Complex Background Removal Method for Video of an Inclined Cable Based on UAV Detection of Structural Vibration Frequencies

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Introduction
Inclined cables constitute integral elements within the loadbearing structures of cable-stayed bridges.Te precise measurement of the vibration frequency of these inclined cables holds great signifcance [1,2] for cable force assessment [3].Currently, methods for measuring the vibration of inclined cables can be categorized into two primary domains [4]: contact measurement methods and noncontact measurement methods.
Most contact measurement methods rely on the utilization of accelerometers for monitoring purposes [5,6].Nevertheless, structural health monitoring systems employing contact monitoring methods necessitate a substantial number of connection wires due to the extended distances and numerous inclined cables involved, resulting in elevated costs [7].Wireless sensors [8] ofer a notable reduction in the number of needed connection wires but introduce the challenge of potential wireless data loss.
Alternatively, noncontact measurement methods, such as laser Doppler techniques [9] and microwave remote sensing [10], can achieve high-precision measurements.However, the equipment associated with these methods is relatively costly and demands specialized operational expertise [11].In contrast, noncontact measurement methods founded on computer vision algorithms ofer a more cost-efective and user-friendly approach [11].As early as 1998, Gehle and Masri [12] employed a video camera to capture footage for measuring the vibration frequency of cables.Subsequently, Guo et al. [13] integrated deep learning methods with traditional optical fow techniques to assess the vibration frequency of an inclined cable.Kim et al. [14] conducted a comparative study evaluating accelerometers and various smart devices under diverse weather conditions, afrming the measurement accuracy of computer vision algorithms.Zhao et al. [15] employed a smartphone to record vibrations in an inclined cable and utilized a computer vision algorithm to determine the vibration frequency.
Noncontact measurements using smartphones or industrial cameras ofer increased efciency and cost savings in comparison to contact measurements [4].However, when applying these methods to photograph large civil engineering structures, challenges may arise in camera setup and the identifcation of suitable angles for video capture [16].Te advent of unmanned aerial vehicles (UAVs) has presented a novel solution.UAVs, capable of swiftly capturing video footage of sizable structures, fnd myriad applications in civil engineering, including 3D reconstruction of buildings, dams, and bridges [17][18][19], assessment of seismic damage in buildings [20], long-term monitoring of slope displacements [21], and detection of structural cracks [22][23][24].
Moreover, UAVs have been harnessed for measuring structural vibrations.Tese methodologies concentrate on tracking alterations in natural features or artifcial markers on a structure to derive structural displacement.For instance, Weng et al. [25] combined the optical fow method with perspective transformation to identify the displacement of a supertall building from video footage captured by a UAV.Hoskere et al. [26] employed an optical fow method to discern the vibrations of a pedestrian suspension bridge from UAVcaptured video.Khadka et al. [27] utilized a UAV to capture video footage of a wind turbine model and applied a digital image correlation method to evaluate the structural integrity of the turbine blades.Tian et al. [16], utilizing a UAV to record video of an inclined cable, employed a line segment detector (LSD) to determine the vibration frequency of the cable.
However, when a UAV captures video footage of an inclined cable, it invariably records images of the surrounding landscape, including mountains, rivers, and urban structures situated behind the inclined cable.Te presence of complex background imagery can introduce interference in the images of inclined cable [16], potentially leading to inaccuracies in the analysis results of computer vision algorithms.In the domain of computer vision, methods for distinguishing between foreground targets and background images can be categorized into traditional algorithms and deep learning algorithms.
Traditional algorithms typically employ videos acquired through stationary cameras and analyze multiframe images to distinguish static backgrounds from moving foreground objects.To eliminate static backgrounds, a common approach involves applying flters to the results [28], such as median fltering [29] and Frame Diference [30].However, these methods exhibit limited efectiveness when dealing with dynamic backgrounds.Te proposed method, which entails using a UAV to capture cable videos, introduces a dynamically shifting background, albeit with relatively minor movements compared to the displacement of the cables.
In recent years, an increasing number of researchers have recognized the signifcance of background removal and have undertaken relevant investigations.For instance, Wei and Peng [31] proposed a block Frame Diference method and conducted experiments in various scenarios.Tis algorithm succeeded in removing most dynamic backgrounds of sailing ships but occasionally misclassifed certain areas of the sea surface as foreground.Additionally, other background modeling techniques, such as the hybrid Gaussian model [32] and Vibe's algorithm [33], calculate the video's background by tracking pixel intensity changes from frame to frame, achieving the extraction of moving objects.Nevertheless, these methods encounter difculties in eliminating the complex backgrounds encountered in cable videos captured by UAVs.Among these approaches, Vibe and Frame Diference yield results with numerous erratic straight lines, as observed in Figures 1 and 2.
In contrast, deep learning methods discern the foreground from the background in images through the training of convolutional neural networks [34][35][36].However, the accuracy of background removal using deep learning methods relies on the chosen deep learning models and image datasets [37][38][39].Aside from selecting an appropriate deep learning model, the quality of the image dataset signifcantly impacts recognition.Consequently, the collection of an extensive image dataset, comprising a minimum of 1000 images, becomes crucial.When applied to cable region recognition in this study, the necessity arises to capture and annotate a substantial number of cable images.It is worth noting that labeling data entail substantial manual efort [38].In cases where the image dataset lacks comprehensiveness, the model trained with images from a specifc bridge may exhibit limited generalization, potentially resulting in inaccuracies in cable background removal if the cable features difer.
