We selected the Jining and Huaibei mining areas in China as the study areas. The two mining areas are rich in coal resources and have a long mining history. There are many mines in the two areas with a complex distribution. The Jining mining area (115°50′–117°48′E, 34°58′–35°59′N) is located in the southwest of Shandong Province, China, with a cumulative proven coal reserve of nearly 15.1 billion tons. The Huaibei mining area (116°23′–117°12′E, 33°16′–34°14′N) is located in the north of the Huaihe River of Anhui Province, China, with a cumulative proven coal reserve of 13 billion tons. The locations of the study areas are shown in Figure 1.

We used 24 Sentinel-1A images acquired from November 2017 to March 2020 over the Jining mining area and used 34 Sentinel-1A images acquired from November 2017 to March 2020 over the Huaibei mining area. The specific information of the partial interferometric pairs is shown in Table 1. The experimental Sentinel-1A data are interferometric wide swath imaging mode (Level 1 single-look complex images products) and in VV polarization with the 38.9° incidence angle. The revisit period of Sentinel-1A is 12 days and has a pixel size of about 2.33 × 13.91 m. Moreover, the shuttle radar topography mission digital elevation model (SRTM DEM) released by the National Aeronautics and Space Administration (NASA) was applied to remove both the flattening and terrain phases in D-InSAR data processing.

In order to obtain the differential interferograms of the two mining areas, we used the two-pass D-InSAR technology (Ou et al., 2018; Dai et al., 2020) to process these Sentinel-1A data. The procedures of D-InSAR technology mainly include interferogram generation, SAR simulation based on digital elevation model (DEM), differential processing between the real interferogram and the simulated interferogram, phase unwrapping, transformation from phase to deformation, and geocoding (Ilieva et al., 2019; Chen D. H. et al., 2020). Figure 2 is a flow chart of the two-pass D-InSAR data processing. Interferograms with serious decoherence and large noise influence were excluded. We set the temporal baseline threshold of the interferogram to 36 days and the spatial baseline threshold to 200 m. The longest spatial baseline of the interferogram in this paper is 155.71 m. We obtained 62 interferograms in the Jining and Huaibei mining areas. The ratio of multi-looking is 1:5. The pixel size in the range direction is 18.54 m, and the pixel size in the azimuth direction is 13.89 m for the interferogram. The interferograms are too large to be used by the deep neural architecture, which generally accepts an image with a size of 416 × 416 as an input. Therefore, we segment the interferograms into smaller sub-images with a size of 416 × 416 according to the standard of the YOLO V5 model. The image data annotation software called “LabelImg” was used to draw the outer rectangular boxes of the subsidence basins on each sub-image, realizing the manual annotation of the border and labels of the ground truth box. The ground truth boxes were annotated according to the features of the subsidence basin. The subsidence basin on the InSAR interferogram is a series of approximately circular or elliptical interferometric fringes with a small scale and obvious edge features (Wang et al., 2021b). We have obtained a total of 1,160 sample images. In this study, 812 sample images were randomly selected from 1,160 images as the training samples; the remaining 30% were selected as the testing samples, which had a total of 348 images. The partial examples of the sample datasets are shown in Figure 3. In order to alleviate the over-fitting phenomenon during the training model incurred by limited sample datasets, rotation, translation, and flipping were used for data augmentation.

We selected two Sentinel-1A images acquired from December 2020 to January 2021 over the Jining mining area and two Sentinel-1A images acquired from January 2021 over the Huaibei mining area, constituting a total of two interferometric pairs to test the performance of the proposed model for detecting the subsidence basins from the interferograms. The parameters of the two interferometric pairs are listed in Table 1.

The YOLO V5 model, as the basic framework for detecting the subsidence basins in this paper, mainly consists of three components: backbone network, neck network, and detection head. The backbone network is designed to extract the features of the subsidence basin, mainly composed of the CSPDarknet53 network and spatial pyramid pooling (SPP) (Purkait et al., 2017). The neck network adopts the path aggregation network instead of feature pyramid networks in YOLO V5. The detection head, as the final detection part of the model, is used to output the detection results of the subsidence basin. It utilizes the high-level semantic information outputted from the neck network to classify the category and regress the location of the objects.

The loss function of the YOLO V5 network mainly consists of three parts: bounding box regression loss, classification loss, and confidence loss (Shi P. F. et al., 2021). Since this paper only has the category of the subsidence basins, we only used confidence loss and bounding box regression loss, as shown in Formula (1).

where L_obj and L_DIoU mean confidence loss and bounding box regression loss, respectively. λ is the balancing factor and the value is 5 (Yan et al., 2021).

