Screening Image Features of Collapsed Buildings for Operational and Rapid Remote Sensing Identification

: The accurate detection of collapsed buildings is of great significance for post-disaster rescue and reconstruction. High-resolution optical images are important data sources for identifying collapsed buildings, and the identification accuracy mainly depends on the features extracted from the images. However, existing research lacks a comprehensive screening and general evaluation of the ability of remote sensing features to detect collapsed buildings


Introduction
Building collapse caused by disasters is an important damage to lives and properties.Rapid identification of collapsed buildings is of great significance for post-disaster rescue [1] and reconstruction [2].In recent years, remote sensing has become an important method of obtaining building damage information because of its advantages of non-contact, low cost, wide field of view, and fast response [3].Due to the urgency of post-disaster rescue, it is necessary to make the process of remote sensing identification of collapsed buildings operationalized so that we can rapidly identify collapsed buildings while maintaining high recognition accuracy.
Remote sensing identification essentially involves the following processes: data collection → feature extraction → feature selection → target identification using an appropriate Remote Sens. 2023, 15, 5747 2 of 18 classification method.The current methods for remote sensing identification mainly include traditional machine learning methods and deep learning methods, both of which essentially follow the process mentioned above.The deep learning methods avoid manual feature extraction and feature selection [4][5][6], but they require a large number of samples for training [7], which are limited in the case of collapsed buildings [8].Although methods like data augmentation [9], transfer learning [8,10], or pseudo-labeled training sample production [11] could alleviate this problem, they all rely on the samples from the study area.Due to the small sample volume, it is easy to suffer from the uneven distribution of training samples, which affects the training accuracy of the model [8].Therefore, current deep learning methods are still unable to meet the operationalization needs of rapid identification of collapsed buildings after disasters.In contrast, traditional machine learning methods do not require as many samples, and the effectiveness of their identification largely depends on the features used.The enhancement in either feature extraction or feature selection can contribute to improving the accuracy of collapsed building recognition.However, this study primarily focuses on feature selection.
There have been many features used for remote sensing recognition of collapsed buildings in previous studies.For example, Ye et al. [12] used texture and local spatial statistical features to identify collapsed buildings in the post-earthquake images of the 2015 Nepal earthquake; Zeng et al. [13] used grayscale mean and inverse different moment to identify collapsed buildings in post-earthquake images of Haiti and Yushu; Ye et al. [14] used local Moran'I, texture, and gradient to identify collapsed buildings in post-earthquake images of the Yushu earthquake; Sumer et al. [15] used grayscale values and gradient to identify collapsed buildings in post-earthquake images of the Kocaeli earthquake.The features used for collapsed building identification in previous studies include spectral features [16,17], Entropy, Coefficient of Variation, Local Mean, Local Standard Deviation, Local Moran'I [12,14], Gradient, Gradient Orientation [14,18], Edge, Edge Density [19], Gray Level Co-Occurrence Matrix (GLCM) [19,20], Local Binary Patterns (LBP), Fractal feature [21], and Gabor feature [21], etc.These features can be summarized into spectral features and spatial features (Figure 1), where spectral features include original bands and their derived features, and spatial features include spatial statistical features, gradient and edge features, and texture features.The research mentioned above has achieved good recognition results for collapsed buildings in specific areas, but there has been no study on how to select the optimal features.Instead, several features were directly used for identification based on prior knowledge, making the individual roles of these features unclear in the process.Furthermore, existing studies are all case studies conducted in a certain area, so it is still unknown whether the features can be equally applicable in other regions.In summary, although many features have been used for the recognition of collapsed buildings, their recognition ability and transferability have not been widely evaluated, and there is a lack of theoretical guidance on which features should be used for practical identification work.Therefore, there is still a gap in the operational process of rapid recognition of collapsed buildings in remote sensing.
This article is dedicated to screening out remote sensing features of collapsed buildings.By using a large building sample set collected from different regions around the world, this study evaluated the capability of 25 different features in detecting collapsed buildings and explored the optimal parameters for the features with good performance to make the best use of the features.For the features with good distinguishing ability for collapsed buildings, we test their effectiveness on the application test image set.This article is dedicated to screening out remote sensing features of collapsed buildings.By using a large building sample set collected from different regions around the world, this study evaluated the capability of 25 different features in detecting collapsed buildings and explored the optimal parameters for the features with good performance to make the best use of the features.For the features with good distinguishing ability for collapsed buildings, we test their effectiveness on the application test image set.