Te Region Growing algorithm [40] represents a regionbased image segmentation technique capable of gradually expanding and merging small regions based on predefned rules.It has found applications in various domains.For instance, Wei et al. [30] applied the Region Growing algorithm to identify road cracks, while Shao et al. [41] used it to segment roofs from UAV-captured images.Lin [42] employed a modifed Region Growing algorithm for automatic detection of remote sensing images, and Lu et al. [43] utilized it for segmenting abdominal CT images.
However, when evaluating the suitability of the Region Growing algorithm for displacement detection in cable structure analysis, several challenges come to the forefront.Te algorithm inherently lacks robust edge detection capabilities, a critical requirement for precise delineation in such analyses.Furthermore, when combined with algorithms such as LSD, it results in noticeably extended processing times.Additionally, during motion, cables often overlap with backgrounds having similar grayscale values, leading to segmentation errors when relying solely on grayscale values of neighboring pixels.To address these 2 Structural Control and Health Monitoring challenges, this study introduces RGv2, an enhanced iteration of the Region Growing algorithm rigorously optimized for structural cable system analysis.RGv2 not only exhibits markedly improved accuracy in segmenting cable structures compared to its conventional counterpart but also excels in directly extracting displacement information from cables during the segmentation process.In terms of efciency, RGv2 accomplishes its objectives with only one-third of the processing time needed by the traditional combination of the Region Growing algorithm and LSD, representing a substantial advancement in processing speed.Furthermore, RGv2 adopts a more comprehensive growth approach, enhancing its accuracy in managing cable structure scenarios.A detailed exposition of RGv2's mechanism is provided in Section 2.1.2 of this paper.If a substantial color disparity exists between foreground and background images, the removal of the background can be achieved through the application of a clustering algorithm such as K-Means [44].It has found applications in various domains.For instance, Ding [45] utilized K-Means to extract dominant colors from an image, while Zhang et al. [46] adapted K-Means for hyperspectral image classifcation.In this study, RGv2, the Region Growing algorithm, and K-Means are employed based on the unique image characteristics of inclined cables to discern cables from complex backgrounds.
Unlike capturing video with a stationary camera, UAVs are adept at recording video footage of inclined cables.Nevertheless, videos captured by UAVs inherently contain relative displacements of both the tested structure and the UAV itself.Te absolute displacement of the cable can be defned as the discrepancy between the displacement recorded during UAV hover shooting and the UAV's absolute displacement, as illustrated in Figure 3.
Presently, signifcant research attention is directed towards addressing this issue, and methods for mitigating or eliminating UAV motion can be categorized into three principal approaches: (1) Utilizing Inertial Measurement Devices [47][48][49].Tis methodology entails measuring the UAV's motion using either the UAV's fight data or additional devices such as gyroscopes, GPS, and accelerometers.Mathematical models are then constructed using these supplementary data to compensate for the UAV's movement.However, this method necessitates the incorporation of additional devices alongside a consumer-grade UAV, leading to an increase in monitoring costs.(2) Employing Stationary Objects as References [25,50,51].UAV motion is determined by tracking feature points within stationary backgrounds or through a template matching algorithm [51].Subsequently, UAV motion can be nullifed through photogrammetry techniques.Nevertheless, the success of this method relies on high-quality backgrounds, as it may yield errors in cases where background quality is compromised.(3) Leveraging Frequency Characteristics.some literature [26,52] mentions the use of high-pass flters to eliminate low-frequency components of UAV motion from raw data.Nevertheless, this approach necessitates the defnition of a cutof frequency and can be relatively complex.Conversely, empirical mode decomposition (EMD) [53] represents an adaptive decomposition technique that simplifes the process and breaks down the original data into multiple intrinsic mode functions (IMFs).EMD efectively removes the low-frequency components, leaving behind the high-frequency aspects of the data.EMD and its extended algorithms have already been applied in a variety of felds.For instance, these applications span across medical [54], engineering [36,55,56], and mechanical [57][58][59][60] felds.In this paper, EMD is employed to decompose displacement data collected by a UAV.
Te primary focus of this paper is to utilize the proposed RGv2 algorithm for the purposes of background removal and cable tension detection.Additionally, a series of algorithms based on Region Growing and K-Means have also been employed to achieve these objectives.In analyzing the dynamic characteristics of the inclined cable, this paper employs EMD to reduce the infuence of the UAV's own vibration.Te paper is organized as follows, as shown in Figure 4. Section 2 introduces the computer vision algorithms used for background removal and displacement extraction.Additionally, this section describes the experiment conditions at the Chaijiaxia Yellow River Bridge and experimental equipment used.Section 3 presents the efects of the background removal algorithms on time and frequency domains.Additionally, this section analyzes the efect of EMD and estimates the cable force of the inclined cable.Te results show that the processing method proposed in this paper can accurately identify vibration frequencies of the inclined cable.

