US 12,340,533 B2
Three dimensional trajectory model and system
Ernest Chen, Kowloon (HK); and Victor Tan, Kowloon (HK)
Assigned to Infinity Cube Limited, Kowloon (HK)
Filed by Infinity Cube Limited, Kowloon (HK)
Filed on Apr. 19, 2022, as Appl. No. 17/724,049.
Prior Publication US 2023/0334689 A1, Oct. 19, 2023
Int. Cl. G06T 7/70 (2017.01); G06F 17/13 (2006.01)
CPC G06T 7/70 (2017.01) [G06F 17/13 (2013.01); G06T 2207/10028 (2013.01); G06T 2207/30241 (2013.01)] 15 Claims
OG exemplary drawing
 
1. A computer-implemented method for reconstructing a three-dimensional projectile object trajectory for a projectile object using one or more image capture devices, the method comprising:
capturing one or more videos of a projectile object trajectory for the projectile object, using the one or more image capture devices coupled to at least a first computing device, the first computing device communicatively connected to a second computing device over a communications network;
transmitting the one or more videos to the second computing device over the communications network, wherein the one or more videos from the one or more image capture devices are sorted into one or more data groups and at least one solution for the one or more data groups is computed by the second computing device using a projectile trajectory model; and
receiving the solution computed for the one or more data groups by the first computing device,
wherein the projectile trajectory model is implemented according to a function (⊖,t) that returns three-dimensional coordinates of the projectile object at time t governed by the projectile trajectory model with an initial state ⊖,
wherein the initial state ⊖ is a tuple (x, y, z, vx, vy, vy, wx, wy, wz) which denotes the coordinates, velocity and spin of the projectile object in a three-dimensional environment, and
wherein a loss function ƒ of the projectile trajectory model is defined by the function (⊖,t) as:

OG Complex Work Unit Math
wherein xijt denotes a sample trajectory object J observed by at least one of the one or more image capture devices i at time t and Pi is the projection matrix for the capture device i and τi represents the time lag of the capture device i, and the function d measures distances between two homogeneous points on the capture device i frame.