Sliding Performance Evaluation with Machine Learning-Based Trajectory Analysis for Skeleton

Abstract

Skeleton is an extreme sliding sport in the Winter Olympics, where formulating targeted sliding strategies, based on training videos to navigate complex tracks, is particularly important. To make in-depth use of training video records, this study proposes an analytical method based on Mixture of Gaussians (MoG) and K-means clustering to extract and analyze trajectories from recorded videos for sliding performance evaluation and strategy development. A case study was conducted using data from the Chinese national skeleton team at the Yanqing Sliding Center, obtaining 741, 834, and 726 sliding trajectories from three representative curves. These trajectories were divided into groups based on sliding completion time (fast, medium, and slow groups). The consistency of trajectories within each group was calculated to evaluate sliding stability, while trajectory patterns in the fast group were clustered and described based on the average values of multiple features (starting position, ending position, and apex orthogonal offset). The results showed that more skilled athletes exhibited greater sliding stability (lower ${\rho }_C$-values), and on each curve, there were sliding patterns that performed significantly better than others. This research quantifies the characteristics of athletes’ sliding trajectories on curves, facilitating the visual tracking of training effects and the development of personalized strategies. It provides coaches and athletes with scientific decision-making support and clear directions for improvement, ultimately enabling precise enhancements in training efficiency and competitive performance, while also laying a technical foundation for the future development of intelligent training systems.

1. Introduction

Skeleton is one of the three sliding sports in the Winter Olympic Games that is held in manmade bobsleigh tracks, and is well-known for its high speed and difficulty. The sport of skeleton uses a one-man sled, on which the athlete travels headfirst after acceleration by pushing and running, down a mile long-track reaching speeds of up to 147 km/h [1].

Sled tracks are inherently unique due to their mountainous terrain integration, demanding precise strategy customization. Unlike standardized venues, these inherently variable courses demand sport-specific adaptability [2]. For example, athletes and coaches classify tracks by technical challenge level, categorize tracks by technical difficulty: “push tracks” prioritize explosive start phases on straighter sections where initial acceleration critically influences overall time (a 0.1 s push gain can yield 0.3 s run-time advantage). Conversely, “driving tracks” challenge athletes with intricate curves and steep drops, driving techniques like steering precision dominate performance. Thus, while push-tracks reward raw power optimization, driving-tracks require microsecond navigational mastery, proving that terrain-specific adaptation, not universal tactics, unlocks victory.

To gain a competitive edge in the highly competitive sport of skeleton—particularly on technically demanding “driving tracks” with complex curves—it is essential to conduct a precise, track-specific sliding strategy analysis to achieve quantifiable performance improvements. However, current training support methods in this sport remain relatively limited, heavily relying on coaches’ and athletes’ manual review and subjective interpretation of training videos as the primary feedback mechanism [3]. This approach presents significant limitations: the manual analysis of large volumes of video data is inefficient, making it difficult to systematically extract key sliding patterns. Moreover, the results are often influenced by individual experience and subjective judgment, lacking objective and consistent quantitative standards, which hinders the scientific accuracy and precision of training feedback. To automate and objectify the analytical process, computer vision techniques have been widely adopted in various sports for applications such as athlete and object detection [4,5], motion trajectory tracking [6,7], and quantitative analysis of technical movements and performance [8,9,10]. Although intelligent analytical tools have become integral to enhancing training and tactical analysis in well-commercialized sports like basketball and soccer, their research and application in high-speed sliding sports, such as skeleton, remain considerably limited.

In light of this, to better leverage training video records for improving athlete performance and to address the gap in computer vision applications within skeleton racing, this study proposes an intelligent computer vision-based framework for analyzing sliding trajectories. The process begins by using skeleton training videos as input data and employing a Mixture of Gaussians (MoG) model to extract sliding trajectories and define their features. The trajectories are then grouped based on sliding completion time, and the consistency within each group is computed to evaluate sliding stability. Finally, the k-means clustering method is applied to analyze trajectory patterns within the fast group, generating optimized strategy recommendations for different curves. This machine learning-driven methodology digitizes and quantifies sliding patterns across various curves of a track, providing data-driven decision support for enhancing athletic performance.

The remainder of this study is structured as follows: Section 2 provides a literature review on skeleton and computer vision-related research; Section 3 describes the methodology, including trajectory extraction and feature definition, stability assessment, and trajectory pattern clustering; Section 4 applies the proposed method to a practical case study, presenting experimental results and discussion; and Section 5 concludes the study.

