High-precision measurements of curling stone dynamics: Curl distance by digital image analysis

Abstract

Curl distance is one of the most important factors for a curler to control carefully and seriously in a game of curling. Curl distance was measured with high-precision digital image analysis in order to obtain its precise relationship with the number of rotations. Motion of the curling stone was recorded in sequential images with two cameras located on the ceiling. Calibrations to remove lens aberration and to connect the imaging areas of the two cameras were done prior to the experiment. The initial direction of the stone in each delivery was calculated as a reference line using the positions of the stone derived from the sequential images. Then, the curl distance was measured as a distance from the stop position of the stone perpendicular to the reference line, which was corrected as to convert the translation of the stone equivalent to the distance between the hog line and the tee line, 93 ft (28.3 m). It was found that the curl distance decreases as the number of rotations increases in the range of measurements made in the experiment. The decrease rate was 0.047–0.064 m per rotation and varied slightly with ice sheet conditions.

Assignments and progress of curling stone dynamics

“…It can be concluded in Figure 3 that the curl distance shows a general tendency to increase with the total number of rotations, amounting to 2 m at 70 turns. Figure 4 is a result of the high-precision measurement of curl distance conducted recently by Hattori et al 35,36 They recorded the motion of a stone using two high-definition video cameras set on the ceiling of a curling stadium at 0.1-s intervals and then the digital images were analyzed to give accurate translational and angular velocities of the center of mass together with the sliding and curl distances. Errors due to various sources were made as small as possible, and the final accuracy of position was 66 mm.…”

“…Numerical data from Komagome et al 38 The curl ratio is the ratio of the curl distance (D) and the slide distance (L = 0.5 m in this case). 35,36 Different signs correspond to different curlers, rotation directions, and release positions on the same ice sheet.…”

“…Curl distance obtained by a high-precision measurement. Numerical data read from Hattori et al 35,36 Different signs correspond to different curlers, rotation directions, and release positions on the same ice sheet.…”

Research on Evaluation Indicator of Ice Rink and Curling Stone Motion for the 2022 Beijing Winter Olympic Games Based on Video Recognition Method

“…A pivot-slide-based model has recently been used to study how the stone follows a curved trajectory [12,13]. In short, despite several proposed models in the surveyed literature, the mechanism remains under scientific debate, primarily due to the complicated moving process and a lack of sufficient observational data [5,14].…”

Curling stone tracking based on an enhanced mean-shift algorithm using optimal feature vector

“…Hattori et al proposed a method for predicting curl distance by recognizing the marker attached to the stone from a high-resolution image calibrated in the curling house. 6 Takahashi et al used the Kernelized Correlation Filter (KCF) tracker to detect the location of the stone as a way to visualize its trajectory during a curling game broadcast. 7 Therefore, this paper proposes a method to automatically track the position of stones in curling sport videos using computer vision technology.…”