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Using Complete Polarimetric
Information in Fuzzy Neural Classification of SAR Image Based on Complex
Gaussian Distribution
Chia-Tang CHEN1 and K. S. CHEN1,2
1Institute of Space Science
2Center for Space and Remote Sensing Research
National Central University
Chung-Li, TAIWAN
Chia-Tang CHEN1 and K. S. CHEN1,2
1Institute of Space Science
2Center for Space and Remote Sensing Research
National Central University
Chung-Li, TAIWAN
Keywords: Polarimetric,
Fuzzy, Neural Network, SAR, Classification
Abstract
This paper develops a supervised algorithm by incorporating the polarimetric statistics into a fuzzy dynamic neural network (Chen et al., 1996)(Tzeng and Chen, 1997) using a multilook complete polarimetric information. The method makes use of inherent statistical properties of the polarimetric data and hence the information is fully explored. A set of P-L-C-band images acquired by JPL airsar during the PACRIM'96 campaign were used as test images. Validation and effeteness of the proposed scheme were able to demonstrate the utilization of complete polarimetric information. It has been shown that with complete polarimetric data, the fuzzy neural network has substantially reduced its training time and improved the classification accuracy as well. A Lee polarimetric filter was applied to reduce speckle level while preserving the polarimetric properties and is proven to be useful to improve the classification accuracy. The approach also demonstrates the adaptability and flexibility for high dimensional feature vectors such as the complete polarimetric presented here.
1. Introduction
In classification of SAR image, three linear polarized data (diagonal term of covariance matrix) is often used and a proper classification results could be obtained (Chen, 1996; Tzeng, 1997). As stated in (Lee et al., 2000), there are basically three approaches: 1) algorithms based on image processing techniques, 2) algorithms based on a statistical model, and 3) algorithms based on em wave scattering mechanisms. Approach 1) can be supervised or unsupervised, while 2) and 3) are devised to be supervised only. Supervised and unsupervised algorithms are complementary to each other; each has its own advantages and disadvantages, depending on their purposes and applications. In all image classifications, still only partial polarimetric data are mostly often utilized. Hence, one has not yet taken full advantage of polarimetric data. This certainly does not necessarily mean that partial polarimetric data is not sufficient for the applications cited there. However, it may miss some important information that is embedded in the off-diagonal term of covariance matrix. For this purpose, a neural fuzzy classifier based on Wishart distribution for fully polarimetric SAR is demonstrated in this paper.
2. Polarimetric Sar Image
2.1 Statistical Properties
A polarimetric SAR records the matrix S. A scattering matrix S is a relationship between the incident field and the scattering field
where the subscripts in S denote the polarized states, and k is incident wavenumber, r the range from radar antenna to target center. With the complex scattering matrix S available, the interactions of radar waves and target medium can be fully described in the sense of complete polarization response. For simplicity, a complex vector v may be defined by elements of S as
where T denotes the matrix transpose and q the dimension of v, q = 4 for bistatic case and q = 3 for backscatter case by duality theorem stating Svh==Shv for a reciprocal medium. SAR is a coherent imager and thus unavoidably suffers from speckle noise. This degrades image quality. Thus, SAR images are usually multi-look processed by averaging several neighboring one-look pixels. For polarimetric SAR system, it requires averaging several one-look covariance matrices
where vi is ith look elements vector in Eq. (3), n is number of looks, Z is a Hermitian matrix. The statistics of the Z has a complex Wishart distribution [Lee, 2000)
where C= < Z > denotes the feature covariance matrix and < > the ensemble average.
2.2 Polarimetric Speckle Filter
SAR image records the scattered echoes from the scatterers within the illuminating cell. It causes speckle phenomena. To obtain better classification results, the despeckle procedure is performed before the SAR image is applied for classification. A new despeckle technology proposed and proven well suited for fully polarimetric SAR data [Lee, 1999] is applied in filtering the speckle of the SAR image in this study.