Proposed Approach
A video of an inclined cable's vibration captured by a UAV may have complex background images, which will afect the recognition of the cable edge features.Te misidentifcation of cable edge could seriously afect the accuracy of displacement time history.In this paper, according to the image characteristics of the inclined cable, three algorithms are used to remove the inclined cable's background, respectively.
Te proposed method is structured into two distinct segments.Te initial segment involves the processing of video footage capturing the vibrations of an inclined cable recorded by a UAV.Te subsequent segment focuses on converting the obtained displacement time history, derived from the frst segment, into the frequency domain for comprehensive analysis.A schematic representation of the proposed method is shown in Figure 5.
During the image processing phase, to assess the effectiveness of various methodologies, we implemented four distinct approaches.Te frst approach harnessed our newly developed RGv2 algorithm, which served the dual purposes of background removal and displacement detection.Te second method employed the Region Growing algorithm for background subtraction, followed by the application of LSD to determine the cable displacement data.In the third approach, the K-Means algorithm was applied for background elimination and subsequently integrated with LSD for the determination of displacement information.Finally, as a control method, we directly utilized LSD to calculate displacement information without any prior background removal, thus providing a baseline for comparative evaluation against the other techniques.
In the subsequent phase involving frequency domain processing, the displacement data undergo analysis through EMD, facilitating the extraction of cable vibration frequencies utilizing fast Fourier transform (FFT).It is noteworthy that all the computational procedures described can be efciently executed using MATLAB.

Tree Background Removal Algorithms for Inclined Cable
2.1.1.Region Growing Algorithm.Te exterior surface of an inclined cable is enveloped with a polyethylene sheathing, rendering the surface predominantly white in appearance.Within the video footage captured by a UAV, there is minimal variation in the image intensity across its surface.Consequently, the entirety of the inclined cable region can be efectively outlined using the Region Growing algorithm [40].Te original Region Growing method includes either 8region or 4-region expansion.For instance, considering the 8-connected domain, the algorithm compares the gray   Structural Control and Health Monitoring threshold of a seed point with that of its eight adjacent points.Points exhibiting a gray diference below the gray threshold are earmarked for potential expansion.As depicted in Figure 6, points highlighted in blue represent preselected seed points.If the grayscale threshold is set to 30, the algorithm can ultimately extend to include the points indicated in green.
After removing the background image, the LSD algorithm [61] is deployed to deduce the straight lines defning the edges of the inclined cable.
In the growing process of Region Growing, the gray threshold determines the acceptable tolerable of gray value diference.As shown in Figure 7, for backgrounds where the gray values are too similar, if they are too close to each other, it is difcult to obtain good results even by adjusting the gray threshold.

RGv2 Algorithm.
In pursuit of superior results, taking into account the cable's specifc attributes, we have introduced a more efcient growth rule, which concurrently allows for the direct extraction of linear information pertaining to the cable's edges.
Te precise growth rules are outlined as follows: initially, we segment the images into clusters predicated on the inclination of the cable.As illustrated in Figure 8, the cluster where the seed point resides (indicated in blue) is designated the seed cluster.Subsequently, we assess the average gray value between the two neighboring clusters.If the value is less than the grayscale threshold, the growth process is initiated.If it exceeds the grayscale threshold or the image boundaries, meeting the termination criteria, the growth is then halted.Ultimately, all segments marked in green can be expanded.Tis procedural insight is elucidated in Figure 9. Te linear attributes of the cable's edge can be discerned through the positioning of the seed cluster and the frequency of adjacent expansions, obviating the necessity for cable edge detection.Tis method results in a notable optimization of the processing time.
In comparison to the previous Region Growing and LSD algorithms, our proposed RGv2 algorithm demonstrates swifter processing times and heightened accuracy.A comprehensive comparative analysis with additional algorithms is provided in Section 3 of this paper.

K-Means Algorithm.
In instances where the background image of the inclined cable contains limited white regions, cluster algorithms such as K-Means can be efectively employed to diferentiate between the inclined cable and the background image.Te steps involved in K-Means clustering can be summarized as follows.
In a color image, each individual pixel comprises three components: red (R), green (G), and blue (B).Te R, G, and B components of all pixel points collectively form a threedimensional sample space.Trough the utilization of K-Means, pixel points within the image that closely resemble the color of the inclined cable are grouped into a single cluster, while other colors are distributed across multiple clusters.Following the clustering process, only the results of the initial cluster are retained, leading to the efective removal of the majority of the complex background.
Following the removal of the background, the edge information pertaining to the cable is computed utilizing the LSD algorithm, ultimately yielding the displacement data for the cable.Tis sequence of operations is depicted in Figure 10.

