A multi-target tracking method based on "digital model + video data"

Abstract

The application discloses a multi-target tracking method based on a "digital model + video data", which is applied to the field of target tracking, and aims at the fact that existing tracking algorithms are more likely to lose targets in complex scenes or dense areas of aircrafts, leading to tracking interruption or incorrect target association. The appearance prior information of the digital model is used to guide the segmentation and tracking results of multi-aircraft targets, aircraft targets of specific angles and specific sizes are matched with aircraft models in a digital model library through an effective matching mode, so that stable target appearance representation is obtained in the tracking process. Finally, a better multi-aircraft tracking result is obtained through a complete segmentation result and a feature matching method.

Description

Technical Field

[0001] This invention belongs to the field of target tracking, and specifically relates to a multi-aircraft target tracking technology. Background Technology

[0002] With the sustained growth of China's economy and the improvement of people's living standards, China's aviation industry has made significant progress in policy support, market demand, technological innovation, and talent cultivation. In recent years, the rapid development of computer vision has brought numerous opportunities to airport construction and greatly improved airport operational efficiency, safety, and service levels. As a complex transportation hub, the intelligent construction of airports in the field of computer vision involves multiple aspects. Intelligent construction utilizes computer vision technology to achieve comprehensive monitoring, management, and optimization of airport operations through automation, data analysis, and intelligent decision-making. Multi-object tracking algorithms are an important component of intelligent airport construction, contributing to the realization of automated and intelligent airport management. With the development of artificial intelligence and computer vision technology, the application of multi-object tracking algorithms in airport scenarios is becoming increasingly widespread, driving continuous improvement in airport management levels and service quality.

[0003] Multi-aircraft target tracking algorithms are a class of algorithms used for real-time monitoring and tracking of multiple aircraft within airports or other airspaces. These algorithms typically use sensor data (such as radar, cameras, ADS-B, etc.) to acquire the aircraft's position, velocity, and other relevant information, and then use data processing and tracking techniques to track these targets. However, the limitations of a single data source can lead to poor adaptability of tracking algorithms to environmental changes or aircraft behavior. For example, relying solely on camera data may fail at night or in inclement weather, while relying solely on radar data may not accurately estimate the aircraft's morphological characteristics. Furthermore, tracking algorithms are more prone to losing targets in complex scenarios or areas with dense aircraft, leading to tracking interruptions or incorrect target association.

[0004] In the field of aircraft tracking, aircraft motion typically follows certain patterns. However, the main challenge lies in the high degree of visual similarity between aircraft. This can lead to correlation issues between different targets when using traditional appearance extraction methods, increasing the frequency of aircraft ID exchange and potentially causing trajectory interruptions, thus affecting tracking robustness. Furthermore, for special targets like aircraft, their trajectories are usually three-dimensional, fast, and may involve more dynamic changes and uncertainties.

[0005] Existing multi-aircraft target tracking algorithms for airport scenarios mainly suffer from the following problems:

[0006] 1) The aircraft in the airport scene have a high degree of similarity in appearance, which will result in a large number of ID conversions in scenarios such as the apron or connecting taxiway due to the increase in aircraft targets;

[0007] 2) For special targets like aircraft, their trajectories are usually three-dimensional and move at high speeds, resulting in more dynamic changes and uncertainties. Existing multi-target tracking algorithms are often unable to effectively address the challenges of tracking aircraft in airport scenarios. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention proposes a multi-target tracking method based on "digital models + video data". It utilizes existing aircraft digital model libraries to provide prior appearance information for the aircraft in the multi-target tracking algorithm, thereby enhancing the network's ability to distinguish between aircraft and effectively improving the tracking accuracy and efficiency of multi-aircraft tracking.

[0009] The technical solution adopted in this invention is: a multi-target tracking method based on "digital model + video data", comprising:

[0010] S1. Use a segmentation framework based on a fully convolutional neural network to extract the aircraft target from the image and obtain the aircraft target mask;

[0011] S2. Use the improved 2D SIFT to extract features from the aircraft target mask obtained in step S1 to obtain mask features;

[0012] S3. Use the 3D SIFT algorithm to characterize the aircraft targets in the 3D digital model library; obtain the 3D digital model features;

[0013] S4. Match the mask features extracted in step S2 with the three-dimensional digital model features obtained in step S3; to obtain the digital model of the corresponding aircraft target.