The Light YOLO-Basin model used the Focal Loss (Lin et al., 2017b) function confidence loss to alleviate the problem caused by the imbalanced number of hard and easy samples, as shown in Formula (2), in which the positive sample p with the high confidence is the easy sample and vice versa. Focal loss reduces the weight of easy samples so that the model can focus more on hard samples, ensuring that the contributions of all samples to model parameter updating are relatively balanced.

where y = 1 means positive samples and y = 0 means negative samples; the parameter α is used to balance the weight of the positive and negative samples during the model training; the parameter γ is used to balance the weight of the easy samples in the model; the parameter p ϵ [0,1] is the model estimated probability for the confidence loss. The bounding box regression loss of the original YOLO V5 model adopts generalized intersection over union loss (GIoU Loss), but it only focuses on the overlapping areas and other non-overlapping areas, which ignores the impact of the bounding box on the IoU. The Light YOLO-Basin model used distance IoU loss (DIoU Loss) (Luo et al., 2020) as the bounding box regression loss. DIoU Loss is defined as Formula (3). It not only considers the distance of the center and the overlapping area between the ground truth box and prediction box, but also minimizes the center point distance.

where A represents the area of the prediction box and B represents the area of the ground truth box; the parameter b and b^gt mean the center points of the prediction box A and ground truth box B, respectively; ρ² is the Euclidean Distance between b and b^gt; the parameter c represents the diagonal length of the smallest closed shape that includes the ground truth box A and the prediction box B.

The detection head module of the YOLO V5 model directly uses a single convolutional layer to calculate the classification loss, confidence loss, and bounding box regression loss. However, there is no classification loss in our study, the structure of the detection head requires to be changed. Some researches demonstrated that there is a conflict between classification and regression tasks (Song et al., 2020; Wu et al., 2020), so referencing the ideas of FCOS (Tian et al., 2019) and the literature (Song et al., 2020), the Light YOLO-Basin model used double-head as the detection head module. The Light YOLO-Basin model architecture after decoupling is shown in Figure 4. The double-head splits the output features of the subsidence basin into regression and confidence branches. The regression branch provides prediction box coordinates. Meanwhile, the confidence branch calculates the probability of positive samples.

At present, the YOLO V5 model has achieved great success in natural image datasets such as PASCAL VOC, ImageNet, and MS COCO. However, compared with objects in natural images, subsidence basins on the interferograms have more obvious edges and texture features and simpler shapes. Intuitively, the detection of the subsidence basins on the interferogram from D-InSAR is simpler than the multi-category detection on natural images. This also leads to the conjecture of whether the heavy CSPDarknet53 network is necessary for detecting the subsidence basins. In order to verify that, we used the three versions of the YOLO V5 model (Large, Middle, and Small) to detect the subsidence basins from the interferograms. The variation of detection accuracy is shown in Figure 5. Experimental results show that as the number of parameters and computations of the model reduces, the detection accuracy of the model shows a rising trend instead of decreasing. The results demonstrate that the detection of subsidence basins does not require a heavy network. In addition, since the swath of SAR images is large wide, for example, the swath of Sentinel-1 is about 250 km, a lightweight model is used to detect subsidence basins from the interferograms to lighten the burden on the computer hardware. Therefore, we introduced depthwise separable convolutions to make the CSPDarknet53 network lightweight.

Compared with standard convolution, depthwise separable convolution generally sacrifices a small amount of detection accuracy to save the computations and parameters of the model. Depthwise separable convolution is a form of factorized convolutions that factorizes a standard convolution into a depthwise convolution and a pointwise convolution. Firstly, the depthwise convolution applies a single convolution to each channel feature map to extract feature information and keeps the number of feature maps unchanged. Secondly, the pointwise convolution applies multiple 1 × 1 convolutions to combine the feature maps obtained by the depthwise convolution. The process of performing depthwise separable convolution on a feature map with the size of W × H × C (W and H are the spatial width and height of the feature map, respectively, and C is the number of feature channels) is shown in Figure 6. The computation of the standard convolution is 3 × 3 × C × N × W × H, while the computation of the depthwise separable convolution is 3 × 3 × C × W × H+1 × 1 × C × N × W × H = (3 × 3+N) × (C × W × H), which is approximately 1/N + 1/(3 × 3) of the standard convolution. The parameter of the standard convolution is 3 × 3 × C × N, while the parameter of the depthwise separable convolution is 3 × 3 × C + 1 × 1 × C × N, which is about 1/N + 1/(3 × 3) of the standard convolution. The depthwise separable convolution has the effect of drastically reducing the computation and model size. In this study, the depthwise separable convolution is introduced into the CSPDarknet53 network, which is combined with the scaling of the depth (the number of convolutional layers) and the width (the number of channels of the convolution kernel) to realize the lightweight of the model, as shown in the orange part of Figure 4.

