A Change Detection Method of Multi -temporal SAR Images Based on Contourlet Transform

International Journal of Remote Sensing Applications (IJRSA) Volume 6, 2016 doi: 10.14355/ijrsa.2016.06.006

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A Change Detection Method of Multi-temporal SAR Images Based on Contourlet Transform Shiqi Huang, Wenzhun Huang, Ting Zhang Department of Electronic Information Engineering, Xijing University, Xi’an, 710123, China huangshiqi@xijing.edu.cn Abstract Synthetic aperture radar (SAR) imaging is very sensitive to direction, so the information that SAR images contain is often not completely same from different directions. The information obtained from multi-directions must be more abundant and more accurate than that of from a single direction in a SAR image. The Contourlet transform is a multi-scale geometric analysis theory, holding many advantages for signal processing, such as multi-resolution, multi-direction and anisotropy; therefore, it is in favor of extracting different direction information for SAR images. According to the directional sensitivity of SAR imaging and the characteristics of multi-scale and multi direction to the Contourlet transform, this paper proposed a new SAR image change detection method based on Contourlet transform, called CTCD algorithm. Using the multi-direction characteristic of Contourlet transform, the CTCD method can get more accurate changed information for multi-temporal SAR images. The practical SAR image data is employed to test the CTCD algorithm and results show that the CTCD algorithm is a feasible change detection algorithm for multi-temporal SAR images, and it can obtain more abundant and more accurate information than the direct difference change detection (DDCD) algorithm.

Keywords Change Detection; SAR Image; Contourlet Transform; CTCD Algorithm

Introduction Remote sensing image change detection refers to employing the same or different sensors to obtain the remote sensing images of the same scene but at different time, and then performs the processing and analysis between the two remote sensing images (or two time series remote sensing images), extracting the state or information that the ground objects have taken place in a period of time. This technology obtaining the change information is very important for the global change monitoring, resource and environmental monitoring, natural disaster monitoring and assessment, dynamic battlefield perception and hitting effect evaluation [1-5].

Synthetic aperture radar is an active microwave imaging radar, having the ability to obtain remote sensing data in all-weather and all-time, so it plays a very important role in obtaining change information in the dynamic monitoring. At the same time, the change detection theory is not only an important content of SAR image processing, but also is an important application field for SAR images [6-9].

There are a lot of change detection methods on remote sensing images. But these methods are usually introduced for different sensors and different application purposes, so it is very difficult for these algorithms to have the universality. There are several reasons. The first is that the parameters of imaging sensors and ground objects are not same at every time, which results in different image quality at every time; the second is that the specific purpose of image processing is not exactly same every time, so the precision and the requirements of obtaining information are different; the third is that the technologies and means are different every time in image processing.

So far, the techniques and methods of remote sensing image change detection can be divided into the following five categories. The first category of change detection methods is directly based on image domain. Namely, the processing or operation is directly performed between the two different temporal remote sensing images, such as the gray difference method, the gray ratio method, the texture feature difference method, the correlation coefficient method, the regression method and the typical correlation method [10-12]. The second category of change

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detection methods is based on image feature domain. The features of different temporal images are extracted and then these features are to be compared and processed for obtaining the change information, such as the maximum likelihood estimation method, the Bayesian estimation method and the statistical feature method [13-15]. The third category method is based on the transform domain. The multi-temporal images are transformed by these theories so that some change information could be obtained in the transformed domain, such as the Fourier transform, the wavelet transform and the principal component analysis [16-18]. The fourth category method is based on image classification. Every remote sensing image at different time is be classified, respectively, and then different classifications perform the comparison and analysis to obtain the change information, such as the support vector machines and the clustering analysis [19, 20]. The fifth category method is based on the new theory and cross discipline, such as the multi-scale geometric analysis theory, the fuzzy theory, the artificial intelligence and the information fusion theory [21-23].

SAR is the coherent imaging radar, its complex imaging mechanism and speckle noise bring great challenge and difficulty for multi-temporal SAR image change detection, and SAR imaging is very sensitive to the direction.

