a)                             Trans. GRS, vol. 37, no.5, pp2249-2258, Sept. 1999.
polarimetric color coded image b) optimal                         [8]     E. Pottier, J.S. Lee, "Unsupervised Classification of
coherence set color coded image c) volume                             PolSAR images based on the Complex Wishart
diffusion classification results d) surface                           Distribution and the H/A/α Polarimetric Decomposition
reflection classification results e) Global                           Theorem", EUSAR, Munich, Germany, May 2000.
classification into three canonical mechanisms                    [9] L. Ferro-Famil, E. Pottier, J.S. Lee, " Classification and
                                                                      Interpretation of Polarimetric Interferometric SAR data",
including double bounce reflection                                    "Frontiers of Remote Sensing Information Processing".
                                                                      C.H. CHEN. Chief Editor, Ed. World Scientific
                                                                      Publishing, July 2003




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