3. A Statistical Fuzzy Neural Classifier
3.1 Fuzzy Clustering
In the fuzzy c-means algorithm, the position of a class or cluster center is found to be the average of the positions of all the patterns in that cluster, based on minimizing the sum of the variances of all variables i within a domain D for each pattern in each cluster l. And membership function![]()
, is introduced to weight the distance
measure and to define the problem of finding the fuzzy c-partitions with a
fuzzy index m, ![]()
. That is, to adjust the position of , the
cluster center, by minimizing the fuzzy c-means functional
where
is a fuzzy c-partition of X , X=(x1, x2, xN) is a set of training N vector, and![]()
is the membership of the
ith pattern to lth cluster; ![]()
is
the cluster center of X; In [Bezdek, 1987), the distance measure is
defined by ![]()
where ![]()
denotes the matrix norm. In
order to incorporate the statistical information of SAR, the distance in
fuzzy c-means functional is replaced by the following form
where is class center of the l-th class, C1 is the feature covariance matrix of class l, and Tr denotes the trace of a matrix. Without a prori information, an equal probability for each class is assumed. To merge multifrequency data, a linear combination leads to a similar distance measure as
where Ci(J) and Zi(J) are the feature matrix and the covariance matrix for j-th band, and K is the total number of frequency bands.
Differentiating![]()
with respect to ![]()
and
applying the constrain
to find the minimum of![]()
, we obtain
and
In fuzzy c-means algorithm, the fuzzy membership is obtained by iterative procedure of Equation (11) and (12).
3.2 Neural Implementation
The classification scheme used in this study is a neural network, called dynamic learning neural network (DLNN). DLNN has been applied in many applications. Such a neural network plays the role of connecting the input feature vector of SAR and the output membership vector. The input-output relationship can be simply expressed as
y=Wx (13)
where y is the output nodes and x is the input nodes. In this study, they are the membership vector of each pixel to a specific class and the feature vector of SAR, respectively. W is the weighting matrix of neural network. And the weighting matrix W is tuned by training process. By the use of the fuzzy membership vector as the output, DLNN becomes a fuzzy neural network (FDL)[Tzeng and Chen, 1997].
Fig 3: Configure Setup of FDL
The training process is a standard procedure for a supervised neural network. The necessary training set is formed by a set of input information and desire output. For purpose of using complete polarimetric information, the input data is the covariance matrix, and the desire output is the corresponding membership vector. The training set must be sufficient and non-ambiguous. Fig. 1 shows the configuration of the neural network. 4. Test Data and Results
The test data used in the study the L-band polarimetric SAR of San Francisco acquired by JPL AIRSAR. The image size is 1024x900 pixels. The land covers were classified into four class; they are ocean, tree (the park and the hill), urban and grass (the playground and ball park). Fig. 2 shows the un-filtered and filtered SAR image of San Francisco. To train the neural network, totally 1600 pixels training set is chosen from location of each class for training. For comparison, four setups using different inputs were devised, as given in Table 1.
Table 1 The setup of Test
Setup A and D used Wishart distribution as distance measure, while Setup B and C are to used to test the suitability of Euclidean to covariance matrix containing the polarimetric information. Fig.3 shows the final classification results with four different setups. It is observed that the Euclidean distance, devised in Setup B and C, confuses the FDL due to the ambiguity of the off-diagonal terms in polarimetric covariance matrix,; Setup A performs classification well but lack of the fuzzy information in it; Setup B uses only three linear polarizations (diagonal term in covariance matrix) information for classification, and loses some important information contained in off-diagonal term. Setup D uses the covariance matrix and applies the Wishart Distribution in fuzzy c-means iterations. Among the four setup, Setup D clearly outperforms the other three. From the network learning curves (not shown here) of all setups, it is also indicated that Setup D convergence much faster than the rest of setups. It means that by using the Wishart distribution in FDL, the algorithm could quickly hit the class center, and at the same time speed the learn rate.
5. Conclusion
A classification scheme for fully polarimetric SAR imagery data based on a dynamic fuzzy neural network has been proposed and its effectiveness and efficiency has been demonstrated. Complete polarimetric matrix can be easily formed as an n-tuple vector data as inputs to the network and all polarimetric information are naturally implicitly contained in the network. In conclusion, a fuzzy neural network-based classification method has been successfully developed to take advantage of fully polarimetric SAR.
![]()
(a)
![]()
(b)
Fig 2: SAR Image of San Francisco (a) Unfiltered (b) Filerted
![]()
(a)
![]()
(b)
![]()
(c)
![]()
(d)
Fig 3: The classifications Results (a)setup A, (b)setup B,
(c)setup C, (d)setup D.