Building Sample Set
The building sample set of this study includes 2630 pairs of building samples distributed in 6 regions worldwide.Each pair of building samples includes the pre-and postcollapse images of the same building.The samples are all visible-light images with a spatial resolution of about 0.5 m.Each sample is approximately 100 rows × 50 columns of pixels in size.The samples were selected from the xBD dataset [22] and the Open Data Program dataset (https://www.digitalglobe.com/ecosystem/open-data,accessed on 3 March 2023) of Maxar.The xBD dataset contains over 850,000 pairs of pre-and post-collapse building images as well as boundary vector data for pre-collapse buildings.In this study, a total of 2508 pairs of samples were selected through visual interpretation from the xBD dataset.The Open Data Program dataset provides remote sensing images before and after disaster events.A total of 122 pairs of pre-and post-collapse building samples were selected through visual interpretation, and the vector boundaries of pre-collapse

Building Sample Set
The building sample set of this study includes 2630 pairs of building samples distributed in 6 regions worldwide.Each pair of building samples includes the pre-and post-collapse images of the same building.The samples are all visible-light images with a spatial resolution of about 0.5 m.Each sample is approximately 100 rows × 50 columns of pixels in size.The samples were selected from the xBD dataset [22] and the Open Data Program dataset (https://www.digitalglobe.com/ecosystem/open-data,accessed on 3 March 2023) of Maxar.The xBD dataset contains over 850,000 pairs of pre-and post-collapse building images as well as boundary vector data for pre-collapse buildings.In this study, a total of 2508 pairs of samples were selected through visual interpretation from the xBD dataset.The Open Data Program dataset provides remote sensing images before and after disaster events.A total of 122 pairs of pre-and post-collapse building samples were selected through visual interpretation, and the vector boundaries of pre-collapse buildings were manually outlined.Figure 2 shows image examples of some samples, and the detailed information of all samples is shown in Table 1.
buildings were manually outlined.Figure 2 shows image examples of some samples, and the detailed information of all samples is shown in Table 1.The application test image set consists of three large-scale remote sensing images, namely post-disaster remote sensing images from Joplin (6408 rows × 4734 columns), Moore (13,560 rows × 10,019 columns), and Tuscaloosa (8431 rows × 5941 columns).These large-scale images are also visible light images derived from the Open Data Program dataset, with a spatial resolution of approximately 0.5 m.The application test image set is used to test the practical application ability of selected features in this study.

Methodology
Based on the building sample set, this study evaluated the ability of 25 features to distinguish collapsed buildings from non-collapsed buildings by two indicators (Jeffries-Matusita distance and Transformed Divergence) and explored the optimal parameters for the features with good performance.For the features with good distinguishing ability for collapsed buildings, we test their effectiveness on the application test image set.

Ability Evaluation of Features
The indicators used to evaluate the ability of features are Jeffries-Matusita distance (J-M distance) and Transformed Divergence (TD), which can measure the distance between collapsed building samples and non-collapsed building samples in the feature space.Both J-M distance and TD are in the range of 0 to 2, and the higher value indicates a better distinguishing ability of the feature.
The calculation formula for the J-M distance is shown in Equations ( 1) and ( 2): where U is the mean vector of the sample, ∑ is the covariance matrix, and i and j are non-collapsed and collapsed building samples, respectively.The calculation formula for TD is shown in Equation ( 3): where D ij is the divergence between non-collapsed and collapsed buildings, and its calculation formula is shown in Equation ( 4): where U is the mean vector of the sample, ∑ is the covariance matrix, t r [A] is the sum of diagonal elements in matrix A, and i and j are non-collapsed and collapsed building samples, respectively.The extraction methods for various features are shown in Table 2.

Optimization of Parameters in Feature Extraction
The Local Mean, Local Standard Deviation, Local Entropy, and Local Coefficient of Variation are easily affected by the window size.If the window size is too small, the feature cannot reflect the fragmentation of collapsed buildings, while the feature calculated by an oversized window may exaggerate the grayscale variations of non-collapsed buildings, resulting in a larger feature value than it should be.Therefore, an inappropriate window size may lead to a decrease in the ability of the feature to identify collapsed buildings.To explore the optimal window size, we calculated the above features under a series of window sizes and used J-M distance and TD as the measures of distinguishing ability.
Features calculated based on GLCM, such as Contrast, Correlation, Energy, and Homogeneity, are not only easily influenced by the window size but also by the gray level.If the gray level is not large enough, the difference between different fragments of collapsed buildings in grayscale will be diminished, so that the distinguishing ability for collapsed buildings of the feature can be weakened.If the gray level is huge, it can not only lead to excessive computation but also exaggerate the grayscale differences of non-collapsed buildings, and the extracted texture feature is more susceptible to noise.To explore the optimal combination of window size and gray level, we calculate the above features under a series combination and use J-M distance and TD as measures of distinguishing ability.J-M distance and TD only illustrate the ability of the selected features to distinguish collapsed buildings from non-collapsed buildings in feature space, so we test the application effect of the features by using the images in the application test image set as an example.We used the thresholding method as the algorithm for extracting collapsed buildings instead of using a more complex machine learning algorithm, as it is the simplest and most intuitive method.Using the thresholding method can demonstrate that the extraction effect of collapsed buildings is derived from the contribution of the features rather than from the contribution of the classification algorithm.The technical flowchart for the assessment is shown in Figure 3. ability.