YOLO V5, an anchor-based method, predicts boxes by fitting the deviation of the anchor boxes, where the anchor boxes have a preset width and height. Although anchor-based methods improve the detection accuracy to a certain extent, there are still some drawbacks (Fu J. M. et al., 2020). First, a large number of anchor boxes are used in the model, resulting in excessive redundant computation and slowing down the detection speed of the model. Second, only a tiny fraction of the anchor boxes is labeled as positive samples, resulting in a huge imbalance between positive and negative samples. Third, fixed anchor boxes cannot be applied to various data, which increases the difficulty of model optimization. Anchor boxes generally require to be reset according to different data. Currently, the anchor boxes obtained by clustering objects in natural images are quite different from the features of the subsidence basins in the InSAR interferograms. In addition, since the training data cannot represent all the subsidence basins, the anchor-boxes obtained by clustering the characteristics of the subsidence basins cannot guarantee their versatility. Therefore, we used an anchor-free method to detect the subsidence basins from interferograms.

The location of the prediction box in the original YOLO V5 model is determined by the center point and the width and height of the anchor box, as shown in Figure 7A. The coordinate value of the center point is represented by the offset from the top left corner of the cell, and the width and height are the scaling ratios of the corresponding anchor box. However, if the anchor box is abandoned, the width and height cannot be expressed. Hence, the Light YOLO-Basin model directly fits the width and height instead of the ratio of the anchor box and keeps the computation of the center point unchanged to achieve anchor-free (Law and Deng, 2018; Duan et al., 2019), as shown in Figure 7B.

The lack of the constraint of anchor boxes in the anchor-free method increases the degree of freedom of the model and also increases the difficulty of optimizing the prediction box. Adopting IoU at a certain threshold as positive and negative assignment criterion, which is commonly used in anchor-based detection methods, is usually not suitable for the anchor-free method. For example, the two-stage Faster R-CNN network labels the prediction box with an IoU value greater than 0.7 as a positive sample and less than 0.3 as a negative sample; the one-stage YOLO V3 model labels the prediction box with the highest IoU value as a positive sample, as shown in Figure 8B. Moreover, based on the anchor-free method, using a certain IoU threshold to assign prediction boxes will cause a large number of useful prediction boxes to be discarded. To increase the number of positive samples, the YOLO V5 model expands the selection range of positive samples to the surrounding pixels, reducing the difficulty of model optimization, as shown in Figure 8C. However, the YOLO V5 model still selects a fixed number of positive samples with a certain IoU threshold, and it cannot adaptively determine the number and assignment of hard and easy positive samples. Therefore, we used the OTA (Ge et al., 2021) to model the positive and negative samples assignment as an optimal transmission problem, which selects and balances positive and negative samples in an adaptive manner.

The OTA method treats the ground truth box as the supplier in the optimal transport theory, and the prediction box in the model training as the demander. The unit transportation cost between each demander and supplier is defined as the weighted summation of losses between the ground truth box and prediction box. If a demander receives enough goods from the supplier, this demander becomes one positive sample. The model needs the best positive and negative samples assignment solution to minimize the global transportation cost. Concretely, assuming that there are m ground truth boxes and n prediction boxes for image I, the ground truth box, namely supplier, holds k units of goods, while the prediction box, namely demander, needs d units of goods. c_i,j represents the transporting cost of each unit of good from the i-th supplier to the j-th demander. The positive and negative sample assignment problem can be defined as finding an optimal transmission strategy π = {π_i,j|i = 1, 2, …, m, j = 1, 2, …, n} to minimize the transportation cost, as shown in Formula (4). The formula behind s.t. is a condition that needs to be satisfied during optimization.

The key of the OTA is how to define the transportation cost. The original OTA method defines transportation cost between the ground truth box and the prediction box as the weighted summation of their regression loss and classification loss. Since there is only the category of subsidence basin in our study, the transporting cost was defined as the weighted summation of confidence loss and bounding box regression loss. The computation equation is as follow:

where L_obj and L_reg represent the binary cross-entropy and bounding box regression loss; Pjobj and Giobj denote the confidence score of the model prediction box and ground truth box, respectively; Pjbox and Gibox, respectively, represent the coordinates of the prediction box and the ground truth box. α is the balanced coefficient with the value of 3. The visualization result of transporting cost value is shown in Figure 8D.