Therefore, if the general image change detection methods are directly applied to multi-temporal SAR images, it is very difficult to obtain the ideal effect. Usually employing the combination of some new theories and methods of signal processing and the characteristics of SAR images achieves the extraction of change information. The theory of wavelet analysis is a kind of non-stationary and nonlinear signal processing method, but its direction is limited; namely, each scale only can provide three decomposition directions. Wavelet transform has a good ability of catching the singular points, but for the high dimensional linear singular and surface singular, it is incapable of action. Do et al. proposed a new multi-scale geometric analysis theory in 2002, i.e. Contourlet transform [24]. The Contourlet transform is an image expression mode with the characteristics of the multi-direction, multi-scale, local part and anisotropic, and it is also a sparse image representation. The direction numbers are variable in different decomposition scales and the number can be set according to the requirements of the image processing and analysis, so the Contourlet transform has good advantages in directionality and anisotropy. According to the mechanism of SAR imaging and the characteristic of Contourlet transform, this paper proposed a multi-temporal SAR image change detection algorithm based on Contourlet transform, i.e., the CTCD algorithm. The new algorithm fully employs the advantage of multi-direction and anisotropy of the Contourlet transform, which is just consistent with the characteristics of anisotropic scattering of ground objects and is consistent with the directional sensitivity of SAR imaging. Therefore, using the CTCD algorithm to process different time SAR images can get more accurate change detail information. The biggest advantage of CTCD algorithm is that it can set the directional decomposition numbers in each scale according to the resolution of input SAR images and the changed detail information can be obtained; meanwhile, it still reduces some influence brought by speckle noise.

This paper consists of five sections, and the second section introduces the theory of the Contourlet transform. The realization process of CTCD algorithm is detailedly represented in the third section. The experimental results are analyzed and compared in the fourth section, and the fifth section is the summary of the full text.

Contourlet Transform Theory The detail process of Contourlet transform can refer to the reference [24]. The Contourlet transform is separately realized by the scale decomposition and the direction decomposition. First it uses the Laplacian Pyramid filter banks (LPFB) to perform the multi-scale decomposition, and then uses the direction filter banks (DFB) to perform the direction decomposition. The Contourlet transform has the advantages of the multi-resolution and multi direction, so it can well describe the details from a different viewpoint and the obtained information is more detailed. It decomposes the input image with LPFB to get the detail image at each scale, and then uses the DFB to decompose the detail image at each scale to get the detail coefficients of every direction; finally, the coefficients of all scales and directions of a decomposed image can be gotten. Fig.1 and Fig.2 are the frame diagram and the flow chart of Contourlet transform, respectively. The high-frequency components obtained by the Laplacian Pyramid filter in every scale are decomposed with the two-dimensional direction filter, and there are 2n directional sub-images in every decomposition scale. Furthermore, the directional number n can be set arbitrarily, which improves the flexibility and selectivity.

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Input image

Pyramid decomposition

Directional Filter

FIG.1 THE FRAMEWORK OF CONTOURLET TRANSFORM LPFB Low pass

LPFB Low pass

LPFB

Approximate image

(2,2)

DFB Low pass

Band pass

(2,2)

Four directional subband

DFB Band pass Image

Eight directional subband

DFB Band pass Sixteen directional subband

FIG.2 THE PRINCIPLE DIAGRAM OF CONTOURLET TRANSFORM

Assume that the input image is f ( x, y ) , then the course of Contourlet transform can be described with Equation (1).

J

lj

f ( x, y )  a j    b j , k

(1)

j 1 k 1

Where a j denotes the low-frequency sub-image, b j ,k is the high-frequency sub-image under the scale j in the direction k , J denotes the decomposed scale number and l j denotes the decomposed direction number. A coefficient of Contourlet transform can be expressed by fˆ ( j, k , m, n) , where

j denotes the scale of LPFB

decomposition, k denotes the directional channel after DFB decomposition at each scale, (m, n) denotes the spatial position that coefficients lie in direction sub-band. The key of the Contourlet transform is the LPFB and DFB filters.

The Description of CTCD Algorithm The CTCD algorithm makes full use of the advantages of Contourlet transform and the directional sensitivity of SAR imaging. Firstly, different SAR images perform pre-processing operations, and then using Contourlet transform performs the multi-scale and multi-direction decomposition. The corresponding sub-images at the same scale and the same direction perform the difference operations. After all difference sub-images are obtained, they will perform the inverse Contourlet transform and the final difference image is obtained. For obtaining the final change information, the mathematical expectation maximum (EM) algorithm [25] is employed to determine the threshold of change detection in the difference image. The flow chart of CTCD algorithm is shown in Fig.3, and the detail steps are as follows.

