Tracking an object with multiple asynchronous cameras

A system for determining a path of a moving object used at an event, comprising:

• at least first and second cameras capturing images of the moving object at the event at different time points during a time interval to provide captured images, as the moving object travels in a path during the time interval, the at least first and second of cameras capture the images asynchronously, the first camera has a pixel space which is related to a world coordinate system by an associated transformation matrix and the second camera has a pixel space which is related to the world coordinate system by an associated transformation matrix;
• and
• at least one processor which receives the captured images from the at least first and second of cameras, the at least one processor:
• a) provides a matrix S, for each image captured by the first camera, which indicates a position of the moving object in the pixel space of the first camera, and for each image captured by the second camera, which indicates a position of the moving object in the pixel space of the second camera, and b) solves for coefficients of equations of motion of the moving object to provide solved coefficients, based on the positions, the equations of motion with the solved coefficients describe the path of the moving object during the time interval, the coefficients of the equations of motion include velocity and acceleration coefficients and are in a matrix A, and the at least one processor solves for the coefficients of equations of motion by providing a matrix U for each image which relates the matrix A to the matrix S of the image by an equation U×AT=ST, where AT is a transpose of the matrix A and ST is a transpose of the matrix S of the image, and solves for the matrix A from the equation U×AT=ST.

At least one processor readable storage device having processor readable code embodied thereon for programming at least one processor to perform a method, the method comprising:

• receiving images of a moving object from at least first and second cameras at different time points during a time interval, as the moving object travels in a path during the time interval, the at least first and second cameras capture the images asynchronously, the first camera has a pixel space which is related to a world coordinate system by an associated transformation matrix and the second camera has a pixel space which is related to the world coordinate system by an associated transformation matrix;
• providing a matrix S, for each image captured by the first camera, which indicates a position of the moving object in the pixel space of the first camera, and for each image captured by the second camera, which indicates a position of the moving object in the pixel space of the second camera;
• and
• solving for coefficients of equations of motion of the moving object to provide solved coefficients, based on the positions, the equations of motion with the solved coefficients describe the path of the moving object during the time interval, the coefficients of the equations of motion include velocity and acceleration coefficients and are in a matrix A, and the solving includes providing a matrix U for each image which relates the matrix A to the matrix S of the image by an equation U×AT=ST, where AT is a transpose of the matrix A and ST is a transpose of the matrix S of the image, and solving for the matrix A from the equation U×AT=ST.