2. Related Work

2.1. Research on Skeleton

The skeleton event consists of two phases: the push-start and the run itself. Current research on the sport focuses on different aspects of these two phases, including the run-up, aerodynamics, and ice friction [11,12].

During the push-start phase of skeleton, numerous factors influence performance, and related research primarily focuses on two key areas: physical fitness and technique. In terms of physical fitness, studies cover body morphology, strength and power, and speed [13,14,15]. For example, Colyer et al. [16] investigated predictors of physical ability during the push-start phase in skeleton sledding, conducting a series of two-day physical ability and push-sled tests multiple times over six months on 13 elite skeleton athletes. Similarly, Sands et al. [17] investigated the physical characteristics of 14 U.S. national team skeleton athletes, finding that stronger and more powerful athletes achieved better sprint and push-start performance. In terms of technique, Kivi et al. [18] analyzed the kinematic characteristics of two push-start stances in skeleton: the parallel-foot stance and the staggered-foot stance. Colyer et al. [19] demonstrated through their research that velocity prior to sled mounting, distance covered, and mounting efficiency are significantly correlated with push-start performance. Li et al. [20] found that during the push-start phase, the one-handed sled-pushing technique is more agile and prevalent than the two-handed approach, though it exhibits slightly lower stability. To enhance speed, athletes should prioritize increasing step frequency.

During the gliding phase of skeleton, research primarily focuses on aerodynamic drag and ice friction. For instance, Niu et al. [21] employed computational fluid dynamics (CFD) to investigate how athletes’ head movements affect aerodynamic drag, aiming to optimize competitive performance. Li et al. [22] employed wind tunnel testing to optimize the baseline aerodynamic posture of skeleton athletes during the gliding phase, reducing aerodynamic drag and enhancing competition performance. Irbe et al. [23] utilized on-track timing sensors and miniature accelerometers mounted on sleds to obtain precise drag coefficient data, applying two numerical models and one experimental model to analyze ice friction coefficients. Furthermore, by identifying vibrational signatures at structural natural frequencies, Irbe et al. [24] characterized friction properties during gliding and evaluated performance variations across blades of differing stiffness to minimize sliding friction.

2.2. Machine Learning-Driven Performance Evaluation

Machine learning technology, a critical subfield of artificial intelligence, not only enables precise recognition and detection of human motion, but also plays a vital role in providing real-time training feedback and supporting decision-making processes [25,26,27]. Consequently, it has gained widespread adoption in competitive sports such as football and basketball [28].

In basketball applications, Jia et al. [29] employed machine vision to analyze player foul actions, driving advancements in basketball strategy and gameplay refinement. Pang et al. [30] integrated computer vision with sports biomechanics to develop a DeepLabCut-based framework for efficient athlete motion identification and kinematic analysis. Xia et al. [31] proposed a method integrating computer vision and inertial capture for recognizing basketball player movements, aiming to address common visual analysis errors in basketball action recognition techniques, such as action-intensive scenarios and insufficient feature extraction. Du [32] investigated an athlete error action recognition model based on artificial intelligence algorithms and computer vision. They constructed this model using a dual-channel 3D convolutional neural network (CNN) to objectively evaluate basketball players’ performance.

In football applications, Zhang et al. [33] deployed artificial intelligence and computer vision to develop a novel AI-driven image recognition system for automated detection of offside violations and foul incidents. AbuKhait et al. [34] leveraged the YOLOv7 real-time object detection model integrated with computer vision to track ball trajectory while identifying and classifying players and referees on the pitch. Wang et al. [35] implemented stereo vision technology for moving target detection and tracking, specifically applied to kinematic analysis of shooting techniques. Zuo [36] engineered a multi-camera system using computer vision and deep learning to achieve long-duration, high-accuracy athlete tracking across football fields.

An essential application of computer vision technology in competitive sports lies in the precise tracking and analysis of athlete or ball movement trajectories [37]. For instance, Wei [38] proposed an image feature analysis method based on infrared thermal imaging, integrating computer vision and machine learning technologies to enhance the accuracy and real-time performance of athlete trajectory detection. Zhang et al. [39] proposed a computer vision-based technique to track athlete movement trajectories, applying it to analyze dance trajectories of gymnasts and racket swing trajectories of badminton players. Asano et al. [40] employed computer vision technology to detect the 3D spatial positions of tennis balls and rackets, enabling quantitative analysis and evaluation of tennis swing motions. He et al. [41] utilized computer vision technology to analyze the flight characteristics and force trajectory model of a shuttlecock, thereby predicting its landing point. Lu et al. [42] employed computer vision technology to study how to accurately identify, locate, and predict the flight trajectories and landing points of table tennis balls.

