A STUDY OF UNSUPERVISED CHANGE DETECTION BASED ON TEST STATISTIC AND GAUSSIAN MIXTURE MODEL USING POLSAR SAR DATA

: To solve the problems of existing method of change detection using fully polarimetric SAR which not takes full advantage of polarimetric information and the result of false alarm rate of which is high, a method is proposed based on test statistic and Gaussian mixture model in this paper. In the case of the flood disaster in Wuhan city in 2016, difference image is obtained by the likelihood-ratio parameter which is built using coherency matrix C3 or covariance matrix T3 of fully polarimetric SAR based on test statistic, and it becomes a reality that the change information is automatic extracted by the parameter of Gaussian mixture model (GMM) of difference image based on the expectation maximization (EM) iterative algorithm. The experimental results show that the overall accuracy of change detection results can be improved and false alarm rate can be reduced using this method by comparison with traditional constant false alarm rate (CFAR) method. Thus the validity and feasibility of the method is demonstrated.


INTRODUCTION
Accurate and timely change detection of Earth's surface features is extremely important for understanding relationships and interactions between people and natural phenomena.It has been widely recognized in the scientific community as a key element in a variety of applications, such as environmental impact assessment (Almeida, 2007;Chavez, 1994;Engeset,2002), ecological monitoring (Cihlar, 1992;Zhu, 2006), global change monitoring (Bruzzone , 1997), state and local planning (Hame , 1998;Lu, Sader , 2001), and regulatory policy development (Ridd, 1998;Zhang, 2001).Due to its all-weather mapping capability independently of, for instance, cloud cover, change detection of polarimetric synthetic aperture radar (PolSAR) plays an important role in many application domains (Grover, 1999;Rignot, 1993;Stramondo, 2006).Meanwhile, unsupervised change detection techniques do not need to explicitly identify the types of land cover or land use transitions that have taken place in the region of concern (Qiu, 2003).Hence, these techniques are suitable for many applications.
However, existing method of unsupervised change detection using fully polarimetric SAR which not takes full advantage of polarimetric information and the result of false alarm rate of which is high (Bovolo, 2006).To solve the problems of existing method of change detection using fully polarimetric SAR which not takes full advantage of polarimetric information and the result of false alarm rate of which is high, a method is proposed based on test statistic and Gaussian mixture model in this paper.
In section 2, the proposed change-detection methodology is derived, and the method of similarity measure and Gaussian mixture model are introduced.Section 3 reports the results of the proposed approach on the multi-temporal SAR data over WuHan.Finally, conclusions are drawn in section 4.

METHODOLOGY
Let us consider two full PolSAR images both follow a complex Wishart distribution (Gong, 2014), i.e. ( , , ) According to a test statistic theory (Stramondo, 2006), we make the hypothesis as follows, Null hypothes is H0 (two data have no change), the alternative hypothes is H1 (two data have change) (Bruzzone, 1997).
If the null hypothesis is true, the likelihood ratio parameter of fully polarimetric SAR is .exp .exp ( ) If m=n, Eq.( 1) is changed as below. ( where lnQ describes the similarity of corresponding features and its range is (-∞,0], the more lnQ close to 0, the more similar of the corresponding features, which means less likely it is to change and vice versa.Hence, similarity parameter lnQ criticizes the similarity of two covariance matrixes and judges that change happens or not (Seto, 2003).We selected as best threshold and obtained difference image, where, Meanwhile, The data distribution P(xd) of feature vectors can be modeled as a weighted sum of two distributions representing the ''changed'' class and ''unchanged'' class data distributions (Celik , 2011), i.e., can also be modelled using N component GMM (Goodman, 1963), i.e., The data distribution modeled with Eq. ( 7) can be separated into two distributions representing the data distributions of ''changed'' and ''unchanged'' classes.Each pixel at the coordinate (i, j) with feature vector Xd(i, j) is going to be labeled with one of the two classes, wc or wu, according to The optimum combination with index m0 is obtained by finding an intermediate change detection mask CM m0 for which the sum of the mean square error (Em0) of ''changed'' and ''unchanged'' pixel values of the difference image is the minimum (Zhao, 2016), i.e., It is worth to note that the EM-based algorithm (Sader, 2001) is a special case of GMM algorithm when feature vector for each pixel is constructed with no contextual information, i.e. w = 1, and two components (N = 2) are used for GMM representation (Lu, 2005).Figure 1 shows the study procedure of the Gaussian mixture model.