[0014] S5. Based on the aircraft digital model, obtain a complete and accurate representation of the corresponding aircraft target on the plane; perform Harris corner detection on the complete and accurate representation of the aircraft target on the plane; use the feature descriptions obtained from the Harris corner detection as a complete set of aircraft target feature points for the corresponding aircraft target, and add each complete set of aircraft target feature points to the feature codebook.

[0015] S6. Construct an appearance model for each aircraft target extracted in step S1;

[0016] S7. Calculate the center position of the aircraft target using the feature codebook and the aircraft target appearance model to obtain the final tracking result.

[0017] The beneficial effects of this invention are as follows: The method of this invention utilizes prior appearance information from digital models to guide the segmentation and tracking of multiple aircraft targets. Through an effective matching method, it matches aircraft targets of specific angles and sizes with aircraft models in a digital model library, thereby obtaining a stable target appearance representation during the tracking process. Finally, through complete segmentation results and feature matching methods, it achieves better multi-aircraft tracking results. This invention has the following advantages:

[0018] 1) Traditional methods are usually based on two-dimensional image processing for target tracking, which is easily affected by occlusion and changes in lighting, resulting in inaccurate target position; while algorithms based on the three-dimensional model of the aircraft can use depth information to accurately determine the position and attitude of the target, thus improving the accuracy of target localization.

[0019] 2) In complex environments, targets may be partially or completely occluded by other objects, making it difficult for traditional methods to effectively track them; however, algorithms based on 3D models can better cope with occlusion by predicting the target's position in 3D space, thus improving the robustness of tracking.

[0020] 3) Traditional methods usually rely on the target's motion information between consecutive frames for tracking, which is easily affected by factors such as the target's speed and acceleration, resulting in the target being lost. However, algorithms based on 3D models can combine the target's geometric features and motion information to track the target more stably, reduce the risk of losing track, and improve the reliability of tracking. Attached Figure Description

[0021] Figure 1 This is a flowchart of a multi-target tracking method based on "digital model + video data".

[0022] Figure 2 This is a schematic diagram of the video frame image segmentation results.

[0023] Figure 3 This is a schematic diagram for target mask feature extraction.

[0024] Figure 4 This is a schematic diagram of 3D SIFT feature extraction and feature matching.

[0025] Figure 5 This is a schematic diagram of the tracking results. Detailed Implementation

[0026] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0027] Three-dimensional digital models can provide appearance information of an aircraft target from various angles. Properly utilizing 3D digital models helps overcome the challenges of segmentation defects and improves segmentation-based tracking accuracy. This invention proposes a novel aircraft tracking algorithm based on feature point matching and tracking. First, key aircraft feature points, such as the nose tip, the intersection of the wing and fuselage, and the engine center point, are extracted from the segmented mask. Because segmentation is not 100% accurate, the resulting feature point set may be incomplete. Then, based on the matching relationship between the extracted feature point set and the true feature point set provided by the 3D digital model, the 3D aircraft model is projected onto the image plane to obtain a two-dimensional model mask. Because the model mask is absolutely accurate, a complete and rich feature point set of the aircraft target can be directly obtained from the model mask. Next, combining local feature point tracking and global appearance modeling, iterative reasoning yields the aircraft tracking result. Because point tracking is based on a complete feature point set, it effectively utilizes the prior information of the 3D digital model, thus achieving better tracking results. The tracking process is as follows: Figure 1 As shown below, the specific steps of our proposed "digital model + video data" target tracking algorithm are as follows:

[0028] Step 1: Obtain the segmentation results of the target in the video image.

