Image Processing for Remote Sensing - Chapter 15 pot

C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 341 3.9.2007 2:07pm Compositor Name: JGanesan 15 SAR Image Classification by Support Vector Machine Michifumi Yoshioka, Toru Fujinaka, and Sigeru Omatu CONTENTS 15.1 Introduction 341 15.2 Proposed Method 342 15.3 Simulation 348 15.3.1 Data Set and Condition for Simulations 348 15.3.2 Simulation Results 349 15.3.3 Reduction of SVM Learning Cost 349 15.4 Conclusions 352 References 352 15.1 Introduction Remote sensing is the term used for observing the strength of electromagnetic radiation that is radiated or reflected from various objects on the ground level with a sensor installed in a space satellite or in an aircraft The analysis of acquired data is an effective means to survey vast areas periodically [1] Land map classification is one of the analyses The land map classification classifies the surface of the Earth into categories such as water area, forests, factories, or cities In this study, we will discuss an effective method for land map classification by using synthetic aperture radar (SAR) and support vector machine (SVM) The sensor installed in the space satellite includes an optical and a microwave sensor SAR as an active-type microwave sensor is used for land map classification in this study A feature of SAR is that it is not influenced by weather conditions [2–9] As a classifier, SVM is adopted, which is known as one of the most effective methods in pattern and texture classification; texture patterns are composed of many pixels and are used as input features for SVM [10–12] Traditionally, the maximum likelihood method has been used as a general classification technique for land map classification However, the categories to be classified might not achieve high accuracy because the method assumes normal distribution of the data of each category Finally, the effectiveness of our proposed method is shown by simulations 341 © 2008 by Taylor & Francis Group, LLC C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 342 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 342 15.2 Proposed Method The outline of the proposed method is described here At first, the target images from SAR are divided into an area of 8Â8 pixels for the calculation of texture features The texture features that serve as input data to the SVM are calculated using gray level cooccurrence matrix (GLCM), Cij, and gray level difference matrix (GLDM), Dk The term GLCM means the co-occurrence probability that neighbor pixels i and j become the same gray level, and GLDM means the gray level difference of neighbor pixels whose distance is k The definitions of texture features based on GLCM and GLDM are as follows: Energy (GLCM) E¼ X i ,j C2 ij (15:1) Entropy (GLCM) X H¼À Ci j log Cij (15:2) i,j Local homogeneity Lẳ X Cij i,j ỵ (i j) (15:3) Inertia I¼ X (i À j)2 Cij (15:4) i ,j Correlation C¼ X (i À mi )(j À mj ) si s j i ,j mi ¼ X X X X i Cij , mj ¼ j Cij i s2 ¼ i X i Variance Cij j j (i À mi )2 X i s2 ¼ j Ci j , X j V¼ j X i ,j (i À mi )Cij (j À mj )2 X Cij (15:5) i (15:6) Sum average Sẳ X i,j â 2008 by Taylor & Francis Group, LLC (i ỵ j)Cij (15:7) C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 343 3.9.2007 2:07pm Compositor Name: JGanesan SAR Image Classification by Support Vector Machine 343 Energy (GLDM) Ed ¼ X D2 k (15:8) k Entropy (GLDM) Hd ¼ À X Dk log {Dk } (15:9) k Mean M¼ X k Dk (15:10) {k À M}2 Dk (15:11) k Difference variance V¼ X k The next step is to select effective texture features as an input to SVM as there are too many texture features to feed SVM [(7 GLCMs ỵ GLDMs)  bands ¼ totally 88 features] Kullback–Leibler distance is adopted as the selection method of features in this study The definition of Kullback–Leibler distance between two probability density functions p(x) and q(x) is as follows: ð L ¼ p(x) log p(x) dx q(x) (15:12) Using the above as the distance measure, the distance indicated in the selected features between two categories can be compared, and the feature combinations whose distance is large are selected as input to the SVM However, it