The original OTA method uses Sinkhorn-Knopp Iteration (Cuturi, 2013) to solve the optimal transmission problem, but the multiple iteration optimization of the Sinkhorn-Knopp greatly reduces the training efficiency of the model. Hence, the Light YOLO-Basin adopted an approximate method to solve the optimal transmission problem. The OTA solution mainly consists of two parts: (1) k value, which is the number of positive samples of each ground truth box; (2) the assignment of the k value, that is, how the positive samples are assigned to the prediction box. Since the cost matrix has been determined, the assignment solution of k can be simplified to assign k of each ground truth box to the prediction box with the lowest cost in turn, as shown in the blue grid in Figure 8D. The determination of the value of k for each ground truth box is simplified to a statistical problem: first, sorting all the prediction boxes in the model according to the IoU value, and then adding up the cost value of the prediction box with the top Z (default 10) IoU value to round to get the estimated value of k, as shown in Formula (6).

where k_i means the k value of the i-th ground truth box; λ is set to 0.1 derived from experiments.

According to the standard of the YOLO V5 model, we divided the Light YOLO-Basin into three versions: Large (L), Middle (M), and Small (S). The three versions are distinguished by three scaling ratios of the depth (the number of convolutional layers) and the width (the number of channels of the convolution kernel), which are (1.0, 1.0), (0.67, 0.75), and (0.33, 0.50), respectively. The model that does not introduce depthwise separable convolution in this paper is called YOLO-Basin. Examples of the qualitative comparison results of the Light YOLO-Basin model and the YOLO V5 model are shown in Figure 9. It can be seen that the Light YOLO-Basin model can detect the subsidence basin misdetected by the YOLO V5 model. Importantly, in order to verify the performance of the Light YOLO-Basin model in the actual scene, we selected two representative InSAR interferograms with the size of 7,636 × 8,205 and 8,127 × 10,338, respectively. We first cut the whole images regularly to obtain a large number of sub-images with a size of 416 × 416, then used the Light YOLO-Basin model to detect the subsidence basins for each sub-image, and finally stitched the detection results of each sub-image. Figure 10 exhibits part of the detection results of subsidence basins using the Light YOLO-Basin model. It can be seen that most subsidence basins have been correctly detected. 42 and 40 subsidence basins were detected in Jining and Huaibei mining areas, respectively. Regardless of the time consumption on image segmenting and stitching, the Light YOLO-Basin model only consumed 16.28 s to detect the whole image. We made statistics on the deformation values of the detected subsidence basins from the Jining and Huaibei mining areas, among which, the deformation value of the subsidence basin with the smallest deformation is 1.5 cm.

The detection accuracy of the Light YOLO-Basin model and the YOLO V5 model are shown in Table 2. The experimental results demonstrate: (1) with the same experimental method, the smaller the scaling ratio of the model is, the higher the detection accuracy is. The value of mAP increased from 45.92% of the YOLO V5-L model to 47.65% of the YOLO V5-S model. This further verified the hypothesis proposed above that the detection of subsidence basins does not require a heavy network. (2) Benefiting from the introduction of the anchor-free detection box encoding method and OTA, the mAP value of the YOLO-Basin-S model has greatly improved compared to the YOLO V5-L model which was 6% higher than that of the original YOLO V5-L model. By comparing the detection accuracy in Table 2, it can be found that the improvement of the YOLO-Basin model detection accuracy is mainly manifested by the strict evaluation indicators such as AP₇₀ and AP₈₀. The AP₇₀ value increased from 65.70 to 71.24%, and the AP₈₀ value increased by 15.20%. (3) The detection accuracy of the Light YOLO-Basin model is further improved, benefiting from the introduction of the depthwise separable convolution. Similarly, the improvement of the Light YOLO-Basin model detection accuracy is also mainly manifested by the evaluation indicators such as AP₇₀ and AP₈₀. The AP₇₀ value improved from 71.24 to 75.20%, and the AP₈₀ value increased by 7.85% compared to the non-lightweight model. In summary, on the one hand, the experimental results prove the effectiveness of anchor-free and OTA methods in detecting the subsidence basins. On the other hand, depthwise separable convolution can improve the detection accuracy of the Light YOLO-Basin model with less model parameters.

The lightweight module of the Light YOLO-Bain model mainly includes scaling and depthwise separable convolution. The lightweight detection model needs to pay attention to two aspects: (1) whether the lightweight module can improve model computing efficiency and reduce memory utilization; (2) whether the lightweight module affects detection accuracy. We used network parameters, GFLOPs, and inference memory as the evaluation indicators of model efficiency and mAP as the evaluation indicator of model accuracy. The results are shown in Table 3. The image size is set to 416 × 416 and the batch size is set to 1 when training the model.