Assessment of the Application Effects of Selected Features
J-M distance and TD only illustrate the ability of the selected features to distinguish collapsed buildings from non-collapsed buildings in feature space, so we test the application effect of the features by using the images in the application test image set as an example.We used the thresholding method as the algorithm for extracting collapsed buildings instead of using a more complex machine learning algorithm, as it is the simplest and most intuitive method.Using the thresholding method can demonstrate that the extraction effect of collapsed buildings is derived from the contribution of the features rather than from the contribution of the classification algorithm.The technical flowchart for the assessment is shown in Figure 3. (1) Collapsed building identification Take Local Entropy as an example to illustrate the process of collapsed building identification.First, the vegetation index (the calculation formula is shown in Equation ( 5) [23]) was used to mask vegetation areas in the test image.Then, the Local Entropy of every pixel was calculated in the masked image, and the threshold method was used to extract collapsed buildings.For the segmented binary image, majority analysis and opening operations were used to eliminate small and meaningless patches, and the final identification result was obtained.
where VI represents the vegetation index, and R, G, and B represent the pixel values in the red, green, and blue bands of the image.
(2) Accuracy evaluation The confusion matrix calculated by randomly generated pixels is used to evaluate the accuracy of the identification of collapsed buildings.Approximately 1000 pixels were randomly generated from the non-collapsed and collapsed buildings of the classification result, respectively.Then, a confusion matrix is calculated by visually interpreting every random pixel.Based on the confusion matrix, precision, recall, and F1-score were calculated as the recognition accuracy indicators.
Precision reflects the identification method's ability to correctly identify collapsed buildings.Recall, on the other hand, reflects the identification method's ability to avoid misidentifying non-collapsed buildings.The calculation formulas for precision and recall are shown in Equations ( 6) and (7).
where TP is the number of true positive samples, which is the number of the samples classified as collapsed buildings and, in fact, also collapsed buildings; FP is the number of false positive samples, which is the number of the samples classified as collapsed buildings but actually non-collapsed buildings; FN is the number of false negative samples, (1) Collapsed building identification Take Local Entropy as an example to illustrate the process of collapsed building identification.First, the vegetation index (the calculation formula is shown in Equation ( 5) [23]) was used to mask vegetation areas in the test image.Then, the Local Entropy of every pixel was calculated in the masked image, and the threshold method was used to extract collapsed buildings.For the segmented binary image, majority analysis and opening operations were used to eliminate small and meaningless patches, and the final identification result was obtained.
where VI represents the vegetation index, and R, G, and B represent the pixel values in the red, green, and blue bands of the image.
(2) Accuracy evaluation The confusion matrix calculated by randomly generated pixels is used to evaluate the accuracy of the identification of collapsed buildings.Approximately 1000 pixels were randomly generated from the non-collapsed and collapsed buildings of the classification result, respectively.Then, a confusion matrix is calculated by visually interpreting every random pixel.Based on the confusion matrix, precision, recall, and F 1 -score were calculated as the recognition accuracy indicators.
Precision reflects the identification method's ability to correctly identify collapsed buildings.Recall, on the other hand, reflects the identification method's ability to avoid misidentifying non-collapsed buildings.The calculation formulas for precision and recall are shown in Equations ( 6) and (7).
where TP is the number of true positive samples, which is the number of the samples classified as collapsed buildings and, in fact, also collapsed buildings; FP is the number of false positive samples, which is the number of the samples classified as collapsed buildings but actually non-collapsed buildings; FN is the number of false negative samples, which refers to the number of samples classified as non-collapsed buildings but actually collapsed buildings.
The F 1 -score takes both precision and recall into account and can comprehensively represent the accuracy of the classification results.The calculation formula is shown in Equation (8).