Registered and Filtered
Obtain difference image using Test statistic Obtain the initial The basic processing flow of the proposed method (Figure 1) consists of data preprocessing, likelihood-ratio parameter construction, change information automatic extraction with Gaussian mixture model algorithm and precision evaluation.First, speckle noise is removed by Refined_Lee filtering for the two registered fully polarimetric SAR images.As the coherency matrix C3 or covariance matrix T3 of fully polarimetric SAR data follows a complex Wishart distribution.The likelihoodratio parameter is built by a test statistic based on Wishart distribution to represent change features and the difference image also is obtained.Then the data distribution of the difference image computed from satellite images of the same scene acquired at different time instances is modeled by using the expectation maximization (EM) iterative algorithm and Gaussian mixture model algorithm and it also becomes a reality that the change information is automatic extracted.Finally, the precision of change detection result is evaluated.

Description of the image datasets
In order to assess the effectiveness of the change detection algorithms for the analysis of the difference image, bi-temporal Radarsat-2 data of the flood disaster in Wuhan city in 2016 are considered in this paper.The SAR image dataset is composed of two images of size 5752×3788 pixels which are regions from two SAR images acquired by the Radarsat-2 over an area near the city of Wuhan, China.on June 25, 2015 and July 6, 2016, respectively.The SAR images are shown in Figure 2. The two red boxes labeled regions are used to give a detailed assessment in Figure 2 (b).All those regions have a common characteristic that are regions of water.Region 1 is YanDong Lake (Figure 3), and region 2 is LiangZi Lake (Figure 4).The image size is 300*500 pixels.The detailed assessments of area is located in LiangZi Lake of Wuhan include some grassland, city and water bodies.The main changes occurred in the water area, because of continuing rain.

Implementation of change detection algorithms
Change detection algorithms which are based on statistical data modeling are utilized to test the performance of GMM algorithm and EM-based algorithm (Ridd, 1998).In the implementation of test statistic and GMM algorithm, the initial estimate of the number of components (N) for the GMM is set as N = 10 which is automatically adjusted by annihilating components that are not supported by the data.Furthermore, in order to make fair comparisons with EM-based algorithm, the parameter w = 1 is used to consider only single pixel information.However, the effect of parameter w on GMM algorithm is separately investigated.

Experiments and Results
The intersection of the two Gaussian distributions representing ''changed' ' and ''unchanged'' class  LiangZi Lake The experimental results (as shown in Figure 5, Table 1 and Figure 6, Table 2) show that the overall accuracy of change detection results can be improved and false alarm rate can be reduced using this method by comparison with some traditional methods, such as constant false alarm rate (CFAR) method.

CONCLUSIONS
Unsupervised change detection based on test statistic and Gaussian mixture model algorithm for multi-temporal PolSAR images is proposed.As GMM algorithm can also adequately handle different types of spatial sampling.The data distribution of the difference image computed from satellite images of the same scene acquired at different time instances is modeled by using GMM algorithm.Consequently, the results show clearly that the test statistic and Gaussian mixture model improved change detection capability for fully polarimetric SAR data.Furthermore, the increase in the initial value of the number of mixture components N will also increase the computational complexity of GMM algorithm.
, and P(wu) and P(wc) are a priori probabilities of the classes wu and wc, respectively.The data distribution d (x ) p n) is the prior probability of the data point having been generated from the component n of the mixture, and d (x ) p n is the nth component density modeled with Gaussian density function.

Figure 3 .
Figure 3.The Pauil-RGB images of YanDong Lake on (a) Jun.25, 2015; (b) Jul.6, 2016; (c) ground truth The bi-temporal PolSAR images shown in Figure 3 (a) (b) were acquired on Jun.25, 2015, and Jul.6, 2016, respectively.The image size is 400*400 pixels.The detailed assessments of area is located in YanDong Lake of Wuhan include some grassland, city and water bodies.The main changes occurred in the water area, because of continuing rain.

Table 2 .
data distributions separates the difference image data into two clusters.The intersection point determines a threshold value that segments the difference image data into two regions representing ''changed'' and ''unchanged'' classes.As shown in Fig.3, GMM algorithm performs better in fitting model to difference image data and in estimating data distributions of ''changed'' and ''unchanged'' classes than constant false alarm rate(CFAR) algorithm.Because of better data modeling, it can separate ''changed'' and ''unchanged'' classes more efficiently.Performance Evaluation of change detection Over (a) Our method (b) CFAR Figure 5. Change detection results of Our method on SAR image dataset with different regions