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SAR image I2 at time t2

SAR image I1 at time t1 Input different temporal SAR image

Perform some preprocessing operations (radiation correction, geometry correction and registration)

Processed SAR image I1

According to the image resolution and detection target details

Processed SAR image I2

Perform Contourlet transform

Set decomposition scale and decomposition direction number

Perform Contourlet transform

Perform difference operations to the corresponding sub-band image in every direction of each scale

Perform Contourlet inverse transform

Obtain the difference image

Produce the change detection threshold T

Perform change detection operations Change detection results

FIG.3 THE FLOW CHART OF CTCD ALGORITHM

(1) Input multi-temporal SAR image and perform pre-processing. The SAR images, which are obtained in the same area but at different time, perform some pre-processing operations, including radiation correction, geometric correction and registration.

(2) Get the basic information of SAR images. Here, the input SAR image will perform a rough estimation, for example, to determine whether the SAR image is a high-resolution or low-resolution image and whether the SAR image contains abundant detailed information. This basic information will provide the prior knowledge for the next step of setting parameters.

(3) Set the decomposition parameters. The Contourlet transform is a kind of multi-scale and multi-direction decomposition theory; furthermore, the number of scale decomposition and direction decomposition can be set arbitrarily. Only does as the number of decomposition increase, the information included decomposition coefficients will be more and more detailed. They reflect the image edge and geometry detail information and they are the high-frequency part of the image, too. Besides the useful detail information in high-frequency part, there exists a lot of useless noise. For SAR images, the main noise is speckle noise. In general, the scale number value is set to five, which is relatively appropriate. Similarly, the number value of direction decomposition is also very important. The directional decomposition number cannot take infinite or too small. If it is too large, the edge and detail geometry information will be split; if it is too small, it cannot reflect the characteristics or advantages of multi-direction. The directional decomposition number is usually represented by 2 k , where k  0,1,2,..., N . In the practical applications, if the value of k is five, it will satisfy the actual demand basically. Of course, how to set the value of k is based on the input image resolution and the detail information of the detected target. If the detail information of ground objects is relative abundance in the image, the value of parameter k will set to be relatively large; if the details are not abundant, the value will set to relatively small.

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(4) Perform Contourlet transform. After the two SAR images are pre-processed, they perform the Contourlet transform, respectively. Before Contourlet transform, it needs setting the transform parameters, namely, the scale decomposition numbers and the direction decomposition numbers, which are set in step three.

According to these parameters, multi-temporal SAR images are decomposed by Contourlet transform.

(5) Obtain all directional sub-images at each scale. After Contourlet transform, all sub-images can be obtained at different scales and different directions in every multi-temporal SAR image.

(6) Perform the difference operations and obtain difference sub-images. The two corresponding sub-images at the same scale and in the same direction perform the difference operations, and the result is that a difference sub-image is obtained between the two different sub-images. These operations do not stop until all sub-images are processed.

(7) Perform the inverse Contourlet transform. Using all difference sub-images in every direction at each scale performs the inverse Contourlet transform, and then the total difference image between the two SAR images is obtained.

(8) Determine the threshold of change detection. To determine the change detection threshold is the key technique in SAR images change detection. The threshold is usually obtained by the expectation maximum (EM) algorithm in the difference image. The EM algorithm is a common method to perform maximum likelihood estimation for the incomplete data [25]. It does not need any external data and prior knowledge, i.e., not needing the actual ground data, but it can get the estimation value of the parameter through itself observed data. The EM algorithm includes two stages which are the solution of an expectation value and the maximum value. The two steps are repeated until they are convergence.

(9) Perform the change detection operations and obtain the changed information. Using the determined threshold T performs the change detection through pixel by pixel in the difference image, and finally the change information can be gotten. The discriminated equation is as follows.  I ( x, y ); I D ( x, y )  T I C ( x, y )   D I D ( x, y )  T 0;

(2)

Where I C ( x, y ) denotes the obtained gray change information image, I D ( x, y ) denotes the gray value of the difference image, ( x, y ) denotes the space location of a pixel in the image. Equation (2) describes the state of single threshold detection. If you want to obtain the change information of different degree, such as the enhanced change or the decreased change, you may set different detection thresholds to obtain the corresponding information, which is the multi-threshold change detection technique.

