Learning Kinematic Formulas from Multiple View Videos

Given a set of multiple view videos, which records the motion trajectory of an object, we propose to find out the objects' kinematic formulas with neural rendering techniques. For example, if the input multiple view videos record the free fall motion of an object with different initial speed v, the network aims to learn its kinematics: Δ=vt-1over 2 gt2, where Δ, g and t are displacement, gravitational acceleration and time. To achieve this goal, we design a novel framework consisting of a motion network and a differentiable renderer. For the differentiable renderer, we employ Neural Radiance Field (NeRF) since the geometry is implicitly modeled by querying coordinates in the space. The motion network is composed of a series of blending functions and linear weights, enabling us to analytically derive the kinematic formulas after training. The proposed framework is trained end to end and only requires knowledge of cameras' intrinsic and extrinsic parameters. To validate the proposed framework, we design three experiments to demonstrate its effectiveness and extensibility. The first experiment is the video of free fall and the framework can be easily combined with the principle of parsimony, resulting in the correct free fall kinematics. The second experiment is on the large angle pendulum which does not have analytical kinematics. We use the differential equation controlling pendulum dynamics as a physical prior in the framework and demonstrate that the convergence speed becomes much faster. Finally, we study the explosion animation and demonstrate that our framework can well handle such black-box-generated motions.