Integration of a vision-based tracking platform, visual instruction, and error analysis models for an efficient billiard training system

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A billiard ball tracking system is designed to combine with a visual guide interface to instruct users for a reliable strike. The integrated system runs on a PC platform. The system makes use of a vision system for cue ball, object ball and cue stick tracking. A least-squares error calibration process correlates the real-world and the virtual-world pool ball coordinates for a precise guidance line calculation. Users are able to adjust the cue stick on the pool table according to a visual guidance line instruction displayed on a PC monitor. The ideal visual guidance line extended from the cue ball is calculated based on a collision motion analysis. In addition to calculating the ideal visual guide, the factors influencing selection of the best shot among different object balls and pockets are explored. It is found that a tolerance angle around the ideal line for the object ball to roll into a pocket determines the difficulty of a strike. This angle depends in turn on the distance from the pocket to the object, the distance from the object to the cue ball, and the angle between these two vectors. Simulation results for tolerance angles as a function of these quantities are given. A selected object ball was tested extensively with respect to various geometrical parameters with and without using our integrated system. Players with different proficiency levels were selected for the experiment. The results indicate that all players benefit from our proposed visual guidance system in enhancing their skills, while low-skill players show the maximum enhancement in skill with the help of our system. All exhibit enhanced maximum and average hit-in rates. Experimental results on hit-in rates have shown a pattern consistent with that of the analysis. The hit-in rate is thus tightly connected with the analyzed tolerance angles for sinking object balls into a target pocket. These results prove the efficiency of our system, and the analysis results can be used to attain an efficient game-playing strategy.