[0029] The task of object segmentation is to extract moving target regions from images. Here, a segmentation framework based on a fully convolutional neural network (BSUV-Net, Brain Surface Vessel Segmentation Network based on Convolutional Neural Network) is adopted to extract aircraft targets from images. The BSUV-Net architecture consists of an encoder and a decoder. In the encoder network, a 2×2 max pooling operator is used to reduce the spatial dimensionality. In the decoder network, an upper convolutional layer is used to increase the dimensionality back to the input dimension. Residual connections from the encoder to the decoder help the network combine low-level visual information obtained in the initial layers with high-level visual information obtained in deeper layers. To improve the segmentation performance of unseen video, we use strong batch normalization (BN) layers and spatial dropout (SD) layers to improve the model's generalization ability. Specifically, a BN layer is used after each convolutional layer and an upper convolutional layer, and an SD layer is used before each max pooling layer. Furthermore, we use an sigmoid growth curve function layer as the final layer of the BSUV network. The current, most recent, and empty color frames, along with their Future Probability Maps (FPMs), are used as input to the BSUV network. Therefore, the input layer of the BSUV network has 12 channels, with each frame consisting of 4 channels (R, G, B, FPM). The resulting segmentation is as follows: Figure 2 As shown.

[0030] The nearest color frame refers to the video frame that is temporally adjacent to the current color frame. Adjacent can be understood as follows: if the current color frame is at the beginning of the video, then the video frame after the current color frame is taken as the adjacent video frame; if the current color frame is in the middle to the end of the video, then the video frame before the current color frame is taken as the adjacent video frame.

[0031] Step 2: Extract key feature points from the aircraft target mask obtained in Step 1.

[0032] We propose a feature point extraction and matching method based on Scale-Invariant Feature Transform (SIFT). Traditional SIFT features are local image features, invariant to rotation, scaling, and brightness changes, and also maintain a certain degree of stability against viewpoint changes, affine transformations, and noise. However, they also suffer from inherent problems such as poor real-time performance and susceptibility to mismatches. Our first step is to reduce the dimensionality of the original SIFT descriptor while expanding its computational range to improve accuracy. Specifically, we select a circular region around the keypoint and divide it into multiple concentric ring regions with a certain step size. We calculate the gradient using Gaussian weighted averages, with the concentric rings representing different computational regions of the descriptor. Because circular regions have good rotation invariance, we can simplify the calculation of the principal direction of feature points, improve algorithm efficiency, and facilitate operation. The feature extraction results are shown below. Figure 3 As shown. In this embodiment, the step size is 3.

[0033] Step 3: Use the 3D SIFT algorithm to characterize the aircraft targets in the 3D digital model library.

[0034] 3D SIFT can detect scale-invariant keypoints. This means that regardless of whether the 3D model is scaled, rotated, or translated, 3D SIFT can detect the same keypoints. Similar to SIFT for 2D images, 3D SIFT detects keypoints at multiple scales to ensure that features at different scales are captured. After detecting keypoints, 3D SIFT precisely locates the position of each keypoint. This typically involves performing Gaussian differences on the local region around the keypoint to determine its precise location. For each keypoint, 3D SIFT also assigns a principal orientation, making the keypoint rotation-invariant. Within the local region around each keypoint, 3D SIFT constructs feature descriptors using gradient information. These descriptors contain information about the local features around the keypoint, such as gradient direction and intensity. The 3D SIFT algorithm exhibits good robustness and reliability in processing 3D models.

[0035] The 3D digital model library in this embodiment is specifically referenced from the 3D model library of https: / / www.cgmodel.com / .

[0036] Step 4: Match the aircraft target mask features with the features of the digital model.

[0037] After extracting feature points and descriptors using 2D SIFT and 3D SIFT algorithms, a feature distance-based matching method is used to match the features of the 2D image and the 3D model. For each pair of feature points, the distance or similarity metric between their descriptors is calculated. Specifically, for each 3D SIFT descriptor, the distance or similarity metric between it and all 2D SIFT descriptors in the 2D image is calculated. Here, the nearest neighbor matching method is used, with Euclidean distance as the distance metric. For each 3D SIFT descriptor, one or more 2D SIFT descriptors with the closest distance are selected as the match. Ultimately, we only retain the three 3D descriptors with the closest distance to the 2D descriptor. The 3D feature extraction and matching are as follows: Figure 4 As shown.

[0038] Step 5: Remove false matches and verify the matching results.