Firstly, by analyzing the values of the evaluation indicators of model efficiency in Table 3, introducing depthwise separable convolution and scaling can exponentially decrease the number of model parameters and speed up model training. The improvement of model efficiency by depthwise separable convolution is mainly reflected in the number of model parameters and detection speed. Note that the smaller the model is, the smaller the effect of the depthwise separable convolution is. In addition, since the depthwise separable convolution factorizes a standard convolution into two parts, the computation memory utilization of the model increases. Table 3 indicates the use of scaling and depthwise separable convolution has a better lightweight effect on the model. Secondly, observing the model accuracy evaluation indicators data in Table 3, compared with the detection method of natural images, the lightweight of the model can improve the accuracy of the detection of subsidence basins rather than reducing the accuracy. Compared with the YOLO-Basin-S model, the Light YOLO-Basin-S model increases the mAP value from 51.92 to 55.12%.

To address the problem caused by the anchor boxes, the Light YOLO-Basin model introduces the anchor-free method and the OTA method. In addition, we also changed the neck network and loss function of the YOLO V5 model, as seen in Section “YOLO V5 Network.” We used mAP and AP₅₀ : AP₉₅ as the evaluation indicators of model accuracy in Table 4, showing the accuracy changes of the modules added to the YOLO V5-S model.

It visually shows the change of model accuracy with added different modules in Table 4. By analyzing the changes in model accuracy, we can draw the following three conclusions: (1) The anchor-free detection box encoding method and OTA have the greatest effect on improving the detection accuracy of the model, greatly increasing the value of AP₇₀ and AP₈₀. The accuracy evaluation indicators mAP has also been significantly improved, increasing from 47.65 to 55.12%. (2) The introduction of depthwise separable convolution did not improve the detection accuracy of the YOLO V5 model. However, it can improve the accuracy of the Light YOLO-Basin model, perhaps benefiting from the combined effects of depthwise separable convolution and OTA. (3) Compared with the OTA, the double-head and Focal loss only less improve the accuracy.

We also analyzed the influence of different IoU loss functions on the Light YOLO-Bain model accuracy, as shown in Table 5. It can be seen from Table 5 that the detection accuracy is the highest when we used the DIoU loss function. Hence, we used DIoU loss as the bounding box regression loss function.

To avoid the inefficient iterative computation of Sinkhorn-Knopp Iteration, we used statistical methods to estimate the k value corresponding to the ground truth box in the Light YOLO-Bain model, each of which represents the number of corresponding positive samples. The k value is obtained by adding up the cost value of the prediction box of the top Z in the IoU value and rounding it. Hence, the number of Z determines the size of the k value to a certain extent. According to Formula (6), the larger the value of Z is, the larger the corresponding k value is. That is, each ground truth box is assigned more positive samples. However, too many positive samples will divide the poorly optimized prediction boxes into positive samples, resulting in incorrect detection of the Light YOLO-Bain model. Too few positive samples will cause the imbalance of positive and negative samples, increasing the difficulty of model optimization. Therefore, it is important to choose a suitable Z. Table 6 shows the effect of different values of Z on the accuracy of the Light YOLO-Basin model. It can be seen that the detection accuracy of the model is highest when the value of Z is 10.

To test the robustness of the model, we, respectively, tested the effects of DEM, decorrelation noise, and the number of interferogram multi looking on detection. We first conducted a set of comparative experiments using DEM with a spatial resolution of 30 and 90 m. The detection results of subsidence basins using different levels of DEM are shown in Figure 11. Since the DEM does not affect the features of the subsidence basins, it has little influence on the detection results where 14 and 13 subsidence basins were detected using DEM with a spatial resolution of 30 and 90 m, respectively. Note that the spatial resolution of DEM used in this paper is 30 m. Then, to test the effect of decorrelation noise on detection, the Gaussian complex noise was used to simulate the decorrelation noise. Figure 12 gives the influence of noise on the detection results. It can be seen that noise has a greater influence on the detection results. Hence, we used the Goldstein filtering method to remove image noise in this paper. Finally, we conducted a set of comparative experiments with different numbers of multi-looking. The comparison of the detection results is shown in Figure 13. It can be seen that the number of interferogram multi-looking changes the aspect ratio of the subsidence basin but has little effect on the detection result of the subsidence basin. We adopted a more appropriate ratio of multi looking is 1: 5.