is difficult to calculate all combinations of 88 features for computational costs Therefore, in this study, each 5-feature combination from 88 is tested for selection Then the selected features are fed to the SVM for classification The SVM classifies the data into two categories at a time Therefore, in this study, input data are classified into two sets, that is, a set of water and cultivation areas or a set of city and factory areas in the first stage In the second stage, these two sets are classified into two categories, respectively In this step, it is important to reduce the learning costs of SVM since the remote sensing data from SAR are too large for learning In this study, we propose a reduction method of SVM learning costs using the extraction of surrounding part data based on the distance in the kernel space because the boundary data of categories determine the SVM learning efficiency The distance d(x) of an element x in the kernel space from the category to which the element belongs is defined as follows using the kernel function F(x): 2    n 1X   d (x) ¼ F(x) À F(xk )   n k¼1 !t ! n n 1X 1X ¼ F(x) À F(xk ) F(x) À F(xl ) n k¼1 n l¼1 n n n n 1X 1X XX ¼ F(x)t F(x) À F(x)t F(xl ) À F(xk )t F(x) ỵ F(xk )t F(xl ) (15:13) n lẳ1 n kẳ1 n kẳ1 lẳ1 â 2008 by Taylor & Francis Group, LLC C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 344 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 344 Here, xk denotes the elements of category, and n is the total number of elements Using the above distance d(x), the relative distance r1(x) and r2(x) can be defined as r1 (x) ¼ d2 (x) À d1 (x) d1 (x) (15:14) r2 (x) ¼ d1 (x) À d2 (x) d2 (x) (15:15) In these equations, d1(x) and d2(x) indicate the distance of the element x from the category or 2, respectively A half of the total data that has small relative distance is extracted and fed to the SVM To evaluate this extraction method by comparing with the traditional method based on Mahalanobis distance, the simulation is performed using sample data and illustrated in Figure 15.1 through Figure 15.4, respectively The distribution of samples and is Gaussian The centers of distributions are (À0.5,0), (0.5,0) in class and of sample 1, and (À0.6), (0.6) in class 1, and (0,0) in class of sample 2, respectively The variances of distributions are 0.03 and 0.015, respectively The total number of data is 500 per class The kernel function used in this simulation is as follows: kx À x0 k2 K(x,x ) ¼ F(x) F(x ) ¼ exp À 2s2 T ! (15:16) 2s2 ¼ 0:1 As a result of the simulation illustrated in Figure 15.2, Figure 15.3, Figure 15.5, and Figure 15.6, in the case of sample 1, both the proposed and the Mahalanobis-based method classify Class Class 0.5 −0.5 −1 −1 FIGURE 15.1 Sample data © 2008 by Taylor & Francis Group, LLC −0.5 0.5 C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 345 3.9.2007 2:07pm Compositor Name: JGanesan SAR Image Classification by Support Vector Machine 345 Class Class Extraction Extraction 0.5 −0.5 −1 −1 −0.5 0.5 FIGURE 15.2 Extracted boundary elements by proposed method (sample 1) Class Class Extraction Extraction 0.5 −0.5 −1 −1 −0.5 FIGURE 15.3 Extracted boundary elements by Mahalanobis distance (sample 1) © 2008 by Taylor & Francis Group, LLC 0.5 C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 346 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 346 Class Class 0.5 −0.5 −1 −1 −0.5 0.5 FIGURE 15.4 Sample data Class Class Extraction Extraction 0.5 −0.5 −1 −1 −0.5 FIGURE 15.5 Extracted boundary elements by proposed method (sample 2) © 2008 by Taylor & Francis Group, LLC 0.5 C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 347 3.9.2007 2:07pm Compositor Name: JGanesan SAR Image Classification by Support Vector Machine 347 Class Class Extraction Extraction 0.5 −0.5 −1 −1 −0.5 0.5 FIGURE 15.6 Extracted boundary elements by Mahalanobis distance (sample 2) data successfully However, in the case of sample 2, the Mahalanobis-based method fails to classify data though the proposed method succeeds This is because Mahalanobis-based method assumes that the data distribution is spheroidal The