Time-based Mapping of Space Using Visual Motion Invariants
Juan D. Yepes Daniel Raviv
This paper focuses on visual motion-based invariants that result in a
representation of 3D points in which the stationary environment remains
invariant, ensuring shape constancy. This is achieved even as the images
undergo constant change due to camera motion. Nonlinear functions of measurable
optical flow, which are related to geometric 3D invariants, are utilized to
create a novel representation. We refer to the resulting optical flow-based
invariants as 'Time-Clearance' and the well-known 'Time-to-Contact' (TTC).
Since these invariants remain constant over time, it becomes straightforward to
detect moving points that do not adhere to the expected constancy. We present
simulations of a camera moving relative to a 3D object, snapshots of its
projected images captured by a rectilinearly moving camera, and the object as
it appears unchanged in the new domain over time. In addition, Unity-based
simulations demonstrate color-coded transformations of a projected 3D scene,
illustrating how moving objects can be readily identified. This representation
is straightforward, relying on simple optical flow functions. It requires only
one camera, and there is no need to determine the magnitude of the camera's
velocity vector. Furthermore, the representation is pixel-based, making it
suitable for parallel processing.