# Correcting Ski Resort Trajectories Extracted from Video
## 1 Introduction  
Accidents at ski resorts are a significant safety concern, particularly as skiing and snowboarding grow in popularity. Despite the implementation of safety regulations by organizations like the International Ski Federation, injuries remain a prevalent issue, highlighting the need for more effective safety measures [1]. The dynamics of these injuries are influenced by a range of factors, including skier behaviour, environmental conditions, and the effectiveness of safety equipment, making it critical to understand these elements in depth [2]. For example, the design and adjustment of ski boots play a crucial role in preventing lower extremity injuries. Research has shown that poorly fitted or adjusted ski boots can lead to severe fractures, underscoring the importance of proper equipment [3]. Additionally, demographic factors such as age and gender also influence injury patterns, with different groups showing varying susceptibility to certain types of injuries [4]. In particular, older adults and younger, less experienced skiers are at higher risk, which necessitates tailored safety strategies [5]. Studies have also highlighted that children and inexperienced skiers often display insufficient knowledge of safety rules, further increasing their risk [6]. Moreover, the risks associated with skiing can be exacerbated by improper training and the lack of physical preparation, leading to a higher incidence of injuries among certain populations [7]. To address these issues, this study develops advanced methodologies for analyzing and correcting the trajectories of skiers captured on video. Leveraging video footagefrom various ski resorts, we apply a combination of scaling factors, reference systems, and mathematical models to adjust the raw trajectory data [8]. Video analysis has become an indispensable tool in sports research, offering detailed insights into complex movements in dynamic environments like skiing [9]. This approach allows for precise calibration of skier trajectories, ensuring that the corrected data accurately reflects actual skier movements, which is essential for reliable safety assessments [10]. The use of such data-driven approaches is crucial, especially as more skiers and snowboarders hit the slopes, increasing the risk of accidents [11]. Here, we deal with a common situation were precise data that allow for a correction of perspective effects, lens distortion, change in landscape, etc., are not available. This can happen, e.g., when footage from webcams or private sources (YouTube, etc.) is used. Despite the limitations, such videos might provide valuable information and deserve to be considered in more detail. Here, we explore different approaches that allow at least for an approximate consideration of these aspects. Moreover, refined data enable a deeper analysis of the conditions under which collisions and other accidents are most likely to occur. By adjusting scaling coefficients and exploring different correction models, this study aims to develop a flexible framework adaptable to various scenarios at ski resorts [12]. This framework not only enhances our understanding of collision risks, but also informs the development of strategies to mitigate these risks, ultimately contributing to improved skier safety [13]. The integration of predictive models and biomechanical analyses can further assist in tailoring preventive measures to the specific needs of different skier populations [11]. Video analysis aids experts in identifying skier injuries and analyzing their biomechanical characteristics during the racing process. This approach not only enhances skier safety, but also helps bridge the gap in understanding the mechanisms of ACL injuries in alpine skiing [14]. Additionally, understanding the specific environmental factors that influence skier behavior can also contribute to more effective risk management strategies [10]. Video analysis in sports, including skiing, has gained significant attention.