EMD.
To enhance the precision of identifying vibration frequencies in inclined cables and reduce the infuence of the UAV's motion, this study employs EMD to analyze the displacement time history.EMD, which can decompose the time history into multiple empirical modes called IMFs [53], represents a nonsmooth time-history decomposition method.
Although the selection of high and low frequencies remains somewhat subjective, this study endeavors to design a method for the automatic selection of suitable IMFs.Tis approach draws inspiration from the technique employed by Zhang and Wei for estimating high-frequency noise boundaries [62], involving the creation of an evaluation system for identifying IMFs with distinct frequency peaks.Furthermore, it is infuenced by the research of Yoon et al. [63], which asserts that UAV motion predominantly occurs between 0 and 0.5 Hz.Te entire selection process is illustrated in Figure 11.
Initially, this method conducts spectral analysis on the signal and compares the energy within the low-frequency range (0-0.5 Hz) with that in other frequency ranges.During the initial fltering step, if the proportion of low-frequency energy is substantial, it indicates that the given IMF predominantly refects the UAV's fight motion characteristics.Consequently, these IMFs are deemed for exclusion.Conversely, when the proportion of low-frequency energy is relatively small, it suggests that interference from the UAV on the signal is relatively limited, making these IMFs suitable for further refnement and analysis.
To select the IMFs capable of refecting the cable's dynamic characteristics, the standard deviation and spectral area with respect to the x-axis are also utilized to describe the data.For the spectral data in this research, a smaller standard deviation implies reduced interference and a more pronounced peak frequency.Additionally, the area enclosed with x-axis of the frequency spectral serves as another indicative measure.A smaller area corresponds to a more 6 Structural Control and Health Monitoring prominent frequency peak and less interference.Notably, the proportion of low-frequency energy exhibits a similar trend to the standard deviation and the area enclosed by the x-axis.Hence, smaller values for these three indicators signify that the IMF is better suited for capturing the cable's dynamic characteristics.Consequently, there is a need to formulate an index that can encapsulate these features.Before constructing the index, data normalization is a prerequisite.Due to the diverse frequency ranges of the IMFs decomposed by EMD, the Fourier transformed spectral diagrams exhibit signifcant variations along the Yaxis.To enable a uniform comparison across all IMFs, the frequency domain data of each IMF are initially normalized using formula (1), where NM denotes the normalization result.

NM � IMF − min(IMF) max(IMF) − min(IMF)
. ( Given the disparate distribution ranges of each IMF within the frequency domain, the analysis is concentrated on the 0-10 Hz range.Taking into account the aforementioned considerations, the standard deviation, area, and lowfrequency energy ratio of the frequency domain separately using X m n , the subscript "n" represents the IMF number, while "m" pertains to the three indices: standard deviation, area, and low-frequency energy ratio.

Structural Control and Health Monitoring
Due to the varying scales of the three indices, namely, standard deviation, area, and low-frequency energy ratio, as depicted in Figure 11, if X m n is used directly to make judgments, some indices will be decisive, while others will be dispensable.However, each X m n is expected to have the same weight.Consequently, the maximum value of each index is set to 1, and the remaining values are scaled accordingly, as demonstrated in formula (2).Tis adjustment yields a more balanced evaluation of standard deviation, area, and lowfrequency energy.
As the objective is to construct an index that attains higher values when the standard deviation, area, and lowfrequency energy ratio are minimized, formula (3) is devised for this purpose.Te fnal score, as denoted in formula (4), is derived by summing all three S m n together.A higher scoring of the T n value indicates that the respective IMF exhibits more pronounced frequency peaks.Tis methodology has been rigorously validated and successfully applied in Section 3.4 of the study.12(a), our experimental procedure involved artifcially exciting one of the inclined cables, followed by capturing video footage using a UAV.Simultaneously, an accelerometer was afxed to the inclined cable to record vibration data for comparative analysis.
For our experimentation, we selected the third inclined cable on the northeastern side of the bridge, counting from the top (as illustrated in Figure 12(a)).Te primary parameters of this inclined cable are summarized in Table 1.Since the bridge had not yet been opened to trafc, we employed a rope-based artifcial excitation method to induce vibrations in the inclined cable.Once the amplitude reached a stabilizing point, we ceased the excitation, allowing the inclined cable's vibrations to gradually attenuate.Troughout the experiment, we utilized a DJI Phantom 4 Pro UAV equipped with a 1-inch 20-megapixel image sensor, and the camera operated at a frame rate of 60 frames per second.
To expand our dataset for the validation of the methodologies outlined in Section 3.4, we also employed UAVs to capture data from two other cable-stayed bridges, namely, the Nongye Road Bridge and Jiefang Road Bridge.Tese bridges are located in Zhengzhou, China.Te distinguishing features of the Jiefang Road Bridge include light green cables and closer alignment of two rows of cables, enabling the UAV to capture two overlapping cables in a single frame.

