Analysis of football player’s motion in view of fractional calculus

Abstract

Abstract:Accurately retrieving the position of football players over time may lay the foundations for a whole series of possible new performance metrics for coaches and assistants. Despite the recent developments of automatic tracking systems, the misclassification problem (i.e., misleading a given player by another) still exists and requires human operators as final evaluators. This paper proposes an adaptive fractional calculus (FC) approach to improve the accuracy of tracking methods by estimating the position of players based on their trajectory so far. One half-time of an official football match was used to evaluate the accuracy of the proposed approach under different sampling periods of 250, 500 and 1000 ms. Moreover, the performance of the FC approach was compared with position-based and velocity-based methods. The experimental evaluation shows that the FC method presents a high classification accuracy for small sampling periods. Such results suggest that fractional dynamics may fit the trajectory of football players, thus being useful to increase the autonomy of tracking systems. PACS

Dynamical Stability and Predictability of Football Players: The Study of One Match

“…These indices can provide deeper information about players' behaviour while improving the sports training quality. For the study of the player's variability, in terms of dynamic trajectory, the concepts associated with the Fractional Calculus (FC) mathematical formalism are adopted [17]. One of the first studies applying FC to trajectory analysis was introduced by Couceiro, Clemente and Martins [17] by estimating the next position of a player based on his previous trajectory.…”

“…Other techniques can be applied in the sports context. For instance, by adopting the insights from Couceiro, Clemente and Martins [17], one can define a player's variability, at each instant, using the FC memory properties as a predictability level. Therefore, the FC approach for the human variability understanding will be discussed in next section.…”

“…Despite FC's potentialities only a limited number of applications based on FC have been reported so far within the sport sciences literature [17,22]. One of them was the development of a correction metric for golf putting to prevent the inaccurate performance of golfers when facing the golf lipout phenomenon [21].…”

“…The authors extended a performance metric using the Grünwald-Letnikov approximate discrete equation to integrate a memory of the ball's trajectory. A more recent study by the same authors benefited from FC to overcome automatic tracking problems of football players [17]. As a prediction method based on the memory of past events, FC features offer a new perspective on understanding players' motion.…”

Intelligent systems for analyzing soccer games: The weighted centroid

“…The process of identifying the virtual positions of the players and the ball in each frame was performed manually. For a more detailed description of the process, see Couceiro, Clemente and Martins (2013).…”