Three dimensional object tracking using combination of radar speed data and two dimensional image data

A method, comprising:

• obtaining two dimensional image data of a golf ball in flight, the two dimensional image data originating from a camera;
• modeling a two dimensional trace of the golf ball in flight using the two dimensional image data;
• obtaining radar speed data of the golf ball in flight, the radar speed data originating from a radar device associated with the camera;
• modeling a speed of the golf ball in flight using the radar speed data, wherein modeling the speed of the golf ball comprises fitting a polynomial function to a first portion of the radar speed data and fitting an exponential function to a second portion of the radar speed data;
• combining the modelled speed of the golf ball in flight with the modelled two dimensional trace of the golf ball in flight to form a three dimensional trace of the golf ball in flight;
• and
• outputting for display the three dimensional trace of the golf ball in flight in three dimensional space;
• wherein modeling the speed of the golf ball in flight using the radar speed data comprises:
• fitting the exponential function to initial values of the radar speed data to form an exponential model of the radar speed data;
• using the exponential model of the radar speed data to identify the first portion of the radar speed data, which does not match the exponential model;
• performing the fitting of the polynomial function to the first portion of the radar speed data and one or more values of the second portion of the radar speed data to form a polynomial model that fits the first portion of the radar speed data and meets the exponential model of the radar speed data at a transition point between the first portion and the second portion of the radar speed data;
• and
• updating the exponential model by performing the fitting of the exponential function to the second portion of the radar speed data as additional values in the radar speed data are received from the radar device;
• wherein performing the fitting of the polynomial function to the first portion of the radar speed data and the one or more values of the second portion of the radar speed data comprises iteratively including more of the one or more values of the second portion of the radar speed data until a threshold level of continuity between the polynomial model and the exponential model is reached at the transition point.

A system comprising:

• a camera;
• a radar device;
• and
• a computer comprising a hardware processor and a memory coupled with the hardware processor, wherein the hardware processor and the memory are configured to obtain two dimensional image data of a golf ball in flight, the two dimensional image data originating from the camera, model a two dimensional trace of the golf ball in flight using the two dimensional image data, obtain radar speed data of the golf ball in flight, the radar speed data originating from the radar device, model a speed of the golf ball in flight using the radar speed data by fitting a polynomial function to a first portion of the radar speed data and fitting an exponential function to a second portion of the radar speed data, combine the modelled speed of the golf ball in flight with the modelled two dimensional trace of the golf ball in flight to form a three dimensional trace of the golf ball in flight, and output for display the three dimensional trace of the golf ball in flight in three dimensional space, wherein the polynomial function is different from the exponential function, and the first portion is different from the second portion.

A non-transitory computer-readable medium encoding instructions that cause a data processing apparatus associated with a camera and a radar device to perform operations comprising:

• obtaining two dimensional image data of a golf ball in flight, the two dimensional image data originating from the camera;
• modeling a two dimensional trace of the golf ball in flight using the two dimensional image data;
• obtaining radar speed data of the golf ball in flight, the radar speed data originating from the radar device associated with the camera;
• modeling a speed of the golf ball in flight using the radar speed data, wherein modeling the speed of the golf ball comprises fitting a polynomial function to a first portion of the radar speed data and fitting an exponential function to a second portion of the radar speed data, wherein the polynomial function is different from the exponential function, and the first portion is different from the second portion;
• combining the modelled speed of the golf ball in flight with the modelled two dimensional trace of the golf ball in flight to form a three dimensional trace of the golf ball in flight;
• and
• outputting for display the three dimensional trace of the golf ball in flight in three dimensional space.