distance function in those methods illustrated in Figure 15.7 through Figure 15.10 clearly shows the reason for the classification ability difference of those methods d1(x,y) 1.15 1.1 1.05 0.95 0.9 0.85 0.8 0.75 0.7 0.5 −1 −0.5 −0.5 0.5 FIGURE 15.7 Distance d1(x) for class in sample (proposed method) © 2008 by Taylor & Francis Group, LLC −1 C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 348 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 348 d2(x,y) 1.3 1.2 1.1 0.9 0.8 0.7 0.6 0.5 0.4 0.5 −1 −0.5 −0.5 0.5 −1 FIGURE 15.8 Distance d2(x) for class in sample (proposed method) 15.3 15.3.1 Simulation Data Set and Condition for Simulations The target data (Figure 15.11) used in this study for the classification are the observational data by SIR-C The SIR-C device is a SAR system that consists of two wavelengths: L-band (wavelength 23 cm) and C-band (wavelength cm) and four polarized electromagnetic radiations The observed region is Kagawa Prefecture, Sakaide City, Japan (October 3, d1(x,y) 1 0.5 −1 −0.5 −0.5 0.5 FIGURE 15.9 Distance d1(x) for class in sample (Mahalanobis) © 2008 by Taylor & Francis Group, LLC −1 C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 349 3.9.2007 2:07pm Compositor Name: JGanesan SAR Image Classification by Support Vector Machine 349 d2(x,y) 14 12 10 0.5 −1 −0.5 −0.5 0.5 −1 FIGURE 15.10 Distance d2(x) for class in sample (Mahalanobis) 1994) The image sizes are 1000 pixels in height, 696 pixels in width, and each pixel has 256 gray levels in eight bands To extract the texture features, the areas of 8Â8 pixels on the target data are combined and classified into four categories ‘‘water area,’’ ‘‘cultivation region,’’ ‘‘city region,’’ and ‘‘factory region.’’ The mountain region is not classified because of the backscatter The ground-truth data for training are shown in Figure 15.12 and the numbers of sample data in each category are shown in Table 15.1 The selected texture features based on Kullback–Leibler distance mentioned in the previous section are shown in Table 15.2 The kernel function of SVM is Gaussian kernel with the variance s2 ¼ 0.5, and soft margin parameter C is 1000 The SVM training data are 100 samples randomly selected from ground-truth data for each category 15.3.2 Simulation Results The final result of simulation is shown in Table 15.3 In this table, ‘‘selected’’ implies the classification accuracy with selected texture features in Table 15.2, and ‘‘all’’ implies the accuracy with all 88 kinds of texture features The final result shows the effectiveness of feature selection for improving classification accuracy 15.3.3 Reduction of SVM Learning Cost The learning time of SVM depends on the number of sample data Therefore, the computational cost reduction method for SVM learning is important for complex data sets such as ‘‘city’’ and ‘‘factory’’ region in this study Then, the reduction method proposed in the previous section is applied, and the effectiveness of this method is evaluated by comparing the learning time with traditional methods The numbers of data are from 200 to 4000, and the learning times of the SVM classifier are measured in two cases In the © 2008 by Taylor & Francis Group, LLC C.H Chen/Image Processing for Remote Sensing 350 66641_C015 Final Proof page 350 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing FIGURE 15.11 Target data first case, all data are used for learning and in the second case, by using the proposed method, data for learning are reduced by half The selected texture features for classification are the energy (band 1), the entropy (band 6), and the local homogeneity (band 2), and the SVM kernel is Gaussian Figure 15.13 shows the result of the simulation The CPU of the computer used in this simulation is Pentium 4/2GHz The result of the simulation clearly shows that the learning time is reduced by using the proposed method The learning time is reduced to about 50% on average © 2008 by Taylor & Francis Group, LLC C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 351 3.9.2007 2:07pm Compositor Name: JGanesan SAR Image Classification by Support Vector Machine 351 Water