Abstract: Methods and systems include, in at least one aspect: determining an optical model of an object in flight using two dimensional image data obtained from a camera, determining a radar model of the object in flight using radar data obtained from a radar device, combining the radar model with the optical model to produce three dimensional location information of the object in flight in three dimensional space, comparing the three dimensional location information of the object in flight with data representing an expected ball launch, and rejecting (or verifying) the object as an actual ball launch in response to the three dimensional location information of the object in flight differing (or not differing) from the data representing the expected ball launch by a threshold amount.

Abstract: Methods and systems include, in at least one aspect: determining an optical model of an object in flight using two dimensional image data obtained from a camera, determining a radar model of the object in flight using radar data obtained from a radar device, combining the radar model with the optical model to produce three dimensional location information of the object in flight in three dimensional space, comparing the three dimensional location information of the object in flight with data representing an expected ball launch, and rejecting (or verifying) the object as an actual ball launch in response to the three dimensional location information of the object in flight differing (or not differing) from the data representing the expected ball launch by a threshold amount.

Abstract: Methods and systems include, in at least one aspect: obtaining from a camera 2D image data of an object, obtaining from a radar device radar data of the object, combining the radar data and the 2D image data to produce 3D location information of the object, and modeling a 2D trace of the object using the 2D image data by finding an initial version of the 2D trace, receiving an initial portion of the 3D location information, extending the initial portion of the 3D location information in accordance with physical-world conditions to find at least one 3D location beyond the initial portion of the 3D location information, projecting the at least one 3D location into a 2D image plane of the camera to locate 2D region, and processing the 2D region in the 2D image data to extend the 2D trace of the object in flight.

Abstract: Methods and systems include, in at least one aspect: obtaining from a camera 2D image data of an object, obtaining from a radar device radar data of the object, combining the radar data and the 2D image data to produce 3D location information of the object, and modeling a 2D trace of the object using the 2D image data by finding an initial version of the 2D trace, receiving an initial portion of the 3D location information, extending the initial portion of the 3D location information in accordance with physical-world conditions to find at least one 3D location beyond the initial portion of the 3D location information, projecting the at least one 3D location into a 2D image plane of the camera to locate 2D region, and processing the 2D region in the 2D image data to extend the 2D trace of the object in flight.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects includes, in at least one aspect, a method including: obtaining 2D camera image data of a golf ball; modeling a 2D trace of the golf ball using the 2D image data; obtaining radar speed data of the golf ball; modeling a speed of the golf ball using the radar speed data, wherein modeling the speed of the golf ball includes 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 with the modelled 2D trace of the golf ball to form a 3D trace of the golf ball; and outputting for display the 3D trace of the golf ball in 3D space.