棒球在台灣為相當盛行的主流運動，也培育出許多棒球好手，像是王建民、陳偉殷等，都已在美國大聯盟上發光發熱，並將台灣帶上國際舞台。而一場棒球比賽，投手往往是扮演比賽勝負的關鍵角色，一位好投手需要精準控制自己的球路，但是投手投出至捕手的好球帶位置是由主審來決定的，因此判別球為好壞球容易影響到一場比賽的勝負。目前大聯盟的K-Zone系統被用來顯示投手好壞球的能力提供觀眾判定，這類系統越來越受到棒球愛好者的矚目。我們嘗試實作類似的系統，以低成本理念下，實作出一套能重建棒球三維軌跡且顯示是否為好球或是壞球。

本系統使用低成本高速攝影機，以自製棋盤格作為校正板和尚未同步的攝影機使用自製同步訊號源來減少誤差。而為了取得棒球軌跡，於是架設兩台攝影機以拍攝影片方式錄影，拍攝完後的影片會先儲存至Wi-Fi SD卡，再經由Wi-Fi網路將影片傳送至電腦作影像處理。影像處理主要處理攝影機校正、圈選好球帶以及偵測棒球。本系統主要是從兩台攝影機偵測棒球並且將偵測到的棒球使用投影轉換矩陣計算出世界三維座標。首先作攝影機校正得到其內部參數和外部參數，有了以上兩者參數後即可算出投影矩陣出來；其次圈選好球帶的四個角點並計算出其三維世界座標；再來取得棒球軌跡並使用gnuplot軟體描繪3D圖形。

本系統成功建立三維軌跡並觀察棒球是否通過好球帶。此外，在系統效能上我們使用OpenMP平行化處理函式庫加快程式執行速度，主要處理棒球候選區和棒球軌跡，比尚未使用平行化處理快上將近兩倍。在假設虛擬好球帶的實驗中，其理論邊長與實際邊長誤差分別為6.13%和7.91%，其值已達到相當精確的程度。

Baseball is one of the most popular sports in Taiwan. In recent years, there are already many baseball players establishing their position as major league starters, such as Chien-Ming Wang, Wei-Yin Chen etc. They have been showing their talent on the U.S. Major League Baseball and helped bringing Taiwan to the international stage. A pitcher plays the major role in a baseball game. A good pitcher has to control his pitch precisely. But the strike zone is up to the chief umpire. In crucial time, whether a pitched ball is a strike or a ball could decide the result in a game. In MLB, the K-Zone system is used to show whether the pitch ball is a strike or a ball to provide viewers to check the umpire call. This system is attracting people who love baseball. We try to implement such a system with low-cost. With the concept of low-cost, our system can reconstruct baseball three-dimensional trajectory and show whether a pitched ball is a strike or a ball.

This system uses low-cost high-speed cameras. We also use easily produced chessboard as calibration board and use external signal lighting device for synchronization. To get the baseball trajectory, we set up two cameras to take the videos. After the videos are saved to Wi-Fi SD card, the video sequences are transferred to computer by Wi-Fi internet for the image processing. The image processing program does camera’s calibration, selects strike zone, and detects baseball. Our system mainly detects baseballs from both cameras and uses projection transform matrix to calculate the world 3D coordinates of the detected baseballs. First, we calibrate two cameras to get their intrinsic parameters and extrinsic parameters. Once we have intrinsic parameters and extrinsic parameters, we can calculate projection matrix. Second, we select four corners of strike zone and calculate their three-dimension world coordinates. Third, we get the baseball trajectory, drawing 3D trajectory with gnuplot software.

Our system can build 3D trajectory successfully and observe whether the baseball pass through strike zone. Furthermore, we improve our system performance on execution speed with OpenMP which is a parallel execution library, making the processing of baseball candidates and baseball trajectory fast. OpenMP implementation doubles computation speed than we without using OpenMP. The differences between the measured values of strike zone border and actual values of border are 6.13% and 7.91% respectively, which is quite precise.