[0039] While the SIFT descriptor exhibits good scale and rotation invariance, it neglects spatial location constraints, frequently generating false matches and impacting the stability of the recognition algorithm. Therefore, we employ the Random Sample Consensus (RANSAC) algorithm to eliminate false matches generated by SIFT, ultimately obtaining suitable feature point matching results. The RANSAC algorithm searches for an optimal homography matrix H to filter out false matches, maximizing the number of data point pairs that satisfy this matrix. This involves obtaining a matrix through random sampling, then verifying whether other point pairs conform to the model; points that conform become "interior points," and those that don't become "outterior points." The next iteration involves sampling points from this "new set of interior points" to construct a new matrix and recalculating the error. The optimal homography matrix H is the one with the minimum error and the maximum number of points. This determines the digital model of the aircraft corresponding to the mask in the video.

[0040] The data points here specifically refer to the point pairs formed by the two-dimensional feature points extracted in step two and the three-dimensional feature points in step three.

[0041] The RANSAC algorithm searches for an optimal homography matrix H, with a size of 3×3. The goal of RANSAC is to find the optimal parameter matrix that maximizes the number of data points satisfying this matrix. Typically, h33 = 1 is used to normalize the matrix. Since the homography matrix has 8 unknown parameters, at least 8 linear equations need to be solved. Corresponding to point location information, a pair of points can be used to derive two equations, thus requiring at least 4 matching point pairs. See the figure below:

[0042]

[0043] Where s represents the scale parameter, represents , represents , and h represents . 11 …h 33This represents the nine parameters in the optimal homography matrix H.

[0044] Four samples are randomly selected from the matching dataset, ensuring that these four samples are not collinear. The homography matrix is ​​calculated, and then this matrix is ​​used to test all data points. The number of data points satisfying this matrix and the projection error (i.e., the cost function) are calculated. If this matrix is ​​the optimal homography matrix, then the corresponding cost function is minimized, and the number of points is maximized. The loss function is calculated as follows:

[0045]

[0046] Step 6: Project the digital model using the matching relationship to obtain a complete two-dimensional feature point set, and add it to the feature codebook.

[0047] First, after obtaining the corresponding digital model of the aircraft, we will also know the specific angles and dimensions of the digital model corresponding to the target mask in the video. Based on this information, we will project the 3D digital model to obtain a complete and accurate representation of the aircraft target on a plane. Then, we will perform Harris corner detection on this complete representation. The feature description obtained from Harris corner detection is our complete set of aircraft target feature points, which we will add to the feature book. After completing the main tracking process in the current frame, we will update the feature book. This step of updating the feature book specifically refers to updating the same set of aircraft target feature points, that is, updating the points that have changed relative to the feature point set of the previous frame.

[0048] Step 7: Establishing the target appearance model. The appearance model constructed for each object is an RGB color model.

[0049] RGB color model A(x m () represents the average appearance value for each pixel. Here, x m These are the coordinates relative to the centroid in the model. Probability mask P sim (x m The corresponding value in the model records the probability of the observed pixel having a similar RGB value to the one in the appearance model. When a new object is initialized, the foreground pixels are copied into the RGB color model, and the probability mask is initialized to its initial value at the foreground point. The new information is then mixed into the model with an update factor so that the model can adapt to slow changes in scale and pose. We update the probability mask based on the similarity between the observed foreground pixels and the RGB color model. We update the appearance model using the following formula:

[0050]

[0051]

[0052] Where xc Here, I represents the centroid coordinates of the image, I is the current frame of the image, and F is the foreground region. For the background area, X is the region from the marker to the object. This refers to the region outside the object, where t represents the sequence number of the current time frame, α and β are update factors typically 0.05, and sim is I_((x c +x m )) and A(x m The similarity between the RGB values ​​of () is measured in a perceptron-like manner:

[0053]

[0054] Here T l It compares the distance at which colors can be considered a perfect match. In this embodiment, T l The value is 3 pixels; a value less than or equal to this indicates a perfect match. (T) h These are thresholds for two completely different colors. In this embodiment, T h The value is 4 pixels, meaning that values ​​greater than or equal to this value represent different categories.

[0055] Step 8: Calculate the target center position using the feature codebook and target appearance model to obtain the final tracking result.