Based on the above analysis, research on skeleton sledding has primarily focused on physical fitness and technique during the push-start phase, as well as factors such as aerodynamic drag and friction during the sliding process. These studies have played a crucial role in enhancing athletic performance and optimizing training methods. However, research on performance optimization through the analysis of sliding trajectories remains notably scarce, warranting in-depth exploration. Although computer vision technology has been widely adopted in team sports such as basketball and soccer, where it plays a crucial role in analyzing athlete movements, ball trajectories, and developing techniques and tactics, its application remains limited in sliding sports. This is especially true in high-speed, complex disciplines like skeleton sledding, where visual-based trajectory analysis tools are still underdeveloped (As shown in Figure 1).

Therefore, this study aims to propose a computer vision-based method for analyzing skeleton sledding trajectories. This approach involves extracting the sliding trajectories of moving targets from training videos, defining trajectory features, evaluating trajectory stability, and performing clustering and analysis of trajectory patterns. The research is expected to enable coaches and athletes to utilize training records more efficiently while providing scientific and precise training feedback.

3. Method

In this study, sliding trajectories of skeleton athletes on these curves were extracted from training recordings using a computer vision algorithm. The trajectories were divided into three groups based on the sliding completion time, and the trajectory stability within each group was evaluated. The faster trajectories were later clustered into several groups to identify distinct patterns. Finally, driving instructions for these curves were derived by analyzing the features of these patterns. The full analytical process is shown in Figure 2.

3.1. Trajectory Extraction from Videos

The Mixture of Gaussians (MoG) is a powerful probabilistic model whose core idea is to represent complex data distributions through a weighted combination of multiple Gaussian distributions. It is commonly used to model complex and dynamic backgrounds, thereby effectively separating moving foreground objects. In order to achieve quantitative analyses of the trajectories’ features, a background subtraction approach of the Mixture of Gaussians (MoG) [43] was employed to extract the sliding trajectories from the videos, storing each trajectory as a sequence of points.

Background subtraction is a technique used to extract moving objects from a video or image sequence. Its aim is to separate the foreground (moving objects) from the background, where the background is assumed to be static [44]. The MoG approach is chosen in this study to reduce the interference of dynamic noises, such as shadows or reflections on ice during the extraction [45,46], as well as the interference by varying lighting conditions [47].

The videos were recorded at 30 frames per second with a resolution of 1920 by 1080 pixels. Fragments of each curve were applied with background subtraction to isolate the athletes and their skeletons as foreground objects in each frame. Subsequently, the minimum bounding rectangle of the foreground objects was calculated, and its center was used to determine the location of the foreground objects in that frame. These locations were stored as a sequence of point coordinates, each corresponding to a pixel location in a 1920 × 1080 window. Connecting the sequent points with polylines, sliding trajectories will be obtained, as shown in Figure 3.

Some trajectories were not extracted properly due to the fast movement speed and low sample rate of the cameras, which could impede the accuracy of subsequent analyses. Poorly extracted trajectories were identified and excluded by calculating the distances between adjacent points and angles of adjacent polylines within the trajectories. Trajectories with apparently shorter total distances, larger distances between sampled points, or segments with acute angles were considered as poorly extracted ones and removed from further processing steps.

With the coordinates of the points stored, let the trajectory, as the set of consistent points, be defined as Equation (1).

$$T_i=[X_i^k{]}_{k=1}^{K_i}$$

(1)

where K_i is the total number of points in the trajectory T_i. The points are described by their coordinates as $X_i^k=\left. [\left(x_i^k,\hspace{0.33em}{y}_i^k\right)\right]$. Total length of a trajectory is calculated by summing up distances between the adjacent points, as shown by Equation (2).

$$L_i={\sum }_{k=2}^{K_i}\sqrt{{\left(x_i^k-x_i^{k-1}\right)}^2+{\left(y_i^k-y_i^{k-1}\right)}^2}$$

(2)

Trajectories with L_i lower than 95% of all trajectories were removed. Average distance is defined by Equation (3).

$$V_i=L_i/K_i$$

(3)

which reflects how quickly the athletes’ position changed between frames in the videos. When outlier positions appear in a frame or some positions are missing, the distances between points increase significantly, resulting in a higher V_i. Consequently, trajectories with V_i values exceeding 95% of all trajectories were also removed.