Results and Discussion
3.1.Analysis of the Tree Proposed Algorithms.Tis section compares the efect of the three algorithms on background removal and their respective time consumption.As shown in Figure 13(a), to make the comparison clearer, the result of the RGv2 is green and the K-Means is blue, while the result of the Region Growing algorithm is changed to red, as shown in Figure 13.
In Figure 13, the area covered by the RGv2 algorithm is noticeably larger than that of the traditional Region Growing algorithm.Tis is due to the diferent growth mechanisms and gray threshold values adopted by the two.In fact, if the Region Growing algorithm were to use a higher gray threshold at this point, it would lead to extensive Te standard deviation was calculated the scale was standardized using formula (2) Calculated area and the scale was standardized using formula (2) Calculate the low-frequency energy ratio and the scale was standardized using formula (2) Calculate the S 1 using formula (3) Calculate the S 2 using formula (3) Calculate the S 3 using formula (3) Using formula (4) to calculate T n 8 Structural Control and Health Monitoring misjudgment like that shown in Figure 7(a).Terefore, the Region Growing algorithm can only use a relatively conservative gray threshold.In fact, even using a smaller gray threshold inevitably leads to the growth of an area that does not belong to the cable.In addition, the outer part of the cable is wrapped in a PE sheath in a spiral, which results in many curved lines on the cable surface that difer in gray value from the cable itself, as shown in Figure 1.Tese curved lines, which the Region Growing algorithm cannot grow, will interfere with the subsequent edge detection.
Tese are the reasons for the poor robustness of the Region Growing algorithm as shown in Figures 14 and 15.In contrast, the RGv2 algorithm proposed in this study judges and grows based on the gray values of a straight line, which can avoid many local minor issues and thus grow a more complete cable.K-Means also has similar issues.
Cable to be measured

Structural Control and Health Monitoring
We employ MATLAB's integral "profle" command to determine the execution times associated with RGv2, Region Growing, and K-Means.To facilitate a precise comparison of the durations for each method, we conducted processing on a personal computer, specifcally focusing on the time expended in tasks such as image retrieval, background removal, displacement computation, and the output of displacement data.As outlined in Table 2, the "Other Processing" category includes time allocation for activities such as image retrieval and displacement data output, while the "Total Time" category represents the cumulative time necessary to process 100 frames.
Table 2 provides a clear depiction of the superior time efciency of the RGv2-based method, requiring only onethird of the time compared to the Region Growing-based approach.

Analysis of the Results of Diferent Background Removal
Algorithms.To quantitatively assess the efcacy of various background removal algorithms, we employ the mean intersection over union (MIOU) and Dice coefcient (Dice) metrics to evaluate the accuracy and consistency of image segmentation methods.Both MIOU and Dice yield values within the range of 0 to 1, where a value closer to 1 indicates a higher degree of overlap between the segmentation result and the ground truth, signifying superior performance [64,65].
In this section, in addition to employing RGv2, Region Growing, and K-Means algorithms, we introduce deep learning, Vibe [33], and Frame Diference algorithms for comparative analysis.Among these, the Vibe algorithm initially models the backgrounds and subsequently removes them, while the Frame Diference method relies on pixel  10 Structural Control and Health Monitoring diferences between frames to eliminate backgrounds.Te efect of these diverse methods on background removal in varying environments is illustrated in Figure 1, accompanied by the corresponding evaluation indices presented in Table 3.
Upon analyzing the evaluation metrics and Figure 1, it becomes evident that the Frame Diference method exhibits suboptimal performance.Tis approach operates under the assumption that moving objects display signifcant pixel value disparities compared to the background.However, in UAV-captured videos, both the pixel values between the cable and the background may exhibit substantial variations, and some background areas might undergo pixel value changes across consecutive frames.Consequently, the Frame Diference method struggles to deliver satisfactory results under these conditions.Moreover, while the Vibe algorithm demonstrates a degree of adaptability to dynamic backgrounds, it faces challenges in accurately segmenting moving cables and is hindered by extended computation times.In contrast, RGv2 proves efective when a pronounced color contrast exists between the cables and the background.However, when the cable and background colors closely resemble each other, as observed in the case of the Jiefang Road Bridge, the results tend to be less favorable.Our proposed RGv2 algorithm, which places greater emphasis on overall grayscale diferences and avoids signifcant local issues, yields higher scores in image segmentation.
Furthermore, RGv2, along with the Region Growing and K-Means algorithms, exhibits certain lighting dependencies.For instance, in the scenario of the Nongye Road Bridge with the sun directly above the cable, UAV photographs of the cables display noticeable light-dark transitions.Tis may lead to inaccurate recognition of the darker portions of the cables during image segmentation.Nevertheless, background removal in the upper section remains efective, allowing for cable displacement determination through tracking the straight line of their upper edge.
Te deep learning results in Figure 1 were chosen from a selection of images that exhibited relatively good performance for comparison with other algorithms.In reality, the efcacy of deep learning methods is contingent upon the size of their datasets.If applied to a diferent bridge, there would likely be a substantial decrease in accuracy, as illustrated in Figure 16.In fact, even when examining the same bridge, variations in the shooting angle or lighting conditions can result in reduced accuracy, as illustrated in Figure 17.While it is capable of identifying the cable region, this method falls short in diferentiating between multiple cables in scenarios such as cable-stay bridges with overlapping cables.Tis shortcoming results in errors in cable edge recognition, as evidenced in Figures 1, 16, and 17.In contrast, our proposed RGv2 algorithm is adept at exclusively recognizing the specifed cables, a capability clearly illustrated in Figure 17.Furthermore, when two cables are in close proximity, it becomes impractical to employ the region of interest (ROI) approach to analyze a single cable independently.Te edge information from multiple independently moving cables can signifcantly interfere with the subsequent calculation of cable displacement.
In fact, besides RGv2, the results of the line segment detection after background removal by other algorithms should also be evaluated.Tis is because the cable edge detection results are related to the displacement recognition accuracy directly.Te straight lines of cable edges can be obtained by algorithms such as Hough transform and LSD.As Hough transform's computational efciency is relatively low when the picture is complicated, the LSD algorithm was used to track the cable edge (Figure 2).To demonstrate the clarity of the edge information obtained by RGv2, the results of the line segment detection after background removal by RGv2 are also presented.However, in reality, RGv2 can determine the information of edge straight lines through the location of seed points and the number of times it grows around, without the need for external edge detection algorithms.
It can be observed that inefective background removal leads to cluttered and numerous straight lines.Tis significantly disrupts the subsequent process of calculating cable displacement, particularly using the Vibe and Frame Difference method.In contrast, the Region Growing and K-Means algorithms demonstrate more consistent performance in detecting cable edges, notwithstanding some spiral lines on the cable's surface.Tis may impact the calculation of cable vibrations.Moreover, although these two algorithms have removed most of the background, some remnants still detected by the LSD could potentially interfere with subsequent calculations.Meanwhile, the RGv2 algorithm yields more concise and clear edge detection results.
It is noteworthy that the deep learning method may struggle with cable edge detection.Tis limitation arises from the difculty in completely separating the cable from the background, as evident in the zoomed image in Figure 18.Te deep learning method would leave a narrow background, which could also cause interference in LSD detection as shown in Figure 2. Structural Control and Health Monitoring