[1] A. Gueziec, “Tracking pitches for broadcast television,” Journal of Computer, Vol.35, pp. 38-43 (2002)
[2] 詹凱鈞，「低成本棒球偵測三維軌跡重建系統」，碩士論文，國立台灣科技大學，台北 (2011)
[3] L. Susman, “Calibration of a six-port reflectometer using projective geometry concepts,” Journal of Electronics Letters, Vol.20, pp. 9 (1984)
[4] 呂傑棋，「3D視覺校正軟體之研製」，碩士論文，中華大學，新竹 (1997)
[5] 馬維章，「以多部攝影機實現棒球偵測與追蹤系統」，碩士論文，國立台灣科技大學，台北 (2008)
[6] R. D. Sampson, A. E. Peterson and E. P. Lozowski, “Photogrammetric calibration of a consumer grade flat-bed scanner,” IEEE Canadian Conference on Electrical and Computer Engineering, Vol.2, pp. 622-626 (1999)
[7] M. Kinsner, D. Capson and A. Spencer, “Scale-Space Feature Detectio for Close Range Camera Calibration,” IEEE Canadian Conference on Electrical and Computer Engineering, pp. 1464-1467 (2007)
[8] R. I. Hartley, “An algorithm for self calibration from several views,” IEEE Conference on Computer Vision and Pattern Recognition, pp. 908-912 (1994)
[9] S. Florczyk, Robot Vision: Video-based Indoor Exploration with Autonomous and Mobile Robots, Wiley-VCH, pp. 113-122 (2005)
[10] W. Guanghui, Q. M. Wu and W. Zhang, “Camera Self-Calibration and Three Dimensional Reconstruction under Quasi-Perspective Projection,” IEEE Canadian Conference on Computer and Robot Vision, pp. 129-136 (2008)
[11] Q. T. Luong and O. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Journal of Computer Vision, Vol.4, pp. 880-883 (1997)
[12] 繆紹綱，數位影像處理，培生出版社，台北，第392-395 頁、726-730 頁 (2009)
[13] 鐘國亮，影像處理與電腦視覺，東華書局，台北 (2004)
[14] W. Niblack, An Introduction to Digital Image Processing, Prentice-Hall, New Jersey (1986)
[15] M. Sonka, V. Hlavac and R. Boyle, Image Processing, Analysis, and Machine Vision, PWS Publishing, pp. 68-102 (1999)
[16] J. R. Parker, Algorithms for Image Processing and Computer Vision, NY, John Wiley & Sons (1997)
[17] Q. Z. Wu, H. Y. Cheng, B. S. Jeng, Motion detection via change-point detection (2004)
[18] R. Yan, X. Song and S. Yan, “Moving object detection based on an improved gaussian mixture background model,” Journal of Computing, Communication, Control, and Management, Vol.1, pp. 12-15 (2009)
[19] S. Ju, X. Chen and G. Xu, “An Improved Mixture Gaussian Models to Detect Moving Object Under Real-Time Complex Background,” International Conference on Cyberworlds, pp. 730-734 (2008)
[20] P. Shrestha, M. Barbieri, H. Weda and D. Sekulovski, “Synchronization of Multiple Camera Videos Using Audio-Visual Features,” IEEE Transactions on Multimedia, Vol.12, pp. 79-92 (2010)
[21] D. N. Brito, “Synchronizing Video Cameras with Non-Overlapping Fields of View,” Journal of Computer Graphics and Image Processing, pp. 37-44 (2008)
[22] G. Bradski and A. Kaehler, Learning OpenCV: Computer Vision with the OpenCV Library, O, Reilly, pp. 370-374 (2008)
[23] Zhengyou Zhang. A Flexible New Technique for Camera Calibration (1998)
[24] 陳勝勇 劉盛，基於OpenCV的電腦視覺技術實現，科學出版社，北京 (2008)
[25] 羅彥雄，「視訊棒球偵測與軌跡重建」，碩士論文，國立台灣科技大學，台北 (2006)