Some other trajectories were properly extracted except for fluctuations in one or two frames. In these cases, the location of the athletes and skeletons deviated sharply in certain frames but returned to proper positions in subsequent frames, resulting in acute angles in the trajectories. To eliminate these acute angles without altering the number of points in each trajectory, the coordinates of the affected points were resampled based on adjacent frames.

3.2. Definition of Trajectory Features

Once the trajectories are extracted from the training videos, it is essential to establish a feature set that accurately captures both the shape attributes of the trajectories and key kinematic characteristics to enable a quantitative analysis and comparison of sliding patterns. The extracted features include curvature compression ratio, apex orthogonal offset, and apex-origin vector magnitude. Curvature compression ratio, apex orthogonal offset, and apex-origin vector magnitude are factors reflecting the shape of each trajectory, as shown in Figure 4. Typically, when athletes slide upon the curves, they would first reach a high position due to the centrifugal force, and then return to the center of the track. Thus, the trajectory is supposed to be a convex curve.

Among these, the curvature compression ratio represents the degree of bending of a trajectory, defined as the ratio of the actual length (arc length) of the trajectory to the linear distance between its start and end points. The shortest linear distance between the start and end points of a trajectory is defined by Equation (4).

$$D_i=\sqrt{{\left(x_i^1-x_i^{K_i}\right)}^2+{\left(y_i^1-y_i^{K_i}\right)}^2}$$

(4)

Subsequently, the curvature compression ratio is defined by Equation (5).

$$R_i=L_i/D_i$$

(5)

A higher R_i value indicates greater curvature in the trajectory. A larger ratio (>1) suggests a more curved path, implying the athlete covered a longer distance within the curve. Conversely, a ratio closer to 1 indicates a trajectory approaching a straight line, reflecting a more direct path through the curve. In practical terms, a higher curvature compression ratio may suggest that the athlete made more adjustments during the curve or was subjected to stronger centrifugal forces.

The apex orthogonal offset, denoted as H_i, represents the maximum among the perpendicular distances from all points on the trajectory to the line connecting the start and end points (denoted as l_i). It reflects the maximum protrusion height of the trajectory, indicating the farthest deviation of the athlete from the straight-line path during the curve. A larger H_i value suggests that the athlete reached a higher position in the curve, typically due to centrifugal force, while a smaller H_i indicates a flatter and more direct path. This metric captures the athlete’s ability to manage height control and centrifugal force during sliding. Although trajectories with higher H_i values tend to exhibit greater curvature (as reflected by a larger R_i), these two factors are not entirely correlated, as trajectories with the same H_i can have different R_i values.

After the maximum height has been calculated, let the point with the maximum distance be $X_i^n$. Make a perpendicular line from $X_i^n$ to l_i, and let the perpendicular foot be p_i^k. The distance between p_i^k to the starting point $X_i^1$ can be calculated, as d_i. The apex-origin vector magnitude is defined by Equation (6).

$${\omega }_i=d_i/D_i$$

(6)

The parameter ${\omega }_i$ indicates the relative position of the apex along the trajectory, describing whether the highest point is closer to the start or the end. Its value ranges between 0 and 1. A ${\omega }_i$ value closer to 1 indicates that the apex $X_i^{K_i}$ is nearer to the end of the trajectory, while a smaller ${\omega }_i$ value suggests that the apex $X_i^{K_i}$ is closer to the start. This ratio reflects when the athlete reaches the maximum height during the curve, providing insight into their entry and exit strategies.

3.3. Stability Assessment

Following the definition of the trajectory features, the trajectories from each curve were sorted according to their sliding completion time and evenly divided into distinct groups. The consistency of the trajectories within each group was then calculated to evaluate the stability of the sliding performance. Given the differences in sliding strategies, the group exhibiting the highest stability will be selected for clustering after the evaluation of sliding stability across all groups, thereby enabling a more effective extraction of distinct sliding patterns.

