A STATISTICAL TEXTURE FEATURE FOR BUILDING COLLAPSE INFORMATION EXTRACTION OF SAR IMAGE

Synthetic Aperture Radar (SAR) has become one of the most important ways to extract post-disaster collapsed building information, due to its extreme versatility and almost all-weather, day-and-night working capability, etc. In view of the fact that the inherent statistical distribution of speckle in SAR images is not used to extract collapsed building information, this paper proposed a novel texture feature of statistical models of SAR images to extract the collapsed buildings. In the proposed feature, the texture parameter of G distribution from SAR images is used to reflect the uniformity of the target to extract the collapsed building. This feature not only considers the statistical distribution of SAR images, providing more accurate description of the object texture, but also is applied to extract collapsed building information of single-, dualor full-polarization SAR data. The RADARSAT-2 data of Yushu earthquake which acquired on April 21, 2010 is used to present and analyze the performance of the proposed method. In addition, the applicability of this feature to SAR data with different polarizations is also analysed, which provides decision support for the data selection of collapsed building information extraction.


INTRODUCTION
Accurate collapse information is essential to providing decision support for the government's post-disaster relief and reconstruction.Synthetic Aperture Radar (SAR) has become one of the most effective means of extracting collapsed building information after a disaster, due to its wide coverage, strong penetrability and all-time/all-weather imaging capabilities. 1  Abundant single-, dual-polarization SAR data provide protection for extracting collapsed buildings information timely after a disaster.The difference between amplitude or backscatter intensity (Ohkura et al, 1997;Matsuoka and Yamazaki, 2005;Hosokawa et al., 2009) and the coherence of (Ito and Hosokawa, 2003;Hosokawa andJeong, 2007, Liu andYamazaki, 2015) are often used to extract collapsed building information based on single or dual-polarization SAR images before and after a disaster.In addition, texture features are widely used in the extraction of collapsed building information with single-or dual-polarization SAR data.Analyzing the Cosmo / SkyMed and Terra SAR-X data from Yingxiu town after the Wenchuan earthquake, Dell 'Acqua et al. (2009) found that homogeneity in urban areas decreased as building damage increased.Polli et al. (2010) calculated the correlations between the earthquake damage level and the eight texture based on the Gray Level Co-occurrence Matrix (GLCM).The results showed that entropy, homogeneity and earthquake damage level had a relatively good correlation.Based on the homogeneity and entropy of GLCM, Dell'Acqua et al. (2010) classified the damage levels into three levels and experiment with postearthquake single-polarization SAR data from the 2008 Wenchuan, the 2009 L'Aquila Italy and the 2010 Haiti earthquake, although the extent of damage for some blocks are overestimated, the follow-up study is still of great significance.

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Compared with the single-and dual-polarization SAR, fullpolarization SAR (PolSAR) obtains richer surface information.Polarization features have been widely used in collapsed building extraction of PolSAR image, and has achieved good results (Guo, 2009;Li et al., 2012;Zhao et al., 2013;Shen et al., 2015).But it is easy to misidentify the intact buildings with large orientation angle as collapsed buildings because of the influence of orientation angle and building structure.Zhao et al. (2013) revised the results of building damage assessment, brought about by normalized circular-pol correlation coefficient (NCCC), with the help of the homogeneity texture features of the GLCM.Shi et al. (2015) extracted 181 features of polarizations, interferences and textures to classify airborne SAR data after Yushu Earthquake and evaluated building damage by random forest classifiers.The result proved that texture features were superior than polarization feature in extracting collapsed buildings, and the variance of Gray-Level Histogram extracted based on X-band intensity data was best.Sun et al. (2016) extracted 5 categories of texture features based on the CASMSAR data of the urban area after the Yushu earthquake.Random forest classifier was used to evaluate the damage levels of buildings.The test indicated the variance of the Gray-Level Histogram and the contrast texture based on GLCM worked well in assessment of collapsed buildings generally.
Texture features play an important part in assessment of collapsed buildings in SAR data.But directly applying the extraction method of optical images to SAR images can't accurately describe the texture information of the object.Owing to it does not consider the inherent statistical distribution of speckle in SAR images.Studying the statistical characteristics of speckle in SAR images can better extract the information needed.In order to better model the extremely heterogeneous regions in urban areas, Frery et al. (2008) modelled the texture variables with inverse gamma distribution and proposed a G 0 distribution suitable for the modelling of extreme heterogeneous regions, which is based on the product model.The texture parameter of the G 0 distribution can reflect the uniformity of the target.The larger the value of the texture parameter, the more uniform the target (Frery et al., 2008;Lee and E. Pottier, 2009).Therefore, in this paper, the texture parameter of G 0 distribution in SAR image is used to describe the uniformity of the target, so as to extract the information of collapsed buildings.In addition, this paper also comparatively analyses the applicability of G 0 texture parameter to SAR image with different polarization in extracting collapsed building information, and provides the basis for the post-disaster collapsed building information extraction in SAR images.The experiments of the RADARSAT-2 data after the Yushu earthquake in 2010 prove the validity of statistical texture features proposed in this paper for extracting collapsed buildings information.