Ability of 25 Features to Distinguish Collapsed Buildings from Non-Collapsed Buildings
There are significant differences in the ability to distinguish collapsed buildings from non-collapsed buildings of different features (Figure 4).Although the results of J-M distance and TD are not entirely consistent, they generally show the same patterns.The result shows Homogeneity, Energy, Local Entropy, Local Standard Deviation, and Gradient are more capable of distinguishing collapsed buildings from non-collapsed buildings (J-M distances are greater than 1.59, TDs are greater than 1.60), followed by Contrast, Local Coefficient of Variation, Edge Density, and Global Entropy (J-M distances are 1.14-1.28,TDs are 1.24-1.48).However, Gradient Orientation Entropy, Fractal Dimension, LBP, Edge, Local Mean, Correlation, Gradient Orientation Standard Deviation, Global Coefficient of Variation, Gabor feature, Local Moran'I, and six spectral features perform relatively poorly (J-M distances are less than 0.73, TDs are less than 1.07).There are also differences in the extraction times of different features; the results are presented in Appendix A.

Ability of 25 Features to Distinguish Collapsed Buildings from Non-Collapsed Buildings
There are significant differences in the ability to distinguish collapsed buildings from non-collapsed buildings of different features (Figure 4).Although the results of J-M distance and TD are not entirely consistent, they generally show the same patterns.The result shows Homogeneity, Energy, Local Entropy, Local Standard Deviation, and Gradient are more capable of distinguishing collapsed buildings from non-collapsed buildings (J-M distances are greater than 1.59, TDs are greater than 1.60), followed by Contrast, Local Coefficient of Variation, Edge Density, and Global Entropy (J-M distances are 1.14-1.28,TDs are 1.24-1.48).However, Gradient Orientation Entropy, Fractal Dimension, LBP, Edge, Local Mean, Correlation, Gradient Orientation Standard Deviation, Global Coefficient of Variation, Gabor feature, Local Moran'I, and six spectral features perform relatively poorly (J-M distances are less than 0.73, TDs are less than 1.07).There are also differences in the extraction times of different features; the results are presented in Appendix A.

Optimal Parameters for Feature Extraction
The ability of Local Mean, Local Entropy, Local Coefficient of Variation, and Local Standard Deviation to distinguish collapsed buildings from non-collapsed buildings varies under different window sizes (Figure 5).Due to the same trend of variation in J-M distance and TD under different window sizes, only the results of J-M distance are shown here (the results of TD are presented in Appendix B).The Local Mean is not a well-performed feature and is not sensitive to changes in window size; therefore, it will not be discussed here.The Remote Sens. 2023, 15, 5747 9 of 18 J-M distances of the other three features exhibit the characteristic of initially increasing and then decreasing as the window size increases.Under the premise of a sample spatial resolution of around 0.5 m, the Local Entropy is optimal when the window size is 7 (i.e., around 3.5 m), and the Local Coefficient of Variation and Local Standard Deviation are optimal when the window size is 5 (i.e., around 2.5 m).

Optimal Parameters for Feature Extraction
The ability of Local Mean, Local Entropy, Local Coefficient of Variation, and Local Standard Deviation to distinguish collapsed buildings from non-collapsed buildings varies under different window sizes (Figure 5).Due to the same trend of variation in J-M distance and TD under different window sizes, only the results of J-M distance are shown here (the results of TD are presented in Appendix B).The Local Mean is not a well-performed feature and is not sensitive to changes in window size; therefore, it will not be discussed here.The J-M distances of the other three features exhibit the characteristic of initially increasing and then decreasing as the window size increases.Under the premise of a sample spatial resolution of around 0.5 m, the Local Entropy is optimal when the window size is 7 (i.e., around 3.5 m), and the Local Coefficient of Variation and Local Standard Deviation are optimal when the window size is 5 (i.e., around 2.5 m).Contrast, Correlation, Energy, and Homogeneity are calculated based on the GLCM; their ability is easily influenced by window size and gray level (Figure 6).The variation trends of J-M distance and TD are the same under different window sizes and slightly different under different gray levels, but this does not affect the optimal parameter results of each feature.Therefore, only the results of J-M distance are shown here (the results of TD are presented in Appendix B).Except for Correlation, which is not a well-performed feature, the J-M distances of Contrast, Energy, and Homogeneity all show a characteristic of initially increasing and then decreasing as the window size increases.The optimal Contrast, Correlation, Energy, and Homogeneity are calculated based on the GLCM; their ability is easily influenced by window size and gray level (Figure 6).The variation trends of J-M distance and TD are the same under different window sizes and slightly different under different gray levels, but this does not affect the optimal parameter results of each feature.Therefore, only the results of J-M distance are shown here (the results of TD are presented in Appendix B).Except for Correlation, which is not a well-performed feature, the J-M distances of Contrast, Energy, and Homogeneity all show a characteristic of initially increasing and then decreasing as the window size increases.The optimal window size is 5 or 7 (i.e., 2-4 m).The J-M distance of Contrast, Energy, and Homogeneity also shows a characteristic of initially increasing and then decreasing with the increase in gray level.The optimal gray level for Contrast is 8, for Energy is 16, and for Homogeneity is 32.
window size is 5 or 7 (i.e., 2-4 m).The J-M distance of Contrast, Energy, and Homogeneity also shows a characteristic of initially increasing and then decreasing with the increase in gray level.The optimal gray level for Contrast is 8, for Energy is 16, and for Homogeneity is 32.