Analysis of the Inclined Cable's Vibration Frequency.
To test the reliability of the above two background removal methods, a short-time condition of 40 seconds and a longtime condition of 300 seconds were collected by the UAV for displacement time history identifcation.Afterwards, the frequency domain diagram is obtained by FFT for comparison.

Result of the Short-Time Condition. Figure 14(a)
presents the displacement time history results for the short-time condition.Notably, the results obtained without employing background removal exhibit numerous abrupt value changes.Tis phenomenon arises due to the presence of interference lines in the background when background removal is not applied.In contrast, the results obtained using   12 Structural Control and Health Monitoring the three background removal algorithms display closer proximity, characterized by improved continuity and robustness in the detection results.Furthermore, no abrupt changes occur in the monitoring results.Te slight discrepancies among the results obtained with the three background removal algorithms can be attributed to variations in the identifcation of inclined cable edges, as depicted in Figure 13(b).Figure 14(b) exhibits the FFT results of the data presented in Figure 14(a).To facilitate comparison with the accelerometer data and account for the low energy of the low-order modes recorded by the accelerometer, the results obtained with background removal algorithms have been attenuated in the frequency domain, as demonstrated in Figure 14(b).
In summary, a substantial disparity is observed between the results obtained with and without background removal.Te results lacking background removal exhibit complex and multifaceted frequency patterns.Conversely, the results obtained with background removal clearly manifest 3-5 discernible peaks when the frequency surpasses 1 Hz.Te frequency diferences among these peaks align with the vibration characteristics of the inclined cable.Tis underscores the crucial nature of processing the original video using background removal methods prior to edge detection of the inclined cable.

Result of the Long-Time Condition. Figure 15(a)
presents the displacement time history and frequency domain analysis for an extended period of 300 s.Remarkably, most of the observations made under the long-time condition align with those from the short-time condition.Te long-time condition also yields favorable detection results when compared to the short-time condition, underscoring the robustness of the proposed method.
In Figure 15(b), the displacement time history obtained from UAV video captures exhibits higher energy at low frequencies, gradually diminishing as frequencies increase.In contrast, the accelerometer data exhibit the inverse trend, with energy increasing as the frequency rises.Notably, the Region Growing and K-Means algorithms can detect three vibration frequencies, while RGv2 can detect fve vibration frequencies.Tis highlights the superior performance of RGv2 in frequency domain analysis.
However, it is important to note that both short-time and long-time conditions feature complex frequency patterns with elevated energy in the low-frequency range, which can complicate the automatic detection of vibration frequencies.To address this challenge, we employ EMD to analyze the obtained displacement time history in subsequent steps.