[0056] First, we can reliably segment the foreground and background, as well as connected component (blob) blocks in the image, using the BSUV-net segmentation network. Foreground objects and connected component blocks can be grouped into similar or dissimilar groups based on a threshold relationship. Here, the threshold is 10 pixels; values ​​less than or equal to this threshold indicate similar groups. For each group, we have the foreground regions of all connected component blocks within that group, and several objects that should be observed within those regions. For each object, we use a feature codebook to estimate some possible locations for the object's center, and then evaluate their likelihood to find the most probable location. We use a threshold T. t All codebook entries are used to estimate the center. t This indicates the minimum observation time at which an entry is considered a credible feature.

[0057] Since the target position in the current frame is not absolutely accurate, using the same target in the preceding and following frames to estimate the target position in the current frame can effectively reduce the error. However, spanning too many frames is not very meaningful for determining the position of a moving target. Through experiments, T was determined... t A value of 5 frames yields the best results.

[0058] In order to efficiently calculate the distribution P(x) of the object center cEach activated entry will use a generalized Hough transform to vote for a center position. Votes are accumulated in the voting graph M. V In the middle. We do not calculate the distribution P(x) during the voting process. c |c i For each activated entry, the probability value 1 / Nmatch will be voted onto M. V The most likely center location. After processing all extracted features, we obtain the summative votes. Because we only voted on a single location for each contributing center distribution, the kernel density estimate is effective for recovering the approximate distribution P(x). c This is necessary. To select promising object centers from the voting results, we first detect the maximum value P. max We then collected all voting locations greater than the maximum value as promising object centers. When a compact, dense voting region exists as we expect, an intermediate value is sufficient to exclude the least likely estimate outside that region.

[0059] The specific entry to be activated is in T t Codebook features of video frames within the range.

[0060] Nmatch represents the number of codebook entries participating in the vote. Threshold T t Once determined, the number of video frames is also determined, and thus the number of codebook entries in the video frames is also determined.

[0061] To validate the center estimation and obtain the true trajectory, we leverage the available appearance model, addressing occlusion through efficient region similarity evaluation and an affordable iterative process, thereby finding the optimal location. Aligning with the center of the appearance model, the evaluation score of the candidate center is measured by a weighted average of pixel-level similarity:

[0062]

[0063] X a Let X represent the set of foreground target points. u λ represents the set of target points in the appearance model, and λ represents the weight parameter.

[0064] After obtaining the scores for all candidate center locations, we select the most likely location for each tracking score that is the highest.

[0065] However, when severe occlusion exists, the first round of matching without depth ordering information is rarely accurate enough. To obtain a clear view of the occlusion state and estimate the depth order, we classify each disputed pixel to the object with the most similar color model at that location. The degree of occlusion of an object can be measured by the ratio between its undeclared disputed pixels and the total number of relevant pixels in the object model. The object that wins the largest portion of the disputed pixels is considered the most important object. If no object has severe occlusion, we can proceed with pixel labeling. Otherwise, we only process the foremost object, as it has no occlusion except for some possible interference from merging objects during center estimation. We simply use its current most likely center as the final result and label the foreground pixel as the foremost object, provided that the pixel is relevant to it (P). sim (xx c The similarity is greater than 0.2 and not too low (sim>0.5). The pixels marked and their features cannot be used to match other objects. We then re-evaluate, running the evaluation process again using the still-available foreground pixels and features of the remaining objects. We do this iteratively until no objects remain unresolved or only negligible occlusion exists, and reliable tracking results are obtained. The tracking results are as follows: Figure 5 As shown.