Application Ability of Selected Features
In practical application testing, the selected features (Local Entropy, Homogeneity, Energy, Local Standard Deviation, and Gradient) can effectively identify collapsed buildings (Table 3).The recall rates for identifying collapsed buildings from test images are all above 90%, while the precision rates are relatively low, ranging from 55% to 95%.The F1 scores are between 0.71 and 0.94. Figure 7 shows the result of collapsed buildings identified in Joplin, and the feature used here is Gradient.It can be seen that almost all collapsed buildings have been extracted, with almost no missing areas.However, there are some non-collapsed areas misidentified as collapsed areas.

Application Ability of Selected Features
In practical application testing, the selected features (Local Entropy, Homogeneity, Energy, Local Standard Deviation, and Gradient) can effectively identify collapsed buildings (Table 3).The recall rates for identifying collapsed buildings from test images are all above 90%, while the precision rates are relatively low, ranging from 55% to 95%.The F 1 scores are between 0.71 and 0.94. Figure 7 shows the result of collapsed buildings identified in Joplin, and the feature used here is Gradient.It can be seen that almost all collapsed buildings have been extracted, with almost no missing areas.However, there are some non-collapsed areas misidentified as collapsed areas.is the corresponding identification result).Note: The strip in the middle of the image represents the area where buildings collapsed due to a hurricane, while the upper and lower red areas are noncollapsed buildings that have been misidentified as collapsed buildings.

The Best Features Selected for Rapid Remote Sensing Identification of Collapsed Buildings and Their Influencing Factors
This study found that the ability of spectral features to distinguish collapsed buildings from non-collapsed buildings is generally poor.Because the spectral characteristics of buildings are mainly related to materials rather than states, a collapsed building may have a similar spectrum to its pre-collapse state [24,25], while buildings with different materials may have quite different spectral characteristics, even though they are all collapsed.
It has also been discovered that Homogeneity, Energy, Local Entropy, Local Standard Deviation, and Gradient can effectively and stably distinguish collapsed buildings from non-collapsed buildings.These features also have high recognition accuracy for collapsed buildings in applications.The ability of these features has also been confirmed in other studies.For example, Li et al. [20] used texture features like Homogeneity extracted from GLCM to identify collapsed buildings in post-earthquake images of Taxian, Xinjiang, with an overall accuracy of 90.45%.Based on various texture features such as Homogeneity, Energy, and Contrast, Samadzadegan et al. [21] extracted collapsed buildings from postearthquake images in Bam, with an overall classification accuracy of 74% and a Kappa coefficient of 0.63.However, these studies only conducted empirical research on one or several features in their respective research areas, while this study comprehensively evaluated 25 features based on large and diverse samples distributed in 6 regions worldwide.In addition, the way we evaluated the distinguishing ability of features was using J-M distance and TD rather than any machine learning algorithm, so the selected features are applicable to all methods.Therefore, the screening results are more universal and have more practical guidance value.
The features selected in this study can stably and effectively identify collapsed buildings, but attention should be paid to the impact of the parameters during the feature extraction process.Based on the results in Section 3.2, the optimal parameters and parameter setting principles for reference are given in Table 4.This study found that the ability of spectral features to distinguish collapsed buildings from non-collapsed buildings is generally poor.Because the spectral characteristics of buildings are mainly related to materials rather than states, a collapsed building may have a similar spectrum to its pre-collapse state [24,25], while buildings with different materials may have quite different spectral characteristics, even though they are all collapsed.
It has also been discovered that Homogeneity, Energy, Local Entropy, Local Standard Deviation, and Gradient can effectively and stably distinguish collapsed buildings from non-collapsed buildings.These features also have high recognition accuracy for collapsed buildings in applications.The ability of these features has also been confirmed in other studies.For example, Li et al. [20] used texture features like Homogeneity extracted from GLCM to identify collapsed buildings in post-earthquake images of Taxian, Xinjiang, with an overall accuracy of 90.45%.Based on various texture features such as Homogeneity, Energy, and Contrast, Samadzadegan et al. [21] extracted collapsed buildings from postearthquake images in Bam, with an overall classification accuracy of 74% and a Kappa coefficient of 0.63.However, these studies only conducted empirical research on one or several features in their respective research areas, while this study comprehensively evaluated 25 features based on large and diverse samples distributed in 6 regions worldwide.In addition, the way we evaluated the distinguishing ability of features was using J-M distance and TD rather than any machine learning algorithm, so the selected features are applicable to all methods.Therefore, the screening results are more universal and have more practical guidance value.
The features selected in this study can stably and effectively identify collapsed buildings, but attention should be paid to the impact of the parameters during the feature extraction process.Based on the results in Section 3.2, the optimal parameters and parameter setting principles for reference are given in Table 4.The window size is about 3.5 m The optimal window size is influenced by the size of the roof area of a non-collapsed building, the size of fragments from collapsed buildings, and the spatial resolution of the image.
Theoretically, the optimal window should be able to contain different fragments of collapsed buildings and should not be larger than the roof area of a non-collapsed building.