METHODOLOGY
The process of this method includes three main steps.Firstly, the G 0 texture parameter is estimated based on the SAR data.Then, the non-building areas are removed with the method of literature (Chen et al., 2016), and the collapsed buildings are extracted utilizing the estimated texture parameter.Finally, the build damage assessment map is obtained according to the building block collapse rate (BBCR).The detailed flow chart is shown in Figure 1.

SAR data
In a reciprocal medium, the full-polarization SAR scattering vector is [ ] , the covariance matrix is where is the transpose of the matrix, indicates the conjugate, 〈 〉 represents the set average, is to ensure that the total power is equal.
Scattering vectors for dual-polarization SAR data can be written directly as [ ] , the polarization covariance matrix is: For the HH / HV combination in dual polarization SAR image, the polarization covariance matrix is: For the HV/VV combination in dual polarization SAR image, the polarization covariance matrix is: For the HH/VV combination in dual polarization SAR image, the polarization covariance matrix is:

G 0 distribution and Parameters Estimation
According to product model, the speckle of SAR data is expressed as the product of texture variable τ and speckle distribution X. (6) For multi-look and multi-polarization SAR data, is covariance matrix ， obeys the Wishart distribution, and the PDF (Probability Density Function) is: where is the expectation of the covariance matrix, n is the number of looks, ( ) denotes the gamma function, ( ) represents the trace of the matrix, d is the dimension of speckle vector, and d is 2 in dual-polarization SAR data.In the reciprocal medium, d=3 for full polarization SAR data.
For multi-look and single-polarization SAR data, indicates intensity, The probability density function of is a special case of d=1 in equation ( 7) and can be expressed as： where is the expectation.
When the texture variable is modelled by inverse gamma ( ̅ ) distribution, where is the texture parameter.
For multi-look and multi-polarization SAR data，covariance matrix follows the G 0 distribution, and the probability density function (PDF) is expressed as: When d=1, equation ( 11) can be simplified to the G 0 distribution of the multi-look and single-polarization SAR intensity image I. Its probability density function is: Based on the second moment, the texture parameter of the G 0 distribution is expressed as: where Var{ } represents variance, for the multi-polarization SAR data , ( ), for the single-polarization SAR data, M is intensity data.
The texture parameter of G 0 distribution reflect the homogeneity of the targets (Frery et al., 2008;Lee and E. Pottier, 2009).The larger the estimated texture parameter is, the smaller the variance of the texture variables become.Therefore, this paper proposes an effective way to distinguish between intact buildings and collapsed buildings using the texture parameters of statistical model.

Building Damage Assessment
Based on the estimated texture parameter, the collapsed buildings are extracted with the threshold which is determined by iterative method.
The building block collapse rate (BBCR) is calculated at the block scale.These blocks are separated by roads, and the structures of building have a strong similarity in one block (Zhao et al., 2013).BBCR is defined as the proportion of collapsed buildings to the total number of buildings (contains intact buildings and collapsed buildings) of the block.The more serious damage the block suffers, the greater BBCR is.The BBCR is expressed as: (14) where and indicate the number of collapsed and intact buildings of the j th block.
The thresholds 0.3 and 0.5 are set based on BBCR, and the blocks are divided into three levels: slight damage, moderate damage and serious damage.

Description of the Experimental Data
The study case is Yushu County in the Qinghai Province of China after a 7.1-magnitude earthquake that occurred on April 14, 2010.The epicenter was at 33.1°N and 96.7°E .The elevation of Yushu County is approximately 3500m, but its terrain is comparatively gentle.The major land cover classes include bare soil, buildings, roads, rivers, and so on.The buildings are mainly rural residential buildings; most do not design to resist seismic events, and some buildings are on slopes or other unstable places.The C band, RADARSAT-2 polarimetric data has a spatial resolution about 8m.The Pauli RGB image after 3-look multi-looking processing is shown in The whole county is divided into 83 blocks according to roads and the similarities of built-up patches, including slight damage, moderate damage and serious damage, and the classification rule for damage levels are refer to other studies (Zhao et al., 2013;Zhai et al., 2016).

