The Sportvision PITCHf/x system is composed of three basic parts: the
pitchtracking cameras, the trajectory reconstruction software, and the image
rendering software. In this brief note, I will discuss only the first two of
these.
Sportvision公司的PITCHf/x系統是由三個基本部分所構成: 投球追蹤攝影機，軌跡重建
軟體，與影像建構軟體。在這篇簡短的文章中，我將只討論前面兩個部分。
To track a pitch in three dimensions requires two cameras with their axes
ideally oriented perpendicular to each other. The PITCHf/x system utilizes
three cameras, but only two are used for the actual tracking. A nontracking
third camera is placed in centerfield and is only used for setting the height
of the strike zone. In a typical setup (e.g., Fenway Park), the tracking
cameras are placed high above home plate looking down ("high home") and high
above the first-base line looking down ("high first"). In other venues, such
as Busch Stadium, there is a "high third" instead of a "high home" camera.
Both of the tracking cameras are permanently afixed to the stadium structure
in an location where they are not easily bumped. The zoom on the lens is
adjusted so that the field of view runs from approximately a few feet in
front of the pitching rubber to the point of home plate. The cameras operate
at 60 frames/s, meaning that a typical pitch of transit time 0.45 sec will
provide up to 27 images for each of the two tracking cameras.
要以三度空間的形式追蹤投手投出的球需要兩部攝影機，且攝影機的中心線方向必須形成
直角。PITCHf/x系統則使用了三部攝影機，但是只有兩部是用來追蹤軌跡。第三台不用來
追蹤軌跡的攝影機架設在中外野，唯一的目的是設定好球帶的高度。以一般的設置(例如
: 芬威球場)而言，追蹤攝影機架設在本壘板上方朝下方拍攝("home high")與一壘邊線上
方朝下拍攝("hign first")。在其他的地點，如布希球場，是以"high third"取代"high
home"攝影機。兩部追蹤攝影機都被固定在球場結構中不易遭受碰撞的位置。鏡頭的變焦
經過調整後使得視角位在投手丘前面幾呎到本壘板。攝影機以每秒60 個畫面拍攝，這代
表兩台追蹤攝影機在一般球的飛行時間0.45秒內各可以提供27張影像。
To do the trajectory reconstruction, very clever proprietary software is used
to do pattern recognition. For each frame, each camera provides a
two-dimensional image of the baseball in pixels. To convert pixels into x,y,z
coordinates, the cameras need to be calibrated, which is accomplished
initally by placing markers at precisely known locations in the field of view
of the cameras. Using this information, a prescription (more precisely, a
matrix transformaton) is established for transforming the 2-dimensional pixel
information from the two cameras into x,y,z coordinates on a frame-by-frame
basis. The resulting trajectory x(t),y(t),z(t) (t is the time) is then
"smoothed" by fitting it to a function corresponding to constant acceleration
(click here for more details). Other quantities, such as the pitch speed, the
location of the pitch as it crosses the plate, the "break" of the pitch,
etc., are derived from the smoothed trajectory.
要達成軌跡重建必須使用非常聰明的專屬軟體來做圖形識別。每個畫面，每部攝影機提供
了以像素為單位的二維棒球影像。要將像素轉換為x,y,z座標，攝影機必須經過教點，起
初先在攝影機視野內的精確的已知位置做記號，使用這些資料可以建立一套規則(更精確
的說法是矩陣轉換)，將從兩台攝影機得到以逐格動畫為依據的二維像素資訊，轉換成
x,y,z座標。產生的軌跡x(t)，y(t)，z(t)(t代表時間)透過一個對應於固定加速度的函數
(點此了解更多細節)做"平滑處理"。其他的數據資料，如球速，球經過本壘版的位置，球
的變化量...等等，也都能由經過平滑處理的軌跡取得。
For a more detailed and technical description of an early version of the
K-Zone tracking technology, see the article "Tracking Pitches for Broadcast
Television", by Dr. Andre Guiziec. This system only tracked the pitch over a
small range close to home plate. The current PITCHf/x system tracks over most
of the distance between pitcher and home plate. For a report on a different
technique for tracking a pitched baseball, see Tracking High-Speed Motion
with Multi-Exposure Images. Although not directly related to the MLB Gameday
system and although the techinque is not applicable outside of a laboratory
setting, it is a very nice piece of experimental work that demonstrates how
smart people can do excellent studies with inexpensive equpiment.
想要得到更多較早版本K-Zone追蹤技術的細節與技術說明，請參閱由Dr Andre Guiziec所
撰寫的"Tracking Pitches for Broadcast Television"這篇文章。這個系統只追蹤球接
近本壘板時的小範圍。目前的PITCHf/x系統則追蹤從投手到本壘板大部分的距離。另一種
追蹤投出的球的技術報導請參閱Tracking High-Speed Motion with Multi-Exposure
Images。雖然這個技術與大聯盟的Gameday系統沒有直接的關係，並且尚未使用在實驗室
以外的環境，但是這是一個非常棒的專題研究，它顯示聰明的傢伙如何運用便宜的設備進
行傑出的研究。
http://webusers.npl.uiuc.edu/~a-nathan/pob/technology.htm