Local Standard Deviation
The window size is about 2.5 m

Local Coefficient of Variation
The window size is about 2.5 m

Contrast
Window size and gray level The window size is about 3.5 m and the gray level is 8 The optimal window setting principle is the same as above.The optimal gray level is influenced by the complexity of the image.
In terms of the identification of collapsed buildings, the more complex the roof structure is, the larger the optimal gray level should be.

Energy
The window size is about 2.5 m and the gray level is 16

Homogeneity
The window size is about 3.5 m and the gray level is 64 Note that the window size measured in length can be converted into pixels based on the spatial resolution of the remote sensing image.For example, for images with a resolution of 0.5 m, the window size of 2.5 m corresponds to 5 pixels.

Operational Implementation Process and Application Prospects of Applying Selected Features to Rapid Identification of Collapsed Buildings
Based on the selected features, we suggested an operational application process to rapidly extract collapsed buildings.First, indexes such as vegetation index are used to mask non-constructed areas as much as possible.Then, features selected based on reliable experiments are used to extract collapsed buildings.Finally, majority analysis and morphological operations are used to eliminate small fragments.Due to the simple algorithm, this process can meet the requirement of a "rapid" response after a disaster.Although the precision rate of this process is low (between 55% and 95%), it can ensure a high recall rate (all above 90%).Therefore, it can quickly identify potential collapsed building areas from post-disaster remote sensing images and exclude the majority of non-collapsed areas, which can save time for post-disaster rescue.
This study demonstrated the application effect of each selected feature on identifying collapsed buildings on single-temporal images.However, these features can be applied under more conditions.Each selected feature can not only be used on a single-temporal image after collapse but can also be used on multi-temporal images before and after collapse.For example, Pesaresi et al. [26] used texture features combined with spectral and morphological features to detect the collapsed areas in bi-temporal images before and after the earthquake.In addition, the selected features can be used alone or in combination with other features; for example, extract spatial statistical features based on the gradient feature [27] or use the ratio of entropy to energy as a new feature for collapsed building recognition [28].Multiple features have complementary information between each other, so the combination of multiple features tends to perform better than a single feature, especially features with a lower correlation.How to combine multiple features, or further develop new feature extraction techniques, is an interesting topic.It will be further explored in future research.

Conclusions
Both in terms of accuracy and feasibility, the current methods for rapid identification of collapsed buildings in remote sensing are still far from operational.This study extensively tested 25 remote sensing features, screened out features that can well identify collapsed buildings individually, and suggested an operational application process from a feasibility perspective.
GLCM and Gabor features take the longest time due to the relative complexity of their algorithms, followed by the features extracted from neighborhoods, and the global features take the shortest time.Although the complexity of extraction varies from feature to feature, the features screened in this study are all low-level features that are simple to extract.With the high computational power of current computers, the extraction complexity of the features selected in this study will not be a limitation for fast recognition.The Contrast, Correlation, Energy, and Homogeneity are calculated based on the GLCM.Therefore, their ability is easily influenced by window size and gray level (Figures A4 and A5).The variation trends of J-M distance and TD are the same under different window sizes and slightly different under different gray levels, but this does not affect the optimal parameter results of each feature.Correlation cannot distinguish collapsed buildings from non-collapsed buildings, so it will not be discussed here.
most reaches its peak when the gray level increases to 16.After that, the fluctuation is minimal as the gray level increases.Therefore, the optimal gray level is 16.The J-M distance and TD of Homogeneity both show a characteristic of first increasing and then decreasing.The J-M distance reaches its peak at the gray level of 32, while TD reaches its peak at the gray level of 64.Taking the feature's ability and computational efficiency into account, the optimal grayscale is 32.As the window size increases, the J-M distances and TDs of Contrast, Energy, and Homogeneity all show a characteristic of increasing first and then decreasing.Taking the feature's ability and computational efficiency into account (the smaller the window is, the faster the calculation is), the optimal window size is 5 or 7 (i.e., 2-4 m) with a sample spatial resolution of about 0.5 m.
As the gray level increases, the J-M distance of Contrast shows a characteristic of first increasing and then decreasing, reaching its peak when the gray level is 8.While TD almost reaches saturation as the gray level reaches 16, afterwards, the fluctuation is minimal as the grayscale level increases.Taking into account the feature's ability and computational efficiency (the smaller the gray level is, the faster the calculation is), the optimal gray level is 8.The J-M distance of Energy also exhibits the characteristic of first increasing and then decreasing, reaching its peak when the gray level reaches 16.Similarly, TD almost reaches its peak when the gray level increases to 16.After that, the fluctuation is minimal as the gray level increases.Therefore, the optimal gray level is 16.The J-M distance and TD of Homogeneity both show a characteristic of first increasing and then decreasing.The J-M distance reaches its peak at the gray level of 32, while TD reaches its peak at the gray level of 64.Taking the feature's ability and computational efficiency into account, the optimal grayscale is 32.