Consistency serves as an important metric that reflects the degree of similarity among trajectories on a specific curve. Unlike metrics that evaluate individual trajectories, consistency is inherently a group-level characteristic, as it depends on the spatial and temporal alignment among multiple trajectories within the same group. To compute this consistency measure, all trajectories belonging to a particular group are plotted together onto a blank background image with a resolution of 1920 by 1080 pixels, which matches the resolution of the original video frames used for data acquisition. Each trajectory is rendered as a thin line exactly one pixel in width, ensuring that no artificial broadening or merging occurs during visualization. Following this visualization process, the number of colored (i.e., non-background) pixels, denoted as N_p, is counted. The consistency is defined by Equation (7).

$${\rho }_C=N_p/{\sum }_{i=1}^I{L}_i$$

(7)

where I represents the number of trajectories in this group.

3.4. Trajectory Pattern Clustering

Trajectory pattern clustering is a data analysis method whose core concept lies in automatically categorizing and grouping raw trajectory data based on the similarity of motion characteristics. This approach enables the discovery of potential, representative, and typical motion patterns from large volumes of data and reveals underlying regular structures embedded within the dataset. The core motivation for conducting a trajectory pattern clustering analysis in this study is to objectively classify sliding trajectories into patterns with significant performance differences based on their features using clustering methods. This process will address the limitations of traditional empirical training, identify key performance optimization factors, and establish quantitative matching relationships between track characteristics and optimal sliding strategies, thereby enabling personalized technical improvements and tracking of training outcomes.

With the factors above calculated, the features of trajectory T_i for clustering are expanded to include the starting and ending locations, curvature compression ratio ($R_i$), apex orthogonal offset ($H_i$), and apex-origin vector magnitude (${\omega }_i$). Then, trajectories in the fast group will be clustered into several sub-groups through the k-means method. K-means is a classic and one of the most popular unsupervised learning algorithms that solves the clustering problem [48]. The proper number of these sub-groups was selected by calculating Silhouette Scores [49] and the within-cluster sum of squares (WCSS) [50]. After clustering, each subgroup represents a distinct trajectory pattern. The average finish time of each pattern is calculated to determine which pattern may be more advantageous during sliding.

4. Experiment

Hypothesis: According to the training experience of athletes and coaches, it was hypothesized that sliding trajectories with a shorter finish time had more similar patterns, and the final finish time was influenced by different sliding patterns. Among those sliding patterns, there should be more suitable patterns for each curve of the track, reducing the final finish time.

This experiment aims to verify the scientific validity and practical applicability of the proposed computer vision-based intelligent analysis method for skeleton sliding trajectories (primarily comprising two core technical modules: trajectory consistency assessment and trajectory pattern clustering) in athletic training guidance through systematic experimental design.

4.1. Dataset

The China National Sliding Center, located in Yanqing, Beijing, was the venue of sliding sports in the 2022 Winter Olympics. The track has a total length of 1975 m, features 16 curves including a 360-degree spiral, and is regarded as one of the most advanced track designs [51]. According to the data derived from competitions in 2021 and the Winter Olympics in 2022 [52], the push time performances of champions on this track were not the best among all athletes, indicating the significance of driving skills on this track.

The video records were provided by the China National Sliding Center, documenting the training sessions of the center’s athletes. There are several static cameras alongside the sliding track, covering the whole track to record the training. Three curves—curve 2 (C2), curve 3 (C3), and curve 9 (C9)—were selected to validate the analysis method proposed in this study, as shown in Figure 5. These curves were selected for their distinct directions, traversal speeds, and the corresponding variations in sliding strategies. Additionally, cameras can capture the whole gesture of the athletes without being covered by some wood structure in the venue, thus, the trajectories can be extracted more precisely. All recordings from athletes of China’s national sliding sports team were authorized for this study.

Although each athlete’s sliding was fully recorded, some recordings were excluded due to abnormal trajectory shapes, resulting in unequal numbers of trajectories for the three curves. Nevertheless, there are sufficient well-extracted trajectories for feature analysis on each curve. The three curves contained 741, 834, and 726 trajectories, respectively. Each trajectory was logged with the corresponding sliding finish time. For each curve, all trajectories were evenly divided into fast, medium, and slow groups according to their sliding completion times.

4.2. Procedure and Results

Based on the proposed methodology and experimental dataset, trajectory consistency across different groups (fast, medium, and slow) for the three curves was assessed, and cluster analysis was performed on the trajectory patterns of the fast group for each curve. The detailed process and results are as follows.

