Estimation of rotational velocity of baseball using high-speed camera movies

Recently, in the field of sports science, movies are being used to analyze a player’s performance and improve his/her skills. For example, the rotational velocity and rotational axis vector of the baseball can be determined on the basis of movies recorded by using high-speed cameras; this information is useful in determining the ball’s trajectory because this trajectory is dependent on the rotational velocity. In a previous study on the estimation of the rotational velocity of a baseball, some lines and markers were drawn on the surface of a baseball, and the rotational matrix was determined by pattern matching. However, such markers cannot be drawn on a ball being used in a real baseball game. In our proposed method, we consider the seam patterns on the surface of the baseball as markers for pattern matching; a database including CG images of the ball recorded at different angles was used for pattern matching. To improve the processing time required for pattern matching, we determine the ball’s posture in each frame by employing the parametric eigenspace method. Finally, we use the time continuity to perform linear approximation of the rotational pattern of the ball. Fig. 1 shows the flowchart of our method. The ball area in the input movie is tracked by linear interpolation. Then the ball area is compared with the images in the database to obtain the rotational parameters. However, the shadings of the input image are different from those of the database CG images. Therefore, we then create the shading image by averaging the ball area in the input images and add the shading image to the database. This method has a serious drawback; the ball images recorded from different positions appear similar because the ball is symmetric, and a result, the estimation of the rotational parameters on the basis of the image information alone is difficult. Therefore, in this method, we consider the ball’s rotation to be linear and resolve the problems of noise and symmetry. We demonstrate the effectiveness of our method by performing two types of experiments. In the first experiment, we use the proposed method to estimate the rotational velocity of a baseball by using real movies shot in a baseball stadium. The results are shown in Fig. 2. The similar image corresponding to the input ball image which could be any frame of the movie, can be selected from the database. In the second experiment, we use a movie consisting of CG images of the baseball as the input movie. As shown in Table 1, our method can be used to estimate the ball’s rotational velocity accurately. In this paper, we present a new method for estimating the rotational velocity of a baseball by using only the ball’s seam pattern. No additional markers have to be drawn on the ball’s surface, and the processing speed of pattern matching is enhanced threefold by adopting the eigenspace method. Therefore, our method is wellsuited for practical applications.