In this step, how to determine the threshold T is a very critical technical problem. Assume that the SAR images I1 ( x, y ) and I 2 ( x, y ) are obtained by a same sensor from the same scene and at different time, and they are processed via the geometric correction, radiometric correction and image registration. The sizes of them are M  N , and I1  {I1 ( x, y ),1  x  M ,1  y  N} , I 2  {I 2 ( x, y ),1  x  M ,1  y  N} . Using x denotes the gray value of any pixel at the difference image I D ( x, y ) , I D  {I D ( x, y ),1  x  M ,1  y  M } , that is to say, I ( x, y ) denotes the gray value of the pixel point ( x, y ) , and I ( x, y )  I 2 ( x, y )  I1 ( x, y ) .

Firstly, only considering that the difference image I D is consisted of two parts, namely the changed type and the unchanged type, and then discussing other situations above two types. Let u and c denote the unchanged type and the changed type, respectively. P(u ) and P(c ) are the priori probability of their respective distributions, respectively. The conditional probabilities of gray value I at u and c are P( x / u ) and

P( x / c ) , respectively. The histogram H ( X ) of I D is approximatively considered to be the estimated value of the probability distribution function P( x ) of x , and the expression is as follows

P( x)  P( x / u )P(u )  P( x / c ) P(c )

(3)

Using the Bayesian equation, then

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P(k / x ) 

P( x / k ) P(k ) ; P( x )

k  (u, c)

(4)

Equation (4) is called the posterior probability of x . The essence of the Bayesian equation is with the observation value x , translating the state prior probability P(k ) into the state posterior probability P(k / x ) . In this way, the Bayesian decision rule based on the minimum error rate is that if P(u / x)  P(c / x) , x is classified into the unchanged type; if P(u / x)  P(c / x) , it considers that x is the changed type. When the threshold T satisfies Equation (5), it is considered to be the best threshold.

P(u ) P(T / u )  P(c ) P(T / c )

(5)

Experimental Results and Analysis In order to verify the feasibility, reliability and the advantages of CTCD algorithm, we use different data and different methods to perform some comparative experiments. The experimental data not only includes the airborne SAR image data, but also includes the spaceborne SAR image data. The DDCD algorithm and the CTCD algorithm are chosen in experiments.

Simulation Experiments The data shown in Fig.4 is from the publicly available data of the USA Sandia National Laboratory. Where Fig.4 (a) is the original SAR image data, Fig.4 (b) is the experimental results got by the CTCD algorithm, and what Fig.4(c) shown is the results obtained by the DDCD algorithm. Fig.4 (A) and Fig.4 (B) are the SAR images at different time, respectively, namely, the corresponding SAR images before and after change. The ground objects are tanks in SAR image and the background is jungle. Assume that the obtained time of the SAR image in Fig.4 (A) is t1 , namely the time of before change; the time of obtaining the SAR image in Fig.4 (B) is t 2 , namely the time of after change.

Compared with the SAR image at time t1 , there not only has the enhanced information in the SAR image at time

t 2 , namely, the appearance of some new tank targets, but also has the weakened information, namely the disappearance of some old tank targets. If only using a single threshold value detects the change information, both of the appeared targets and the disappeared targets can be detected together. But we cannot distinguish these targets between the new appeared targets and the disappeared targets, and only know that the changes have happened. If two thresholds are used, we not only can detect the changed information of ground objects, but also can distinguish between what is the enhanced information and what is the weakened information, i.e., the enhanced regions and the weakened regions. What is shown in Fig.4 (b) is the changed information obtained by the CTCD algorithm. The detection results of the enhanced regions and the weaken regions are shown in Fig.4 (C) and Fig.4 (D), respectively. In order to show the object information more clearly, especially the edge and geometry detail information, so the false color image is employed to describe the experimental results, which is shown in Fig.4 (E) and Fig.4 (F). They correspond to the Fig.4(C) and Fig.4 (D), respectively, and the green denotes the changed information or object regions.