4.2.1. Stability of Sliding Trajectories

It is necessary to first evaluate the sliding stability of different groups for each curve. To facilitate comparison, all available trajectories corresponding to the same curve are evenly divided into three separate groups based on finish time. As shown in Figure 6, a group with higher internal similarity will have its member trajectories overlapping each other, which results in fewer unique pixels being colored on the canvas. In contrast, if the trajectories diverge significantly, more pixels will be painted, indicating lower consistency. All trajectories for the same curve are divided into three groups evenly. The higher the similarity of a trajectory group, the more likely they will overlap with each other and leave more pixels unpainted on the background. Therefore, trajectory groups with a smaller ${\rho }_C$ value are considered to exhibit higher spatial consistency, as they comprise more similar routes that follow nearly identical paths.

For the three groups of each curve, consistency was calculated, and the results are shown in

Table 1. Result of consistency calculation.

Curves	Groups	Numbers of Trajectory N	Consistency	Gaps of Consistency
C2	Fast	247	1.455	—
	Medium	247	1.534	0.079
	Slow	247	1.699	0.165
C3	Fast	278	0.924	—
	Medium	278	0.987	0.063
	Slow	278	1.208	0.221
C9	Fast	242	1.190	—
	Medium	242	1.308	0.118
	Slow	242	1.540	0.350

. Here, the gaps of consistency represent the differences in trajectory consistency metrics among distinct speed groups (fast/medium/slow) for each curve. All curves—C2 (N = 247, ${\rho }_C$ ranging from 1.455 to 1.699), C3 (N = 278, ${\rho }_C$ ranging from 0.924 to 1.208), and C9 (N = 242, ${\rho }_C$ ranging from 1.190 to 1.540)—exhibit an increasing trend in ${\rho }_C$ values. This trend indicates that trajectories with shorter finish times have more concentration. Notably, for each curve, the gap between the slow and medium groups (0.165, 0.221, and 0.350) is larger than the gap between the medium and fast groups (0.079, 0.063, and 0.118). As the athletes’ scores improve during their training, the growth of consistency becomes less.

4.2.2. Trajectory Pattern of Each Curve

Based on the aforementioned trajectory consistency assessment, the fastest trajectory groups (i.e., the fast groups) for each curve were selected for trajectory pattern clustering and analysis, with the clustering results presented in Figure 7. To characterize each pattern, the average starting location $\overline{Y}$, average ending location $\overline{X}$, and average apex orthogonal offset $\overline{H}$ are computed. Here, the starting and ending locations are defined by the y-coordinate and x-coordinate of the initial and final points, respectively, since all curve entrances are horizontal while exits are vertical. Although incorporating more features could improve the clustering performance, these features are not intuitive for interpreting the patterns. Therefore, three features were selected to describe each optimal pattern.

Note: To visualize the clustering results in three-dimensional space, three key features were selected as clustering factors for the K-means algorithm. The resulting clusters were then projected into a Principal Component Analysis (PCA) space, where each coordinate axis (i.e., principal component) represents one of the corresponding features. Meanwhile, as all features are measured in image space, their units are expressed in image-space coordinates, i.e., the number of pixels.

To have a closer look at the obtained results, the trajectories of curve C2 were clustered into five groups, while those of curves C3 and C9 were clustered into three groups, based on the Silhouette Scores and WCSS metrics. Each cluster represents a unique trajectory pattern, as shown in Figure 7 and Figure 8. In the clustering results for each curve, there exists one cluster with a shorter average finish time than the others, indicating the most efficient sliding mode for that curve. Examples include cluster 1 in curve C2 (t = 62.18 s), cluster 2 in curve C3 (t = 62.18 s), and cluster 2 in curve C9 (t = 62.14 s).

(1)

Results of Curve 2

As shown in

Table 2. Clustering results of each curve trajectory.

Curves	Clusters	Numbers of Trajectory N	Average
			Finish Time t (s)	Starting Position $\overline{\mathit{Y}}$(Pixel)	Ending Position $\overline{\mathit{X}}$ (Pixel)	Apex Orthogonal Offset $\overline{\mathit{H}}$ (Pixel)
C2	1	39	62.18	130.69	1598.82	183.97
	2	38	62.38	111.32	1542.53	171.55
	3	45	62.47	124.29	1583.76	172.60
	4	59	62.44	109.24	1585.81	209.68
	5	66	62.35	123.27	1637.80	227.16
	Range (90%)	—	—	107–137	1539–1648	—
C3	1	91	62.25	167.71	385.92	137.21
	2	73	62.18	159.62	333.29	179.91
	3	114	62.30	159.08	364.72	162.30
	Range (90%)	—	—	152–178	331–405	—
C9	1	105	62.28	91.30	520.43	160.71
	2	75	62.14	90.15	464.89	195.32
	3	62	62.50	105.05	470.79	171.61
	Range (90%)	—	—	97–115	453–526	—