Abstract
This paper develops a supervised algorithm by incorporating the polarimetric statistics into a fuzzy dynamic neural network (Chen et al., 1996)(Tzeng and Chen, 1997) using a multilook complete polarimetric information. The method makes use of inherent statistical properties of the polarimetric data and hence the information is fully explored. A set of P-L-C-band images acquired by JPL airsar during the PACRIM'96 campaign were used as test images. Validation and effeteness of the proposed scheme were able to demonstrate the utilization of complete polarimetric information. It has been shown that with complete polarimetric data, the fuzzy neural network has substantially reduced its training time and improved the classification accuracy as well. A Lee polarimetric filter was applied to reduce speckle level while preserving the polarimetric properties and is proven to be useful to improve the classification accuracy. The approach also demonstrates the adaptability and flexibility for high dimensional feature vectors such as the complete polarimetric presented here.
1. Introduction
In classification of SAR image, three linear polarized data (diagonal term of covariance matrix) is often used and a proper classification results could be obtained (Chen, 1996; Tzeng, 1997). As stated in (Lee et al., 2000), there are basically three approaches: 1) algorithms based on image processing techniques, 2) algorithms based on a statistical model, and 3) algorithms based on em wave scattering mechanisms. Approach 1) can be supervised or unsupervised, while 2) and 3) are devised to be supervised only. Supervised and unsupervised algorithms are complementary to each other; each has its own advantages and disadvantages, depending on their purposes and applications. In all image classifications, still only partial polarimetric data are mostly often utilized. Hence, one has not yet taken full advantage of polarimetric data. This certainly does not necessarily mean that partial polarimetric data is not sufficient for the applications cited there. However, it may miss some important information that is embedded in the off-diagonal term of covariance matrix. For this purpose, a neural fuzzy classifier based on Wishart distribution for fully polarimetric SAR is demonstrated in this paper.
2. Polarimetric Sar Image
2.1 Statistical Properties
A polarimetric SAR records the matrix S. A scattering matrix S is a relationship between the incident field and the scattering field
| (1) |
where the subscripts in S denote the polarized states, and k is incident wavenumber, r the range from radar antenna to target center. With the complex scattering matrix S available, the interactions of radar waves and target medium can be fully described in the sense of complete polarization response. For simplicity, a complex vector v may be defined by elements of S as
| (2) |
where T denotes the matrix transpose and q the dimension of v, q = 4 for bistatic case and q = 3 for backscatter case by duality theorem stating Svh==Shv for a reciprocal medium. SAR is a coherent imager and thus unavoidably suffers from speckle noise. This degrades image quality. Thus, SAR images are usually multi-look processed by averaging several neighboring one-look pixels. For polarimetric SAR system, it requires averaging several one-look covariance matrices
| (3) |
where vi is ith look elements vector in Eq. (3), n is number of looks, Z is a Hermitian matrix. The statistics of the Z has a complex Wishart distribution [Lee, 2000)
| (4) (5) |
where C= < Z > denotes the feature covariance matrix and < > the ensemble average.
2.2 Polarimetric Speckle Filter
SAR image records the scattered echoes from the scatterers within the illuminating cell. It causes speckle phenomena. To obtain better classification results, the despeckle procedure is performed before the SAR image is applied for classification. A new despeckle technology proposed and proven well suited for fully polarimetric SAR data [Lee, 1999] is applied in filtering the speckle of the SAR image in this study.
3. A Statistical Fuzzy Neural Classifier
3.1 Fuzzy Clustering
In the fuzzy c-means algorithm, the position of a class or cluster center is found to be the average of the positions of all the patterns in that cluster, based on minimizing the sum of the variances of all variables i within a domain D for each pattern in each cluster l. And membership function
| (6) |
where
| (7) |
is a fuzzy c-partition of X , X=(x1, x2, xN) is a set of training N vector, and
| (8) |
where is class center of the l-th class, C1 is the feature covariance matrix of class l, and Tr denotes the trace of a matrix. Without a prori information, an equal probability for each class is assumed. To merge multifrequency data, a linear combination leads to a similar distance measure as
| (9) |
where Ci(J) and Zi(J) are the feature matrix and the covariance matrix for j-th band, and K is the total number of frequency bands.