Experiment and analysis
In this paper, the G 0 distribution texture parameters of single-, dual-and full-polarization SAR data are calculated by equation ( 13), which also extracts the texture features to reflect the uniformity of the building area.Using the area under the receiver operating characteristic curve (AUC) (Hanley, 1982) assesses the distinguishing ability of the G 0 distribution texture feature (G 0 -para) for collapsed buildings and intact buildings.Contrast texture of Gray Level Co-occurrence Matrix (GLCM) and the variance of the gray histogram (Var-his) were compared to illustrate the effectiveness of the texture features introduced in this paper.Based on the sample in Figure 2 The AUC reflects the ability of the feature to recognize the sample, independent of the threshold.The larger the AUC, the stronger the ability of the feature to recognize the sample.As shown in Table 1, regardless of VV, HH/HV, or fullpolarization SAR data, the recognition ability for collapsed buildings of G 0 texture parameter is significantly better than the contrast features.Basically, the severe damaged areas on the three alluvial fans and the mildly damaged areas on the northeast corner with orientation angles can be accurately evaluated.However, buildings in southeastern of the urban are sparse and uniform, so that mild or moderately damaged areas are easily misjudged as severe damage.Due to the existence of partially intact buildings in the south severe damaged area, the uniformity of the buildings is reduced and is easily misclassified as moderate or mild damage.The assessment of VV in the south severe damaged area is worst.Although the assessment of HH / HV in the south is more accurate, it is easy to identify some of the severe damaged area in northwest as moderately damaged.In order to quantitatively analyze the effect of building damage assessment, the detection rate (DR), false alarm rate (FAR), F1-score (Powers and Ailab, 2011) and overall accuracy (OA) are considered to evaluate the accuracy as shown in

CONCLUSIONS
This study introduced the G 0 distribution texture parameter to reflect the homogeneity of building areas, and it was used for collapsed building information extraction.The introduced statistical texture feature can be applied to single-, dual-and full-polarization SAR images.According to the experiments of RADARSAT-2 SAR image after Yushu earthquake, the texture features proposed in this paper is superior to the comparison features in distinguishing collapsed and intact buildings, and achieves higher accuracy for collapsed building information extraction.When full-polarization SAR image is difficult to obtain, the G 0 distribution texture parameters of dualpolarization, HH and VV SAR images are the suitable choice for collapsed building information extraction.

Figure 1 .
Figure 1.The flow chart of building damage assessment.

Figure. 2
Figure.2(a) at a size of 527  257 pixels, the areas marked in red are the collapsed buildings; blue indicates intact buildings .The ground-truth map of the buildings in Yushu County is shown in Fig. 2(b), which was interpreted according to the 0.5 m optical image acquired on May 6, 2010 and the detailed damage map from the German Aerospace Center (DLR, 2016).The whole county is divided into 83 blocks according to roads and the similarities of built-up patches, including slight damage, moderate damage and serious damage, and the classification rule for damage levels are refer to other studies(Zhao et al., 2013;Zhai et al., 2016).

Table 1 .
(a), the calculated AUC for different features is shown in Table1.The AUC of G 0 distribution texture parameters in SAR data with different polarizations

Table 2 .
The accuracy of PolSAR is better than that of HH / HV, which is 68.01%, 71.51% and 73.70% respectively.

Table 2 .
The accuracies of building damage assessments for RADARSAT-2 data.The G 0 texture parameters of SAR data with different polarizations are shown in Table3, which are based on the sample table 2 in Figure.2(a).For single-polarization SAR data, the AUC values of the G 0 texture parameters of the samepolarization SAR (HH or VV) are not much different but both larger than HV.In dual-polarization SAR data, the AUC values of the combination of co-polarization and cross-polarization (HH/HV or VH/VV) are all greater than HH/VV, and the value of HH/VV is smaller than HH or VV.Table3shows that the G 0 texture parameter of HV is not suitable for information extraction of collapsed buildings.For single-polarization SAR image, the introduced texture feature of HH and VV are similar, and they are better than HV.For dual-polarization SAR image, HH/VV, HH/HV and VV/VH have the similar results, which are close to full-polarization SAR image.

Table 3 .
The AUC of G 0 distribution texture parameters in SAR data with different polarizations