Time-based Mapping of Space Using Visual Motion Invariants

Abstract: 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.