[0066] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A multi-target tracking method based on "digital model + video data", characterized in that, include: S1. Use a segmentation framework based on a fully convolutional neural network to extract the aircraft target from the image and obtain the aircraft target mask; S2. Use the improved 2D SIFT to extract features from the aircraft target mask obtained in step S1 to obtain mask features; S3. Use the 3D SIFT algorithm to characterize the aircraft targets in the 3D digital model library; obtain the 3D digital model features; S4. Match the mask features extracted in step S2 with the three-dimensional digital model features obtained in step S3; to obtain the digital model of the corresponding aircraft target. S5. Based on the aircraft digital model, obtain a complete and accurate representation of the corresponding aircraft target on the plane; perform Harris corner detection on the complete and accurate representation of the aircraft target on the plane; use the feature descriptions obtained from the Harris corner detection as a complete set of aircraft target feature points for the corresponding aircraft target, and add each complete set of aircraft target feature points to the feature codebook. S6. Construct appearance models for each aircraft target extracted in step S1; the implementation process of step S6 is as follows: The aircraft target appearance model is specifically an RGB color model. This represents the average appearance of each pixel. It is the appearance model of the aircraft target relative to Coordinates; probability mask The corresponding value in the record records the probability of the observed pixel having a similar RGB value to the target object's appearance model; the calculation formula is as follows: ； ； in, Here, I represents the center coordinates of the image, I is the current frame of the image, and F is the foreground region. For the background area, X is the region from the marker to the object. It is the area outside the object. This represents the sequence number of the current time frame, α and β are update factors, and sim is... and The similarity between RGB values; S7. Calculate the center position of the aircraft target using the feature codebook and the aircraft target appearance model to obtain the final tracking result; the implementation process of step S7 is as follows: The foreground region of the input image and the connected region blocks in the image are obtained according to the segmentation framework based on the fully convolutional neural network in step S1. The foreground region and the connected region blocks are grouped according to the first threshold. Specifically, the foreground region and the connected region blocks that are less than or equal to the first threshold are grouped into the same group. Each group includes the foreground region corresponding to the connected region block and several objects observed in these foreground regions. For each object, the object center is estimated using the feature codebook, and the feature codebook entries that are less than or equal to the second threshold are used as activated entries; the center position is selected by voting using the generalized Hough transform for each activated entry; thus, candidate centers are obtained. The candidate centers are then aligned with the center of the aircraft target appearance model. The evaluation score of the candidate centers is measured by a weighted average of pixel similarity. ； Represents the set of foreground target points. This represents the set of target points in the appearance model. Indicates the weighting parameter; After obtaining scores for all candidate center locations, the location with the highest tracking score is selected as the final tracking result.

2. The multi-target tracking method based on "digital model + video data" according to claim 1, characterized in that, A segmentation framework based on a fully convolutional neural network includes an encoder and a decoder; In the encoder, a 2×2 max pooling operator is used to reduce the spatial dimension of the original input image; in the decoder network, an upper convolutional layer is used to increase the dimension back to the original input image. It also includes residual connections from the encoder to the decoder; It also includes using a strong batch normalization layer after each convolutional layer and an upper convolutional layer, and a space loss layer before each max pooling layer; An S-shaped growth curve function layer is also used as the last layer of the segmentation framework based on a fully convolutional neural network.

3. The multi-target tracking method based on "digital model + video data" according to claim 2, characterized in that, The input to the segmentation framework based on a fully convolutional neural network is: the current color frame and its foreground probability map, the most recent color frame and its foreground probability map, and an empty color frame and its foreground probability map.

4. The multi-target tracking method based on "digital model + video data" according to claim 3, characterized in that, Step S2 specifically includes: First, key feature points are extracted from the aircraft target mask obtained in step S2 using traditional 2D SIFT. Then, a circular region is selected around the key points and divided into multiple concentric ring regions with a set step size. The gradient is calculated based on Gaussian weighting, and the concentric rings represent different calculation regions of the descriptor, thus obtaining the feature extraction result.

5. The multi-target tracking method based on "digital model + video data" according to claim 4, characterized in that, The specific implementation process of step S4 is as follows: The mask features include 2D SIFT feature points and corresponding descriptors; the three-dimensional digital model features include 3D SIFT feature points and corresponding descriptors. For each 3D SIFT descriptor, select one or more 2D SIFT descriptors to match it, and calculate the distance or similarity metric between the 3D SIFT descriptor and the matched 2D SIFT descriptors. Finally, retain the three 3D descriptors that are closest to the 2D descriptor; thus, obtain the feature point matching result. For the feature point matching results, the random sampling consensus algorithm is used to filter out false matches, and the digital model of the aircraft corresponding to the aircraft target mask in step S1 is obtained.

6. The multi-target tracking method based on "digital model + video data" according to claim 4, characterized in that, The nearest neighbor matching method is used to select one or more 2D SIFT descriptors for matching.

7. The multi-target tracking method based on "digital model + video data" according to claim 4, characterized in that, The distance metric used is Euclidean distance.

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