The results of change detection with the DDCD algorithm are shown in Fig.4 (c). The detected results of weakening and enhancing are shown in Fig.4 (G) and Fig.4 (H), and their false color image is in Fig.4 (I) and Fig.4 (J), respectively. It can be seen from Fig.4 (b) and Fig.4 (c) that the detail information of the object region obtained by CTCD algorithm is more abundant, but the detail information obtained by DDCD algorithm is less. This fully shows the advantage of CTCD algorithm, obtaining more accurate and more abundant geometric detail change information.

A

B

(A) ORIGINAL SAR IMAGES

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C

D

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E

F

(B) CTCD ALGORITHM

G

H

I

J

(C) DDCD ALGORITHM FIG.4 THE DETECTION RESULTS OF SIMULATION CHANGE （A IS THE ORIGINAL IMAGE AT TIME t1 ; B IS ORIGINAL IMAGE AT TIME

t 2 ; C, G IS THE WEAKENED REGIONS; D, H IS THE

ENHANCED REGIONS; E, F, I, J IS THE FALSE COLOR IMAGE ACCORDING TO C, D, G, H, RESPECTIVELY）

Experiments of Forest Monitoring In order to further verify the reliability and the advantages of CTCD algorithm, two practical application examples are employed in the following experiments. The first example is the forest monitoring experiment and the experimental results are shown in Fig.5. The experimental data is from airborne remote sensing data of C/X-SAR of the Canada Centre for remote sensing (CCRS). The experimental area is a piece of forest and the purpose is to monitor deforestation and obtain the change information of forest area. Fig.5 (A) and Fig.5 (B) are the original SAR images according to before and after change, and the acquired time is March 1991and February 1992, respectively.

Both of them are C band and HH polarimetric images, and their spatial resolution is 5m  5m . Assume that the image in Fig.5 (A) is before change, namely, the image that forest does not cut down at time t1 ; What Fig.5 (B) showed is the image after change, namely, the image of forests having been cut down. Because of deforestation, the types of ground objects have changed, which results in that the corresponding SAR images change, too. At the center in Fig.5 (B), because forest was cut down, the scattering intensity of bare ground was less than that of forest area, the corresponding parts in SAR image were changed from a bright area into a darker area. When the forest was cleared, there were strong dihedral corner reflectors between the remaining trees and the ground, which shows bright line in Fig.5 (B). The test results with the CTCD algorithm are shown in Fig.5 (C) and Fig.5 (D), namely, Fig.5(C) is the enhanced information and Fig.5 (D) represents the weakened information. The enhanced and weakened information obtained by the DDCD algorithm are shown in Fig.5 (E) and Fig.5 (F), respectively. The purpose of this experiment is to perform the macro and dynamic monitoring on forest change information, instead of obtaining the detail information. Fig.5 shows that even the detail information is not required, the CTCD algorithm can detect the accurate change information. Comparing with the DDCD algorithm, it stands out the more detail information, which is shown in Fig.5 (C) and Fig.5 (D).

A

B

(A) ORIGINAL SAR IMAGE

C

D

(B) CTCD ALGORITHM

E

F

(C) DDCD ALGORITHM

FIG.5 RESULTS OF FOREST CUT DOWN （A, B IS ORIGINAL SAR IMAGE; C, E IS THE ENHANCED REGION; D, F IS THE WEAKEN REGION）

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Experiments of Flood Disaster Monitoring The second example of practical applications is flood disaster monitoring experiment and the experimental results are shown in Fig.6. Experimental data came from the radarsat-1 and the imaging area is Bengbu, Anhui, China.

Fig.6 (A) and Fig.6 (B) were the original SAR images before and after the disaster, and the obtained time was in summer 2001 and 2005, respectively. Due to being submerged by flood, there are large darker areas in Fig.6 (B). The changed results obtained by CTCD algorithm are shown in Fig.6 (C) and Fig.6 (D), where Fig.6 (C) denotes the area that did not submerged by flood and Fig.6 (D) denotes the submerged area by flood. Similarly, Fig.6 (E) and Fig.6 (F) show the test results obtained by DDCD algorithm; furthermore, they denote the not submerged area and the submerged area, respectively. It can be seen in Fig.6 that the detection effect of CTCD algorithm is better than that of DDCD algorithm, so it further indicates that the accuracy of detail information with CTCD algorithm is more accurate than that of the common using method of DDCD algorithm, which shows that the CTCD algorithm can be used to monitor the changes of flood disaster.