City Cultivation Factory Mountain FIGURE 15.12 (See color insert following page 240.) Ground-truth data for training TABLE 15.1 Number of Data Category Water Cultivation City Factory Number of Data 133201 16413 11378 2685 TABLE 15.2 Selected Features Category Water, cultivation/city, factory Water/factory City/factory Numbers in parentheses indicate SAR band © 2008 by Taylor & Francis Group, LLC Texture Features Correlation (1, 2), sum average (1) Variance (1) Energy (1), entropy (6), local homogeneity (2) C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof page 352 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 352 TABLE 15.3 Classification Accuracy (%) Water Selected All Cultivation City Factory Average 99.82 99.49 94.37 94.35 93.18 92.18 89.77 87.55 94.29 93.39 1600 Learning time (sec) 1400 1200 Normal 1000 800 Accelerated 600 400 200 200 400 600 800 1000 Number of data 2000 3000 4000 FIGURE 15.13 SVM learning Time 15.4 Conclusions In this chapter, we have proposed the automatic selection of texture feature combinations based on the Kullback–Leibler distance between category data distributions, and the computational cost reduction method for SVM classifier learning As a result of simulations, by using our proposed texture feature selection method and the SVM classfier, higher classification accuracy is achieved when compared with traditional methods In addition, it is shown that our proposed SVM learning method can be applied to more complex distributions than applying traditional methods References Richards J.A., Remote Sensing Digital Image Analysis, 2nd ed., Springer-Verlag, Berlin, p 246, 1993 Hara Y., Atkins R.G., Shin R.T., Kong J.A., Yueh S.H., and Kwok R., Application of neural networks for sea ice classification in polarimetric SAR images, IEEE Transactions on Geoscience and Remote Sensing, 33, 740, 1995 Heermann P.D and Khazenie N., Classification of multispectral remote sensing data using a back-propagation neural network, IEEE Transactions on Geoscience and Remote Sensing, 30, 81, 1992 © 2008 by Taylor & Francis Group, LLC C.H Chen/Image Processing for Remote Sensing 66641_C015 Final Proof SAR Image Classification by Support Vector Machine page 353 3.9.2007 2:07pm Compositor Name: JGanesan 353 Yoshida T., Omatu S., and Teranishi M., Pattern classification for remote sensing data using neural network, Transactions of the Institute of Systems, Control and Information Engineers, 4, 11, 1991 Yoshida T and Omatu S., Neural network approach to land cover mapping, IEEE Transactions on Geoscience and Remote Sensing, 32, 1103, 1994 Hecht-Nielsen R., Neurocomputing, Addison-Wesley, New York, 1990 Ulaby F.T and Elachi C., Radar Polarimetry for Geoscience Applications, Artech House, Norwood, 1990 Van Zyl J.J., Zebker H.A., and Elach C., Imaging radar polarization signatures: theory and observation, Radio Science, 22, 529, 1987 Lim H.H., Swartz A.A., Yueh H.A., Kong J.A., Shin R.T., and Van Zyl J.J., Classification of earth terrain using polarimetric synthetic aperture radar images, Journal of Geophysical Research, 94, 7049, 1989 10 Vapnik V.N., The Nature of Statistical Learning Theory, 2nd ed., Springer, New York, 1999 11 Platt J., Sequential minimal optimization: A fast algorithm for training support vector machines, Technical Report MSR-TR-98-14, Microsoft Research, 1998 ă 12 Joachims T., Making large-scale SVM learning practical, In B Scholkopf, C.J.C Burges, and A.J Smola, Eds., Advanced in Kernel Method—Support Vector Learning, MIT Press, Cambridge, MA, 1998 © 2008 by Taylor & Francis Group, LLC ...C.H Chen /Image Processing for Remote Sensing 66641_C 015 Final Proof page 342 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 342 15. 2 Proposed Method... Group, LLC C.H Chen /Image Processing for Remote Sensing 350 66641_C 015 Final Proof page 350 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing FIGURE 15. 11 Target data... homogeneity (2) C.H Chen /Image Processing for Remote Sensing 66641_C 015 Final Proof page 352 3.9.2007 2:07pm Compositor Name: JGanesan Image Processing for Remote Sensing 352 TABLE 15. 3 Classification