The Sportvision Pitch Tracking System (PITCHf/x)
How does it work?
Alan M. Nathan
August 3, 2007
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.
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.
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.
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.