Statistical inference of motion in the invisible

Abstract

This paper focuses on the unexplored problem of inferring motion of objects that are invisible to all cameras in a multiple camera setup. As opposed to methods for learning relationships between disjoint cameras, we take the next step to actually infer the exact spatiotemporal behavior of objects while they are invisible. Given object trajectories within disjoint cameras' FOVs (field-of-view), we introduce constraints on the behavior of objects as they travel through the unobservable areas that lie in between. These constraints include vehicle following (the trajectories of vehicles adjacent to each other at entry and exit are time-shifted relative to each other), collision avoidance (no two trajectories pass through the same location at the same time) and temporal smoothness (restricts the allowable movements of vehicles based on physical limits). The constraints are embedded in a generalized, global cost function for the entire scene, incorporating influences of all objects, followed by a bounded minimization using an interior point algorithm, to obtain trajectory representations of objects that define their exact dynamics and behavior while invisible. Finally, a statistical representation of motion in the entire scene is estimated to obtain a probabilistic distribution representing individual behaviors, such as turns, constant velocity motion, deceleration to a stop, and acceleration from rest for evaluation and visualization. Experiments are reported on real world videos from multiple disjoint cameras in NGSIM data set, and qualitative as well as quantitative analysis confirms the validity of our approach. © 2012 Springer-Verlag.