Comparison with the Accelerometer.
Te instability inherent to a hovering UAV during video capture introduces an additional infuence on measurement results.Notably, the primary energy source related to the UAV's motion consists primarily of a low-frequency component [66], resulting in elevated and complex energy levels below 1 Hz in the frequency domain (as depicted in Figure 15(b)).Consequently, the proposed method is unable to measure the frst vibration frequency of the inclined cable.However, this limitation does not hinder the manual identifcation of higher-order vibration frequencies.
As indicated in Table 4, three background removal methods are capable of observing 3-5 frequencies, closely aligning with the accelerometer's results.Notably, the proposed methods exhibit consistency with the accelerometer results in measuring modes 2, 3, and 4 of the inclined cable, as shown in Table 4. Furthermore, Table 5 provides a comparison of the frequency diferences obtained by the three methods relative to the accelerometer.
Table 5 reveals that the RGv2 method demonstrates mean relative errors of 0.89% and 0.71% across the two working conditions.In contrast, the Region Growing method exhibits mean relative errors of 1.83% and 1.03% for the same conditions, while the K-Means method presents mean relative errors of 3.43% and 0.71%.Consequently, the RGv2 method stands out by delivering superior results in terms of accuracy and consistency.

Vibration Frequency Analysis after EMD.
To enhance the accuracy of detecting the vibration frequency of the inclined cable while mitigating the infuence of the UAV's inherent vibration, EMD is employed to analyze the displacement time history under both short-time and long-time conditions.Te decomposition process of the long-term condition using the RGv2 algorithm is illustrated in Figure 19(a).In this process, the original data are decomposed into 8 IMFs and one residual, with the IMFs organized in descending order of frequency.As demonstrated in Figures 14(b) and 15(b), the UAV's motion exhibits relatively low frequencies, resulting in frequency overlap between the UAV's motion and the inclined cable's motion in the low-frequency range.
To evaluate the EMD data of the three cables on the three diferent bridges, the evaluation metrics discussed in Section 2.2 are employed and the results are presented in Table 6.Tis table facilitates the identifcation and selection of the most suitable IMFs.For instance, the highest scores among the three datasets correspond to IMF2, IMF1, and IMF2, respectively.As illustrated in Figure 19, it becomes evident that IMF2, IMF1, and IMF2 yield the most favorable results for the three cases, confrming the accuracy of the method proposed in this paper.Te optimal IMF is visually represented in Figure 20.
Te optimal IMF is selected for both the long-term and short-term conditions of the Chaijiaxia Yellow River Bridge using this approach.Comparing the calculated results with accelerometer data (Figure 21), it is apparent that the frequency peaks become more distinct and prominent with the application of this processing method.
Te frequencies obtained after implementing the proposed approach are summarized in Tables 7 and 8.In comparison to Table 5, this approach notably reduces the relative error in frequency disparities for all three methods.Furthermore, it aids K-Means in identifying a greater number of frequency peaks in the short working conditions.In summary, EMD, which is well suited for handling data fuctuations induced by a UAV's own vibrations, proves to be a superior method for accurately extracting the vibration frequencies of inclined cables.

Structural Control and Health Monitoring
To better illustrate the efectiveness of the proposed UAV motion fltering method, this article compares some fltering methods similar to EMD.Based on the EMD algorithm, scholars have proposed various improved Structural Control and Health Monitoring algorithms, such as the ensemble empirical mode decomposition (EEMD) [67] algorithm and the variational mode decomposition (VMD) algorithm.EEMD is an improved method where white noise is added to the original signal before each EMD iteration, but it also has the limitation of large computational complexity and interference.As shown in Figure 22, the frequency peak after decomposition is unclear and will cause interference to the frequency diference calculation.Besides, VMD determines the frequency center and bandwidth of each IMF by iteratively searching for the optimal solution of the variational model.Tus, VMD could achieve signal    16 Structural Control and Health Monitoring   Structural Control and Health Monitoring frequency domain division and efective separation of each IMF, as shown in Figure 23.In the decomposition of relative motion of cables, the frequency peaks obtained are the same as those obtained by EMD.However, VMD's decomposition number K lacks unifed theoretical guidance and needs to be determined artifcially [68].Tey currently have numerous applications [69][70][71][72].
At the same time, in order to compare with EEMD and VMD, this study uses the average of Kullback-Leibler divergence (KLD) of all IMFs to evaluate the decomposition efect of each decomposition method.KLD calculates the relative entropy between two random signals from a probabilistic perspective and efectively quantifes their diferences.Te calculation results are shown in Table 9.

Structural Control and Health Monitoring
It can be found that the average KLD of EMD is generally smaller, which indicates that the decomposed distribution, in terms of shape or probability mass allocation, is relatively similar to the original distribution.
Te IMF selection method proposed in Section 2.2 is also used in this section to the decomposition results of EEMD and VMD, and the highest rated IMFs are shown in Figures 24 and 25, respectively.However, due to the characteristics of EEMD decomposition, it has difculties to clearly distinguish frequency peaks.Terefore, the IMF selection method cannot be efectively used in conjunction with EEMD.In contrast, VMD can clearly decompose modes into diferent IMFs.However, the highest-scoring IMF often only contains one frequency peak, making it impossible to obtain frequency diferences.For this reason, the IMF selection method is also difcult to use in conjunction with VMD.Among them, the T n scores of the results computed by EMD, EEMD, and VMD are shown in Tables 6, 10, and 11, respectively.Due to the fact that the frequency diference can be obtained solely based on the IMF with the highest T n score, the proposed selecting IMF method is more applicable when used in conjunction with EMD.Te above analyses refect the applicability of the IMF selection method and can be used to select the ideal IMFs automatically.