The results in Figs.4-6 show that CTCD algorithm is an effective change detection method. Compared with the general change detection methods, CTCD algorithm can obtain more accurate detail change information, and adapt to dynamic monitoring for SAR images of different sensors and different types ground objects.

B

A

C

(A) ORIGINAL SAR IMAGE

E

D

(B) CTCD ALGORITHM

F

(C) DDCD ALGORITHM

FIG.6 RESULTS OF FLOOD DISASTER （A, B IS ORIGINAL IMAGE; C, E IS NOT SUBMERGED AREA; D, F IS SUBMERGED AREA）

Quantitative Analysis Experiments The above experiments from the vision prove that CTCD algorithm is feasible, for further analyzing its performance, next using the concrete evaluation indexes perform quantitative analysis. Because the accuracy of change detection is affected by many factors, such as image quality, detection methods, background complexity, analytical skills and experience [26], so far, there is not a unified standard and parameter index to evaluate the precision of change detection results. The common used parameter indexes on effective evaluation mainly include the miss detection rate, the false detection rate, the total right detection accuracy and the Kappa coefficient of the change pixel [27]. Through the description and analysis on the change detection result data, the pixel classification error matrix (confusion matrix) may be used to perform the quantitative analysis to the estimation indexes of accuracy [28]. The remote sensing image pixel level change detection is basically achieved through pixel classification. The thought of from the classification error matrix of image pixels turning into the change detection error matrix method is acted as a quantitative estimation method of the change detection performance. Table 1 is a simple change error matrix.

In Table 1, N CC denotes the number of pixels which are real change and detected to be change, NUC denotes the number of pixels which are real no change but detected to be as a change pixels, TN DC denotes the total number of pixels detected to be changed by the algorithm and TN DC  NCC  NUC ; N CU TABLE 1 THE ERROR MATRIX OF CHANGE PIXELS

The changed number of pixels detected by algorithm The unchanged number of pixels detected by algorithm Total

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The number of real changed pixels

The number of real no unchanged pixels

Total

N CC

NUC

TN DC  NCC  NUC

N CU

NUU

TN DU  NCU  NUU

TNC  NCC  NCU

TNU  NUC  NUU

TN

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denotes the number of pixels that are real changed without being detected, NUU denotes the numbers of pixels which are not changed and detected to be no change, TN DU denotes the total number of pixels which are detected to be unchanged by the algorithm and TN DU  NCU  NUU ; TN C denotes the total number of pixels which are really changed and TNC  NCC  NCU ; TNU

denotes the number of total pixels without change and

TNU  NUC  NUU ; TN is the total number of pixels of the image, if the size of the image is M  N , and then

TN  M  N . According to each definition of the change detection error matrix in Table 1, we can get the some parameter indexes that are used to perform the quantitative analysis and estimation on the performance of change detection methods.

The definition of the correct detection accuracy PTD refers to the ratio, between the number sum of these pixels which are correct detection including real change and without change pixels, i.e. NCC  NUU , and the number of the total pixels, i.e. TN , as reflects the overall level of detection, and the definition expression is as follows.

PTD 

NCC  NUU  100% TN

(6)

The definition of miss detection ratio PCM of the changed pixels refers to the ratio, between the number of real changed pixels but without being detected by algorithm, i.e. N CU , and the number of real changed pixels, i.e. TN C , which reflects the missing detection degree of the changed pixels. And the definition is given by Equation (7).

PCM 

N CU  100% TN C

(7)

The definition of missing detection ratio PUM of the unchanged pixels refers to the ratio, between the number of real no change pixels but which is detected to be changed by algorithm, i.e. NUC , and the total number of real no change pixels, i.e. TNU , which reflects the missing detection degree of unchanged pixels. And the definition is as following.

PUM 

NUC  100% TNU

(8)

The error detection ratio of change pixels, i.e. the false ratio PCF , is the ratio between the number of pixels which are real not changed but are detected as the changed pixels by algorithm, i.e. NUC , and the total number of pixels which are detected to be changed by algorithm, i.e. TN DC , which reflects the degree of false detection of the change pixels. The definition is given by PCF 

NUC  100% TN DC

(9)

The error detection ratio of the unchanged pixels PUF refers to the ratio between the number of pixels which are real changed but are not detected, i.e. N CU , and the total number of pixels which are not changed by algorithm, i.e.