, cluster 1 also has the largest average starting position ($\overline{Y}$ = 130.69), which corresponds to lower initial positions, since a larger value means the position is closer to the bottom of the background image. In terms of ending position, cluster 1 reaches an average value of 1598.82, which is the second highest among the clusters, slightly lower than cluster 5 ($\overline{X}$ = 1637.80). This reflects a relatively high exit position, considering that the sliding direction of C2 is from left to right in the camera view.

The average apex orthogonal offset of cluster 1 ($\overline{H}$= 183.97) ranks in the middle range among the five clusters. Specifically, it is less than two other clusters—whose values are 209.68 and 227.16, both over 14% higher than that of cluster 1—but is slightly higher than the remaining two, with differences under 8%.

(2)

Results of Curve 3

According to the results in Table 2, although the average starting position of cluster 2 ($\overline{Y}$ = 159.62) is slightly higher than that of cluster 3 ($\overline{Y}$ = 159.08), both values remain lower than the starting position of cluster 1 ($\overline{Y}$ = 167.71). This suggests that cluster 2 begins from a relatively higher location when entering the curve, as lower starting position values correspond to higher physical locations.

As for the average ending position, cluster 2 shows a value of 333.29, which is considerably lower than those of cluster 1 and cluster 3 ($\overline{X}$ = 364.72 and 385.92). Given that curve 3 progresses from right to left in the camera view, a lower x-coordinate indicates a higher physical location at the exit. Therefore, cluster 2 corresponds to the highest exit position among the three.

(3)

Results of Curve 9

As shown in Table 2, clusters 1 and 2 share similar average starting positions, with cluster 2 having the lowest value at 90.15, representing a higher physical location when entering the curve. On the other hand, cluster 3 shows a significantly larger starting position value of 105.05, indicating that its trajectories begin from a lower vertical position relative to the others.

In terms of ending positions, cluster 2 reaches an average value of 464.89, which is higher than those of both cluster 1 and cluster 3. Considering that curve C9 proceeds from right to left in the camera view, a higher x-coordinate corresponds to a higher physical exit position. This further supports the idea that cluster 2 represents a more favorable and possibly more stable sliding pattern on curve C9.

4.3. Discussions

The patterns with the shortest average finish time were identified for each curve. Based on the clustering results, the optimal strategy for curve 2 involves entering low, maintaining a smaller turning radius, and exiting high. However, if athletes are unable to enter the curve from a high position, they should aim to minimize rotation and exit the curve as efficiently as possible. For curve 3, the best-performing pattern has the highest average apex height among the three clusters, indicating a more pronounced turning motion. Therefore, the most appropriate strategy for this curve is to enter high, maintain a significant degree of rotation, and exit high. At the same time, athletes should avoid descending too early within the curve to prevent ending at a low position. In the case of curve 9, the optimal pattern is similar to that of curve 2, involving a high entry, a high trajectory through the turn, and a high exit. However, the most critical factor appears to be entering the curve from a high position, as the average finish time of cluster 1 remains significantly shorter than that of cluster 3, despite other differences.

According to the results of Silhouette Score and WCSS calculations, the optimal number of clusters for each of the three curves is 5, 3, and 3, respectively. Each optimal cluster number has a high Silhouette Score and relatively low WCSS. With these optimal cluster numbers, the patterns within each curve are clearly separated during clustering, as shown in Figure 7. The clusters of curve 3 and curve 9 show distinct boundaries in three-dimensional PCA space; curve 2, under the optimal number of clusters, does not display clear separations in three-dimensional space, but according to the WCSS calculation, it also achieves good clustering performance. Nevertheless, in order to help athletes better understand the differences between sliding patterns, the entry point, exit point, and the highest point of each curve are selected to intuitively describe each pattern.

The average finish time gaps between different patterns are all no more than 0.4 s in every fast group. Considering that the speed of the skeleton is extremely high (can exceed 140 km per hour) and the gaps of finish time can be less than 0.1 s among top athletes, the differences in finish time among these patterns are significant.

