True space tracking of axisymmetric object flight using diameter measurement

Abstract

Methods and apparatus for determining a trajectory of a axisymmetric object in 3-D physical space using a digital camera which records 2-D image data are described. In particular, based upon i) a characteristic length of the axisymmetric object, ii) a physical position of the camera determined from sensors associated with the camera (e.g., accelerometers) and iii) captured 2-D digital images from the camera including a time at which each image is generated relative to one another, a position, a velocity vector and an acceleration vector can be determined in three dimensional physical space for axisymmetric object objects as a function of time. In one embodiment, the method and apparatus can be applied to determine the trajectories of objects in games which utilize axisymmetric object objects, such as basketball, baseball, bowling, golf, soccer, rugby or football.

1 . A non-transitory computer readable medium for storing a computer program used by a computing device, the computer program executed by the computing device to generate a three dimensional (3-D) trajectory of an axisymmetric object used in a play of a game from two dimensional (2-D) digital image data, the computer readable medium comprising:
 computer code for receiving a sequence of 2-D digital images from a single digital camera associated with the computing device wherein the 2-D digital images include the axisymmetric object and a secondary object used in the play of the game and wherein the game is being played and the 2-D digital images are captured using ambient lighting;   computer code for receiving orientation data which is used to determine or to specify an orientation of a lens of the single digital camera in 3-D physical space, said lens configured to receive light used to generate the 2-D digital images;   computer code for transforming pixel data in each of the 2-D digital images based upon the determined orientation of the lens;   computer code for identifying 2-D representations of the axisymmetric object and 2-D representations of the secondary object captured in the transformed pixel data associated with the 2-D digital images wherein a distance between the axisymmetric object and the secondary object is decreasing as a function in time in the 2-D digital images as the axisymmetric object approaches the secondary object;   computer code for determining first pixel coordinates of the 2-D representations of the axisymmetric object and second pixel coordinates of the 2-D representations of the secondary object in the 2-D digital images;   computer code for identifying first characteristic lengths associated with the 2-D representations of the axisymmetric object in the pixels of the 2-D digital images;   computer code for identifying second characteristic lengths associated with the 2-D representations of the secondary object in the pixels of the 2-D digital images wherein the second characteristic lengths are related to a known dimension of the secondary object;   computer code for determining first distances to the identified 2-D representations of the axisymmetric object from the lens based upon the first characteristic lengths, said first distances specified in units associated with 3-D physical space;   computer code for determining second distances to the identified 2-D representations of the secondary object from the lens based upon the second characteristic lengths and the known dimension of the secondary object, said second distances specified in units associated with 3-D physical space; and   computer code for determining 3-D coordinates of the axisymmetric object as a function of time in the 3-D physical space including 3-D coordinates of the axisymmetric object relative to the secondary object based upon the determined first distances, the determined second distances, the pixel coordinates of the 2 D representations of the axisymmetric object and 2-D representations the secondary object captured in the transformed pixel data associated with the 2-D digital images.   
     
     
         2 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a spherically shaped object used in the game. 
     
     
         3 . The computer readable medium of  claim 2 , wherein the first characteristic lengths are a diameter of a circle. 
     
     
         4 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a football having an elliptically shaped cross section. 
     
     
         5 . The computer readable medium of  claim 4 , wherein the first characteristic lengths are a minor axis of an ellipse. 
     
     
         6 . (canceled) 
     
     
         7 . The computer readable medium of  claim 1 , further comprising computer code for receiving input from a touch screen display wherein the input from the touch screen display is used in the identifying of the 2-D representations of the secondary object captured in the transformed pixel data. 
     
     
         8 . (canceled) 
     
     
         9 . The computer readable medium of  claim 1 , further comprising computer code, based upon at least the second distances, for determining the 3-D coordinates of the secondary object in the 3-D physical space. 
     