TN DU , which reflects the degree of false detection of the no change pixels. The definition is as follows.

PUF 

N CU  100% TN DU

(10)

The parameter of Kappa coefficient is calculated with Equation (8). It is a representation method of the classification accuracy [29]. The Kappa coefficient describes the internal consistency of detection results. Compared with the total correct detection accuracy, the Kappa coefficient can more objectively reflect the accuracy of test results, and the larger the value is and the higher the precision is. It is a comprehensive index, combining the user accuracy and mapping precision. The relation between the Kappa coefficients and the detection results are shown in Table 2.

Kappa 

TN  ( N CC  NUU )  (TNC  TN DC  TNU  TN DU ) TN 2  (TNC  TN DC  TNU  TN DU )

(11)

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TABLE 2 THE RELATION TABLE OF KAPPA COEFFICIENT AND THE DETECTION PRECISION

Kappa coefficient

Precision

Less than zero

Very poor

0-0.2

Poor

0.2-0.4

General

0.4-0.6

Good

0.6-0.8

Very good

0.8-1.0

Excellent

In this experiment, the SAR image data came from ERS-2 of the European Space Agency (ESA) and the imaging area is Berne City, Switzerland. It is the monitoring images of the flood. The SAR image is C band and the size is 256 ď‚´ 256 , which is shown in Fig.7. The images in Fig.7 (A) and Fig.7 (B) are the original image of before and after change, and they were obtained in April 1999 and May 1999, respectively. Fig.7 (C) is the ground truth change image obtained by artificial drawing. The changed region is mainly caused by flood disaster. The results in Fig.7 (D) was obtained by the DDCD algorithm and using the CTCD algorithm obtaining results is shown in Fig.7 (E).

Through Fig.7 (D) and Fig.7 (E), it further shows that the CTCD algorithm can get more abundant change detail information. The evaluation values of all parameters are shown in Table 3 and they are from Fig.7. Some parameter values are obtained by CTCD algorithm, such as the total correct detection ratio PTD , the missing detection ratio of unchanged pixels PUM and Kappa coefficients are higher than that of DDCD algorithm, which also shows that the effect of CTCD algorithm is good. At the same time, the false detection ratio of changes pixels, obtained by CTCD algorithm, is higher than that of the DDCD method; in order to reduce disaster losses, the false detection ratio is higher, which means to be good; the military target detection needs high false alarm ratio, too. For the missing detection ratio of change pixels PCM , the value of CTCD algorithm is lower than that of DDCD method, as shows that CTCD algorithm misses fewer pixels. The false detection rate of unchanged pixels of CTCD algorithm is also lower. Through the analysis and comparison of the above parameters, the CTCD algorithm is better than the DDCD algorithm and various performance indexes have been improved.

A

B

D

C

E

FIG.7 RESULTS OF QUANTITATIVE ANALYSIS EXPERIMENTS (A,B IS ORIGINAL IMAGE; C IS TRUE CHANGE IMAGE; D IS DDCD METHOD; E IS CTCD METHOD) TABLE 3 VALUES OF EVALUATION PARAMETERS

Algorithm

PTD

PCM

PUM

PCF

PUM

Kappa coefficient

DDCD

99.0036

51.6883

0.0870

9.1205

0.9196

0.6263

CTCD

99.1394

32.8139

0.2874

19.2508

0.5869

0.7291

Conclusion The Contourlet transform can provide multi-scale and multi-direction information, and is also a kind of sparse representation for images. These characteristics are very consistent with the direction sensitivity of SAR imaging.

Therefore, on the basis of deep studying on the mechanism of SAR imaging and the characteristics of Contourlet transform, a new CTCD change detection algorithm was proposed in this paper for multi-temporal SAR image change detection. Compared with DDCD algorithm, CTCD algorithm can get more abundant detailed information.

Through the different contrast experiments, the test results fully verify the feasibility of CTCD algorithm. The next work is to combine CTCD algorithm with other methods or theories, and further improve the accuracy of change detection.

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ACKNOWLEDGMENTS

The authors would like to thank the anonymous reviewers and editors for their careful reading and constructive criticism. Their comments and suggestions have helped us to improve the clarity of the paper. At the same time, the work was supported by Natural Science Foundation of China (No. 61379031).

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