Cable Force Estimation.
In this section, we utilize the average frequency diferences obtained from various algorithms to compute the cable force using the following formula [16]: where m is the unit mass of the cable, L is the length of the cable, r and s are the modal orders of the correspondingly identifed frequencies, and Δf rs is the diference between the rth and sth frequencies.Te results of this calculation are presented in Figure 26 and Table 12.It becomes evident that the cable force computed using the proposed method aligns closely with the values obtained via the accelerometer.Tis underscores the smaller error margin associated with the

Structural Control and Health Monitoring
RGv2 method proposed in this study during the fnal cable force computation.

Conclusion
Tis study utilizes UAV technology to record the vibrational motion of an inclined cable, capturing these data in video format.To extract the vibrational time history of the inclined cable, complex backgrounds within the video were eliminated using both a Region Growing algorithm and a K-Means algorithm.Due to various limitations in the Region Growing algorithm, an enhanced version named RGv2 was developed and applied for image segmentation and displacement calculation.Subsequently, the displacement time history was analyzed using EMD.Te fnal step involved employing the derived frequency diferences to compute the cable force.Te principal fndings are as follows: (1) In the context of background removal and displacement calculation, the RGv2 algorithm demonstrates a higher accuracy and shorter processing time compared to the methods based on K-Means and Region Growing.In addition, the RGv2 algorithm achieves higher MIOU and Dice scores in background removal.
(2) All three background removal algorithms successfully identify the 2nd-5th cable vibration frequencies, demonstrating an average relative error of less than 3.43%.However, RGv2 outperforms the others by maintaining the error below 0.89% and

Figure 3 :
Figure 3: Demonstration of the relationship between absolute and relative displacement.

Figure 7 :
Figure 7: Te efect of tuning parameters in the Region Growing algorithm.(a) Te gray threshold is set to 0.25; (b) the gray threshold is set to 0.20.
the data from 0-10 Hz are intercepted and then normalized by formula(1)

Figure 12 :
Figure 12: Te Yellow River bridge in Lanzhou: (a) location of the inclined cable to be measured; (b) deployment of the accelerometer and the UAV; (c) data acquisition instrument.

Figure 13 :
Figure 13: Comparison of background removal results.

Figure 14 :Figure 15 :
Figure 14: Calculation results for the short-time condition: (a) displacement time history; (b) frequency domain.

Figure 16 :
Figure 16: Application of deep learning methods to other bridge scenarios.

Figure 17 :Figure 18 :
Figure 17: Results for the Jiefang Road Bridge with changes in lighting or shooting angle.

Figure 19 :
Figure 19: Decomposition results of EMD.(a) Data of Chaijiaxia Yellow River Bridge; (b) data of Nongye Road Bridge; (c) data of Jiefang Road Bridge.

Figure 20 :
Figure 20: Te superimposed results of the highest rated IMFs using EMD.

Figure 21 :
Figure 21: Comparison before and after EMD for the long-time condition: (a) before using the proposed method; (b) after using the proposed method.

Figure 22 :Figure 23 :
Figure 22: Decomposition results of EEMD.(a) Data of Chaijiaxia Yellow River Bridge; (b) data of Nongye Road Bridge; (c) data of Jiefang Road Bridge.

Figure 23 :
Figure 23: Decomposition results of VMD.(a) Data of Chaijiaxia Yellow River Bridge; (b) data of Nongye Road Bridge; (c) data of Jiefang Road Bridge.
To validate the efcacy of the background removal techniques presented in this manuscript, we conducted experiments on an inclined cable situated on a bridge spanning the Yellow River in Lanzhou.As depicted in Figure

Table 1 :
Main parameters of the measured inclined cable.

Table 2 :
Te statistics of algorithm time (unit: s).

Table 3 :
MIOU and Dice of diferent methods.

Table 6 :
Calculated T n using the proposed method.

Table 7 :
Vibration frequencies after the proposed method (unit: Hz).

Table 8 :
Frequency diferences after the proposed method.

Table 10 :
Calculated T n of EEMD using the proposed method.

Table 11 :
Calculated T n of VMD using the proposed method.Figure 26: Diagram of the cable force comparison.

Table 12 :
Comparison of cable force estimation.Utilizing EMD, the study introduces a method for automatically selecting IMFs containing clearer peak frequency information and obtaining the frequency diference of the stay cable vibration.Tis approach enhances the accuracy of vibration frequency identifcation.(4) Cable force computation: by utilizing the frequency diferences derived from the background removal methods and EMD, the relative error in estimating the cable force is limited to below 2%.Specifcally, the cable force error calculated from the frequency diferences detected by RGv2 remains within 1.35%.