Time-to-X: analysis of motion through temporal parameters

Situations involving navigation among manoeuvring agents are critical for the study of visual guidance of autonomous vehicles. This paper addresses the case of translational motion with polynomial regimes and defines a general class of temporal parameters (TP) relevant for navigation, enabling a qualitative description of the observed agents´ depth trajectories. These parameters are shown to be visually recoverable. Instances of such temporal parameters include Time-to-Collision (TTC) and Time-to-Synchronization (TTS), useful for docking or platooning maneuvers. The results are specialized to lower order motions. The recovery of TTC and TTS for arbitrary regimes is a special corollary of our analysis. Computations from direct and feature-based methods are described. A scheme for addressing model order determination, collision detection and temporal parameter estimation as proposed and tested. Experimental results on synthetic and real images are given