Methods and systems for object trajectory reconstruction
Methods and systems for object trajectory reconstruction are disclosed. The methods and systems perform steps of first, receiving a first trajectory in a first image space and a user's location. Next, generating at least one trajectory line based on the user's location and the first trajectory, where the trajectory line can include at least one projection point representing a projection of the object's position. And finally, for the trajectory line, determining an associated second trajectory by determining, for the projection point in the trajectory line, a distance between the object and a plane. Some embodiments of the present invention enable a resource-limited mobile device, such as a smartphone, to efficiently perform this method. Also disclosed are benefits of the new methods, and alternative embodiments of implementation.
1 . A method for reconstructing a 3D object trajectory in-air, comprising:
receiving a 2D trajectory in a 2D image space, wherein the 2D trajectory in the 2D image space has insignificant lateral positional changes;
generating a plurality of on-ground trajectory lines in a 3D space, based on the 2D trajectory, wherein each on-ground trajectory line is associated with a different assumed forward speed for the object, wherein each on-ground trajectory line comprises a plurality of on-ground projection points calculated based on the assumed forward speed, and wherein each on-ground projection point represents an on-ground projection of the object's in-air position at a given time;
determining a plurality of object heights from a ground plane in the 3D space by sampling object positions from the 2D trajectory at the given times;
for each on-ground trajectory line, reconstructing a corresponding candidate 3D trajectory by curve fitting a plurality of 3D object positions defined by the plurality of on-ground projection points of the on-ground trajectory line and the plurality of object heights; and
reconstructing the 3D object trajectory in-air by selecting one of the candidate 3D trajectories.
2 . The method of claim 1 , the method further comprising:
determining the 2D trajectory in the 2D image space from an input video.
3 . The method of claim 2 , wherein the input video is captured using a camera of a mobile computing device.
4 . The method of claim 1 , wherein the on-ground trajectory lines are associated with a direction of the object towards an goal object.
5 . The method of claim 1 , further comprising computing a release angle from the 3D object trajectory.
6 . The method of claim 1 , wherein for each on-ground trajectory line, the associated assumed forward speed is bounded by a function of a distance to the goal object and a time duration of the 2D trajectory.
7 . The method of claim 1 , wherein the selecting the one of the candidate 3D trajectories is based on a trajectory score associated with each candidate 3D trajectory, and wherein the trajectory score is based on gravity errors computed from gravitational accelerations estimated from the curve fitting of the candidate 3D trajectory.
8 . The method of claim 1 , further comprising:
detecting a goal, using an artificial intelligence module, by detecting one or more key feature points of the goal from an input video and wherein the 2D trajectory is directed towards the goal.
9 . A system for reconstructing 3D object trajectory in-air, comprising:
at least one processor; and
a non-transitory physical medium for storing program code and accessible by the processor, the program code when executed by the processor causes the processor to:
receive a 2D trajectory in a 2D image space, wherein the 2D trajectory in the 2D image space has insignificant lateral positional change;
generate a plurality of on-ground trajectory lines in a 3D space, based on the 2D trajectory, wherein each on-ground trajectory line is associated with a different assumed forward speed for the object, wherein each on-ground trajectory line comprises a plurality of on-ground projection points calculated based on the assumed forward speed, and wherein each on-ground projection point represents an on-ground projection of the object's in-air position at a given time;
determine a plurality of object heights from a ground plane in the 3D space by sampling object positions from the 2D trajectory at the given times;
for each on-ground trajectory line, reconstruct a corresponding candidate 3D trajectory by curve fitting a plurality of 3D object positions defined by the plurality of on-ground projection points of the on-ground trajectory line and the plurality of object heights; and
reconstruct the 3D object trajectory in-air by selecting one of the candidate 3D trajectories.
10 . The system of claim 9 , wherein the program code when executed by the processor further causes the processor to:
determine the 2D trajectory in the 2D image space from an input video.
11 . The system of claim 10 , wherein the input video is captured using a camera of a mobile computing device.
12 . The system of claim 9 , wherein each on-ground trajectory line is associated with a direction of the object towards an goal object.
13 . The system of claim 9 , wherein the program code when executed by the processor further causes the processor to compute a release angle from the 3D object trajectory.
14 . The system of claim 12 , wherein for each on-ground trajectory line, the associated assumed forward speed is bounded by a function of a distance to the goal object and a time duration of the 2D trajectory.
15 . The system of claim 9 , wherein the selecting the one of the candidate 3D trajectories is based on a trajectory score associated with each candidate 3D trajectory, and wherein the trajectory score is based on gravity errors computed from gravitational acceleration estimated from the curve fitting of the candidate 3D trajectory.
16 . The system of claim 9 , wherein the program code when executed by the processor further causes the processor to:
detect a goal, using an artificial intelligence module, by program code to detect one or more key feature points of the goal from an input video and wherein the 2D trajectory is directed towards the goal.
17 . A non-transitory physical storage medium for reconstructing 3D object trajectory in-air, the storage medium comprising program code stored thereon, the program code when executed by a processor causes the processor to:
receive a 2D trajectory in a 2D image space, wherein the 2D trajectory in the 2D image space has insignificant lateral positional changes tangent;
generate a plurality of on-ground trajectory lines in 3D space, based on the 2D trajectory, wherein each on-ground trajectory line is associated with a different assumed forward speed for the object, wherein each on-ground trajectory line comprises a plurality of on-ground projection points calculated based on the assumed forward speed, and wherein each on-ground projection point represents an on-ground projection of the object's in-air position at a given time;
determine a plurality of object heights from a ground plane in the 3D space by sampling object positions from the 2D trajectory at the given times;
for each on-ground trajectory line, reconstruct a corresponding candidate 3D trajectory by curve fitting a plurality of 3D object positions defined by the plurality of on-ground projection points of the on-ground trajectory line and the plurality of object heights; and
reconstruct the 3D object trajectory in-air by selecting one of the candidate 3D trajectories.
18 . The non-transitory physical storage medium of claim 17 , wherein the program code when executed by the processor further causes the processor to:
determine the 2D trajectory in the 2D image space from an input video.