Figure 1 .
Figure 1.Features of optical remote sensing images for identifying collapsed buildings.

Figure 1 .
Figure 1.Features of optical remote sensing images for identifying collapsed buildings.

Figure 2 .
Figure 2. Image examples of some samples.Note: The samples are within the blue boundaries.The pre-collapse samples are on the left, and the corresponding post-collapse samples are on the right.

Figure 2 .
Figure 2. Image examples of some samples.Note: The samples are within the blue boundaries.The pre-collapse samples are on the left, and the corresponding post-collapse samples are on the right.

Figure 3 .
Figure 3.A technical flowchart for assessing the application effects of selected features.

Figure 3 .
Figure 3.A technical flowchart for assessing the application effects of selected features.

Figure 4 .
Figure 4. (a) J-M distance and (b) TD of 25 features for non-collapsed and collapsed building samples.Note: Local std is Local Standard Deviation, Local CV is Local Coefficient of Variation, GO

Figure 4 .
Figure 4. (a) J-M distance and (b) TD of 25 features for non-collapsed and collapsed building samples.Note: Local std is Local Standard Deviation, Local CV is Local Coefficient of Variation, GO Entropy is Gradient Orientation Entropy, LBP is Local Binary Patterns, GO Std is Gradient Orientation Standard Deviation, and Global CV is Global Coefficient of Variation.

Figure 5 .
Figure 5. J-M distance of (a) Local Mean, (b) Local Entropy, (c) Local Coefficient of Variation, and (d) Local Standard Deviation under different window sizes.

Figure 5 .
Figure 5. J-M distance of (a) Local Mean, (b) Local Entropy, (c) Local Coefficient of Variation, and (d) Local Standard Deviation under different window sizes.

Figure 6 .
Figure 6.J-M distance of (a) Contrast, (b) Correlation, (c) Energy, and (d) Homogeneity under different window sizes and gray levels.

Figure 6 .
Figure 6.J-M distance of (a) Contrast, (b) Correlation, (c) Energy, and (d) Homogeneity under different window sizes and gray levels.

Figure 7 .
Figure 7. Using Gradient to Identify Collapsed Buildings in Joplin ((a) is the original image, and (b)is the corresponding identification result).Note: The strip in the middle of the image represents the area where buildings collapsed due to a hurricane, while the upper and lower red areas are noncollapsed buildings that have been misidentified as collapsed buildings.

Figure 7 .
Figure 7. Using Gradient to Identify Collapsed Buildings in Joplin ((a) is the original image, and (b) is the corresponding identification result).Note: The strip in the middle of the image represents the area where buildings collapsed due to a hurricane, while the upper and lower red areas are non-collapsed buildings that have been misidentified as collapsed buildings.

1 .
The Best Features Selected for Rapid Remote Sensing Identification of Collapsed Buildings and Their Influencing Factors

Figure A1 .
Figure A1.Extraction time of 25 features.Note: Local std is Local Standard Deviation, Local CV is Local Coefficient of Variation, GO Entropy is Gradient Orientation Entropy, LBP is Local Binary Patterns, GO Std is Gradient Orientation Standard Deviation, and Global CV is Global Coefficient of Variation.

Figure A2 .
Figure A2.J-M distance of (a) Local Mean, (b) Local Entropy, (c) Local Coefficient of Variation, and (d) Local Standard Deviation under different window sizes.

