Image Processing for Remote Sensing - Chapter 15

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 radi-ation 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 342 Image Processing for Remote Sensing 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 88 pixels for the calculation of texture features. The texture features that serve as input data to the SVM are calculated using gray level co-occurrence 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) X E ¼ i,j Cij (15:1) Entropy (GLCM) X H ¼ ÿ Ci j logCij (15:2) i,j Local homogeneity X L ¼ i,j 1 þ (i ÿ j)2 Cij (15:3) Inertia I ¼ X(iÿ j)2Cij (15:4) i,j Correlation X (i ÿmi)(jÿ mj) ij i,j i j X X mi ¼ i Cij, i j X X mj ¼ j Cij j i si ¼ X(i ÿmi)2 XCi j, i j sj ¼ X(jÿ mj)2 XCij (15:5) j i Variance Sum average X V ¼ (i ÿ m )Cij (15:6) i,j X S ¼ (iþ j)Cij (15:7) i,j © 2008 by Taylor & Francis Group, LLC SAR Image Classification by Support Vector Machine 343 Energy (GLDM) X Ed ¼ Dk (15:8) k Entropy (GLDM) X Hd ¼ ÿ Dk log{Dk} (15:9) k Mean X M ¼ k Dk (15:10) k Difference variance X V ¼ {k ÿ M} Dk (15:11) 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 GLCMsþ4 GLDMs)8 bands ¼ totally 88 fea-tures]. Kullback–Leibler distance is adopted as the selection method of features in this study. The definition of Kullback–Leibler distance between two probability density func-tions p(x) and q(x) is as follows: L ¼ ð p(x)logp(x)dx (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, respect-ively. 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): X 2 d (x) ¼ F(x) ÿ F(xk) k¼1 !t X ! ¼ F(x) ÿ F(xk) F(x) ÿ F(xl) k¼1 l¼1 n n n n ¼ F(x)tF(x) ÿ F(x)tF(xl) ÿ F(xk)tF(x) þ 2 F(xk)tF(xl) (15:13) l¼1 k¼1 k¼1 l¼1 © 2008 by Taylor & Francis Group, LLC 344 Image Processing for Remote Sensing 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) ÿ d1(x) 1 r2(x) ¼ d1(x) ÿ d2(x) 2 (15:14) (15:15) In these equations, d1(x) and d2(x) indicate the distance of the element x from the category 1 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 1 and 2 illustrated in Figure 15.1 through Figure 15.4, respectively. The distribution of samples 1 and 2 is Gaussian. The centers of distributions are (ÿ0.5,0), (0.5,0) in class 1 and 2 of sample 1, and (ÿ0.6), (0.6) in class 1, and (0,0) in class 2 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: K(x,x0) ¼ F(x)TF(x0) ¼ exp ÿkx ÿ x0k2 ! (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 1 Class 1 Class 2 0.5 0 −0.5 −1 −1 −0.5 0 0.5 1 FIGURE 15.1 Sample data 1. © 2008 by Taylor & Francis Group, LLC SAR Image Classification by Support Vector Machine 1 0.5 345 Class 1 Class 2 Extraction 1 Extraction 2 0 −0.5 −1 1 −0.5 0 0.5 1 FIGURE 15.2 Extracted boundary elements by proposed method (sample 1). 1 Class 1 Class 2 Extraction 1 Extraction 2 0.5 0 −0.5 −1 −1 −0.5 0 0.5 1 FIGURE 15.3 Extracted boundary elements by Mahalanobis distance (sample 1). © 2008 by Taylor & Francis Group, LLC ... - tailieumienphi.vn