     
         10 . The computer readable medium of  claim 1 , further comprising computer code for receiving a pixel resolution of the 2-D digital images. 
     
     
         11 . The computer readable medium of  claim 10 , wherein the physical distance is determined based upon the received pixel resolution. 
     
     
         12 . The computer readable medium of  claim 1 , further comprising computer code for receiving or retrieving a known dimension of the axisymmetric object measured in the units associated with the 3-D physical space. 
     
     
         13 . The computer readable medium of  claim 1 , wherein the orientation data is received from one or more sensors located on the computing device. 
     
     
         14 . The computer readable medium of  claim 13  wherein the one or more sensors includes an accelerometer. 
     
     
         15 . The computer readable medium of  claim 1 , wherein the 2-D representations of the axisymmetric object in the 2-D digital images is captured while the axisymmetric object is in one or more of free flight, rolling along a surface, in contact with a surface, being held in person's hands and combinations thereof. 
     
     
         16 . The computer readable medium of  claim 1 , wherein the function of the time of the 3-D coordinates is based upon a time associated with each of the 2-D digital images. 
     
     
         17 . The computer readable medium of  claim 1 , further comprising computer code for receiving a recording speed of the camera wherein the recording speed is used to determine the function of the time of the 3-D coordinates. 
     
     
         18 . The computer readable medium of  claim 1 , further comprising computer code for determining a velocity vector and magnitude of the velocity vector as the function of time in the 3-D physical space. 
     
     
         19 . The computer readable medium of  claim 1 , further comprising computer code for generating and outputting a first 2-D digital image including a trajectory curve which connects a plurality of positions of the axisymmetric object wherein the trajectory curve is rendered from the determined 3-D coordinates of the axisymmetric object as the function of the time in the 3-D physical space. 
     
     
         20 . The computer readable medium of  claim 19 , wherein the first 2-D digital image further includes a graphical representation of one or more of a playing field, playing field markings or objects associated with the play of the game in which the axisymmetric object is used, said graphical representation rendered from 3-D models of the playing field, the playing field marking or the objects in the 3-D physical space. 
     
     
         21 . The computer readable medium of  claim 20 , further comprising computer code for identifying a portion of the playing field, a portion of the playing field markings or a portion of the objects in the sequence of the 2-D digital images wherein the graphical representation includes an additional portion of the playing field, an additional playing field markings or an additional portion of the objects not captured in the sequence of the 2-D digital images. 
     
     
         22 . The computer readable medium of  claim 1 , further comprising computer code for a simulation of a trajectory of the axisymmetric object in 3-D in physical space wherein the simulation is used to predict second 3-D coordinates of the axisymmetric object as the function of time in the 3-D physical space using the 3-D coordinates as the function of the time determined from the 2-D digital images as initial conditions for the simulation. 
     
     
         23 . The computer readable medium of  claim 22 , wherein the predicted second 3-D coordinates of the axisymmetric object are used to extrapolate a trajectory of the axisymmetric object in the 3-D physical space determined from the sequence of the 2-D digital images. 
     
     
         24 . The computer readable medium of  claim 1 , further comprising computer code for generating trajectory information associated with a trajectory of the axisymmetric object in the 3-D physical space determined from the sequence of the 2-D digital images. 
     
     
         25 . The computer readable medium of  claim 24 , wherein the trajectory information is used as input for a video game. 
     
     
         26 . The computer readable medium of  claim 24 , where the trajectory information is used to develop training recommendations for improving performance of a participant in the game played using the axisymmetric object. 
     
     
         27 . (canceled) 
     
     
         28 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a football and the secondary object is a goal post. 
     
     
         29 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a soccer ball and the secondary object is a soccer goal. 
     
     
         30 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a basketball and the secondary object is a basketball hoop. 
     
     
         31 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a bowling pin. 
     
     
         32 . The computer readable medium of  claim 1 , wherein the axisymmetric object is a tennis ball and the secondary object is a tennis net.