  Optical flow and disparity are two informative visual features for autonomous
driving perception. They have been used for a variety of applications, such as
obstacle and lane detection. The concept of "U-V-Disparity" has been widely
explored in the literature, while its counterpart in optical flow has received
relatively little attention. Traditional motion analysis algorithms estimate
optical flow by matching correspondences between two successive video frames,
which limits the full utilization of environmental information and geometric
constraints. Therefore, we propose a novel strategy to model optical flow in
the collision-free space (also referred to as drivable area or simply
freespace) for intelligent vehicles, with the full utilization of geometry
information in a 3D driving environment. We provide explicit representations of
optical flow and deduce the quadratic relationship between the optical flow
component and the vertical coordinate. Through extensive experiments on several
public datasets, we demonstrate the high accuracy and robustness of our model.
Additionally, our proposed freespace optical flow model boasts a diverse array
of applications within the realm of automated driving, providing a geometric
constraint in freespace detection, vehicle localization, and more. We have made
our source code publicly available at https://mias.group/FSOF.
