單相機電腦視覺方法在棒球轉速、轉軸、球路軌跡和球種辨識計算之應用

Abstract

隨著運動科學產業的發展，數據化呈現運動表現變得越來越重要。這不僅能讓運動員更了解自己的訓練成果，也為教練或球探提供了更多評價的依據。本研究成功開發出一套系統，能計算出投手的多項投球數據。只需使用一台高速攝影機拍攝投球畫面，即可自動化獲得投手的球速、轉速、轉軸、旋轉效率、有效轉速、出手位置、球路軌跡、位移量、進壘點及球種等資訊。這套系統既方便又多功能，相較於多攝影機的鷹眼系統，成本更低。本論文參考國內外多項研究，轉速計算部分參考SpinTracker開源程式碼，並針對實際球場及投球狀況進行優化。相機校正部分使用棋盤格來計算內部參數，並且利用立方體來求得外部參數。單相機深度估計的部分使用成像半徑，經透鏡成像公式計算，並考慮畸變及失焦等影響。球路軌跡的部分導入了空氣力學公式來模擬，最後透過隨機森林演算法訓練的模型進行球種辨識。這項研究和設備已在職業級球場進行測試，並對不同層級的投手進行測試。無論是在日常訓練還是職業棒球例行賽中，這套系統都能運作並具有一定的準確度。我們將計算出的數據與市面上活躍的商業軟體Rapsodo進行比較，發現幾乎所有投球數據的相關係數都達到0.85以上，包括轉速和轉軸等數據。而旋轉效率、球速及垂直位移量的相關係數甚至可達到0.94以上，出手點的側向距離、出手點高度及水平位移量的相關係數更是高達0.99。

With the development of the sports science industry, the digital presentation of athletic performance has become increasingly important. This not only allows athletes to better understand their training results but also provides coaches and scouts with more information for evaluation. This study successfully developed a system capable of calculating multiple pitching metrics for pitchers. Using just one high-speed camera to capture pitching footage, it can automatically obtain information such as pitching velocity, spin rate, spin axis, spin efficiency, effective spin rate, release point, pitch trajectory, displacement, strike point, and pitch type. This system is convenient and multifunctional, offering a lower-cost alternative to the multi-camera Hawk-Eye system. The spin rate calculation is based on the open-source SpinTracker code, optimized for real-world field and pitching conditions. For camera calibration, a checkerboard was used to calculate internal parameters and a cube was used to determine external parameters. Single-camera depth estimation was performed using the imaging radius calculated through lens imaging formulas, considering distortion and defocus effects. Pitch trajectory was simulated using aerodynamic formulas, and pitch type recognition was achieved through a model trained with a random forest algorithm. This system and equipment have been tested in professional-grade baseball stadiums and with pitchers of different levels. Whether for regular training or professional baseball games, this system can operate with a certain degree of accuracy. We compared our calculated data with the commercially active software Rapsodo and found that almost all pitching data had correlation coefficients above 0.85, including metrics such as spin rate and spin axis. Additionally, spin efficiency, pitching velocity, and vertical displacement had correlation coefficients of 0.94 or higher, while the lateral release point distance, release point height, and horizontal displacement calculations reached as high as 0.99.