Figure A3 .
Figure A3.TD of (a) Local Mean, (b) Local Entropy, (c) Local Coefficient of Variation, and (d) Local Standard Deviation under different window sizes.

Figure A3 .
Figure A3.TD of (a) Local Mean, (b) Local Entropy, (c) Local Coefficient of Variation, and (d) Local Standard Deviation under different window sizes.The J-M distances and TDs of the other three features exhibit a characteristic of initially increasing and then decreasing as the window size increases.Under the premise of a sample spatial resolution of around 0.5 m, the J-M distance and TD of Local Entropy are both highest when the window size is 7 (i.e., around 3.5 m), and the J-M distance and TD of Local Coefficient of Variation and Local Standard Deviation are both highest when the window size is 5 (i.e., around 2.5 m).Therefore, the optimal window size for Local Entropy is 7 (i.e., around 3.5 m), and the optimal window size for Local Coefficient of Variation and Local Standard Deviation is 5 (i.e., around 2.5 m).The Contrast, Correlation, Energy, and Homogeneity are calculated based on the GLCM.Therefore, their ability is easily influenced by window size and gray level (FiguresA4 and A5).The variation trends of J-M distance and TD are the same under different window sizes and slightly different under different gray levels, but this does not affect the optimal parameter results of each feature.Correlation cannot distinguish collapsed buildings from non-collapsed buildings, so it will not be discussed here.

Figure A4 .
Figure A4.J-M distance of (a) Contrast, (b) Correlation, (c) Energy, and (d) Homogeneity under different window sizes and gray levels.

Figure A4 .
Figure A4.J-M distance of (a) Contrast, (b) Correlation, (c) Energy, and (d) Homogeneity under different window sizes and gray levels.

Figure A5 .
Figure A5.TD of (a) contrast, (b) Correlation, (c) Energy, and (d) Homogeneity under different window sizes and gray levels.

Figure A5 .
Figure A5.TD of (a) contrast, (b) Correlation, (c) Energy, and (d) Homogeneity under different window sizes and gray levels.

Table 1 .
Detailed information on all building samples.

Table 1 .
Detailed information on all building samples.

Table 2 .
Feature Extraction methods.Blue Calculate the mean of the red/green/blue band values of all pixels as the Red/Green/Blue feature of the building sample Hue/Saturation/Intensity Calculate the mean of hue/saturation/intensity values of the color space transformed sample image of all pixels as the Hue/Saturation/Intensity feature of the building sample Global Entropy Calculate the entropy of grayscale values of all pixels as the Global Entropy feature of the building sample Global Coefficient of Variation Calculate the coefficient of variation of grayscale values of all pixels as the Global Coefficient of Variation feature of the building sample Local Mean Using a specific-sized sliding window, calculate the mean/the standard deviation/the entropy/the coefficient of variation of the grayscale values in the window as the mean/the standard deviation/the entropy/the coefficient of variation value of the central pixel, and take the mean of the calculated values of all pixels as the Local Mean/the Local Standard Deviation/the Local Entropy/the Local Coefficient of Variation feature of the building sample thresholding segmentation to obtain edges.Calculate the density of edges in each pixel's neighborhood, pixel by pixel.Afterwards, take the mean of the edge density values of all pixels as the edge density feature of the building sample Contrast Based on GLCM, calculate the contrast/correlation/energy/homogeneity value at each pixel and take the mean of the contrast/correlation/energy/homogeneity values of all pixels as the Contrast/Correlation/Energy/Homogeneity feature of the building sample Local Moran'ICalculate the local Moran'I of each pixel, and take the mean of the local Moran'I values of all pixels as the Local Moran'I feature of the building sampleGradientCalculate the gradient value for every pixel by the Sobel operator, and take the mean of the gradient values of all pixels as the gradient feature of the building sampleGradient Orientation EntropyCalculate the gradient orientation for every pixel by the Sobel operator, and take the entropy for the gradient orientation values of all pixels as the Gradient Orientation Entropy feature of the building sampleGradient Orientation Standard DeviationCalculate the gradient orientation for every pixel by the Sobel operator, and take the standard deviation for the gradient orientation values of all pixels as the Gradient Orientation Standard Deviation feature of the building sample Edge Perform a convolution operation using the Laplacian operator, and take the mean value as the edge feature of the building sample Edge Density Perform a convolution operation using the Laplacian operator and apply2.2.3.Assessment of the Application Effects of Selected Features

Table 3 .
The accuracy of collapsed building recognition when applying selected features to largescale remote sensing images.

Table 3 .
The accuracy of collapsed building recognition when applying selected features to large-scale remote sensing images.

Table 4 .
Parameters and parameter setting principles that affect the effectiveness of remote sensing feature extraction.