According to the results of consistency calculations, only the fastest trajectory groups on the three curves were selected for analysis. It is shown that the fastest trajectory groups have the highest trajectory concentration. More skilled athletes not only achieve better scores, but also tend to follow similar routes across different training sessions, demonstrating greater control over their skeletons. Therefore, trajectories with shorter finish times are more suitable for extracting meaningful patterns. Training improvements are also observed to diminish as athletes reach higher performance levels, with a notable bottleneck occurring once their scores exceed the average. The gaps between the stability of their sliding become shorter, and more strategies will be required, including route selection.

The analysis in this study focused on the patterns of different skeleton trajectories, without considering the actual sliding speed and acceleration. Typically, during the training, the sliding speed and acceleration are not recorded throughout the entire run. Secondly, this study primarily conducts measurements in pixel-space coordinates, where the magnitude of trajectory sampling errors varies depending on the athlete’s speed. The potential impact of such errors lies mainly in the precise reconstruction of trajectory shapes, making it difficult to quantify the exact error values. In comparison, real-world spatial coordinates offer higher accuracy, which represents a limitation of this research. In summary, while sampling errors do exist, their impact on the validity of trajectory stability evaluation and pattern clustering analysis in this study is not substantial, particularly with higher sampling frequencies.

Current research on skeleton primarily focuses on physical fitness, techniques during the push-start phase, and factors such as aerodynamics and friction during the sliding phase. However, a systematic analysis of full-course sliding trajectories remains scarce. In contrast, this study establishes a comprehensive framework based on trajectory consistency evaluation and clustering analysis. It enables a systematic analysis, covering trajectory extraction, shape feature definition, stability assessment, and the identification of optimal sliding patterns. This approach addresses the shortcomings of current methods that rely on subjective experience or localized physical parameters. Additionally, unlike traditional approaches that focus on singular time or speed metrics, this study introduces multiple trajectory shape features. These include the curvature compression ratio and apex orthogonal offset. It also identifies optimal sliding patterns for each curve through clustering. This provides actionable strategic recommendations for athletes. Moreover, this methodology offers clear advantages by providing quantitative decision-making support for coaches. It lays the foundation for more in-depth analysis of sliding performance in future studies.

5. Conclusions

This study proposes a computer vision-based method for analyzing skeleton sledding trajectories. By extracting and defining trajectory features of moving objects from training videos, the approach assesses sliding stability and performs clustering analysis on trajectory patterns to identify optimal sliding strategies for each curve. The experimental results demonstrate that: (1) As athletes reach higher performance levels, the improvement effect of training diminishes, and the disparity in sliding stability (time difference) decreases. (2) For each specific curve, there consistently exists an optimal strategy, whose corresponding pattern demonstrates both shorter completion times and distinct sliding characteristics compared to alternative modes. The core theoretical contribution of this study lies in the innovative construction of an intelligent analytical framework for skeleton sledding trajectories, based on computer vision. This framework breaks away from traditional qualitative analysis that relies on subjective experience, providing a quantifiable analytical tool and theoretical support for trajectory research in skeleton or other sliding sports. On the practical side, the proposed method allows for the detailed processing of training videos, enabling the extraction, evaluation, and pattern recognition of sliding trajectories. This provides coaches and athletes with objective, timely feedback and clear guidance for optimizing curve strategies. This approach not only significantly enhances the efficiency and scientific rigor of training analysis, but also lays the core technical foundation for the future development of intelligent training systems, offering considerable engineering application value and potential for widespread adoption. The proposed framework in this study was tested on several curves of a single track, and it can be applied to other curves and sliding tracks as long as a similar camera setting is applied. The method can also be extended to serve other sports scenarios by modifying or including new features based on the intrinsic characteristics of the target sports.

The limitations of this study are two-folds: First, it is challenging to effectively translate the subjective experience of coaches and athletes into consistent and reliable quantitative indicator. As a result, further interviews with coaches and experienced athletes are needed to cross-validate observations in the current study. Second, constrained by hardware conditions and calibration techniques, the current analysis was conducted in the pixel coordinate system without mapping to 3D coordinates, which limits in-depth interpretations of sliding trajectories in a 3D space. Future research will focus on constructing an expert-annotated knowledge base of trajectory strategies and integrating multi-sensor technology to achieve 3D mapping from pixel coordinates to real physical space, thereby systematically addressing the current limitations in strategy quantification and physical-scale analysis.