Differentiating
| (10) |
to find the minimum of
| (11) |
and
| (12) |
In fuzzy c-means algorithm, the fuzzy membership is obtained by iterative procedure of Equation (11) and (12).
3.2 Neural Implementation
The classification scheme used in this study is a neural network, called dynamic learning neural network (DLNN). DLNN has been applied in many applications. Such a neural network plays the role of connecting the input feature vector of SAR and the output membership vector. The input-output relationship can be simply expressed as
y=Wx (13)
where y is the output nodes and x is the input nodes. In this study, they are the membership vector of each pixel to a specific class and the feature vector of SAR, respectively. W is the weighting matrix of neural network. And the weighting matrix W is tuned by training process. By the use of the fuzzy membership vector as the output, DLNN becomes a fuzzy neural network (FDL)[Tzeng and Chen, 1997].
Fig 3: Configure Setup of FDL
The training process is a standard procedure for a supervised neural network. The necessary training set is formed by a set of input information and desire output. For purpose of using complete polarimetric information, the input data is the covariance matrix, and the desire output is the corresponding membership vector. The training set must be sufficient and non-ambiguous. Fig. 1 shows the configuration of the neural network. 4. Test Data and Results
The test data used in the study the L-band polarimetric SAR of San Francisco acquired by JPL AIRSAR. The image size is 1024x900 pixels. The land covers were classified into four class; they are ocean, tree (the park and the hill), urban and grass (the playground and ball park). Fig. 2 shows the un-filtered and filtered SAR image of San Francisco. To train the neural network, totally 1600 pixels training set is chosen from location of each class for training. For comparison, four setups using different inputs were devised, as given in Table 1.
| Setup | A | B | C | D |
| Input Channel | Convariance Matrix | HH, HV, VV | Covariance Matrix | Covariance Matrix |
| Classifier | Minimum distance | FDL | FDL | FDL |
| Distance Measure | Based on Wishart Distribution | Euclidean distance | Euclidean distance | Based on Wishart Distribution |
| Fuzzy | no | yes | yes | yes |
Setup A and D used Wishart distribution as distance measure, while Setup B and C are to used to test the suitability of Euclidean to covariance matrix containing the polarimetric information. Fig.3 shows the final classification results with four different setups. It is observed that the Euclidean distance, devised in Setup B and C, confuses the FDL due to the ambiguity of the off-diagonal terms in polarimetric covariance matrix,; Setup A performs classification well but lack of the fuzzy information in it; Setup B uses only three linear polarizations (diagonal term in covariance matrix) information for classification, and loses some important information contained in off-diagonal term. Setup D uses the covariance matrix and applies the Wishart Distribution in fuzzy c-means iterations. Among the four setup, Setup D clearly outperforms the other three. From the network learning curves (not shown here) of all setups, it is also indicated that Setup D convergence much faster than the rest of setups. It means that by using the Wishart distribution in FDL, the algorithm could quickly hit the class center, and at the same time speed the learn rate.
5. Conclusion
A classification scheme for fully polarimetric SAR imagery data based on a dynamic fuzzy neural network has been proposed and its effectiveness and efficiency has been demonstrated. Complete polarimetric matrix can be easily formed as an n-tuple vector data as inputs to the network and all polarimetric information are naturally implicitly contained in the network. In conclusion, a fuzzy neural network-based classification method has been successfully developed to take advantage of fully polarimetric SAR.
(a)
(b)
Fig 2: SAR Image of San Francisco (a) Unfiltered (b) Filerted
(a)
(b)
(c)
(d)
Fig 3: The classifications Results (a)setup A, (b)setup B,
(c)setup C, (d)setup D.
- Bezdek, J. C., 1987. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press. New York
- Chen, K. S., W.P. Huang, D.W. Tsay and F. Amar, 1996. Classification of multifrequency polarimetric SAR image using a dynamic learning neural network. IEEE Transactions on Geoscience and Remote Sensing, 34(3), pp. 814-820.
- Lee, J. S. et al., 2000. Terrain Classification Using Polarimetric SAR Data - An Overview. PIERS2000, Boston, USA.
- Tzeng, Y. C. and K. S. Chen, 1997. A fuzzy neural network for SAR image classification. IEEE Trans. Geoscience and Remote Sensing, 36(2), pp.301-307.