Interpretation of motion trajectories using focus of expansion

The focus of expansion (FOE) of a group of motion trajectories is defined to be a point in the image plane at which the trajectories intersect when they are extended. The FOE observed over a time sequence defines the locus of the FOE. The authors present an analytical approach for the study of dynamic events as they project on the image plane by analyzing the locus of the FOE. They find that the locus of the FOE can be used to make qualitative assertions regarding the type of motion. Interesting behavior of the locus of the FOE for various types of motion is observed. The cases include a single point and a horizontal, a vertical, and a sloped straight line. It was also possible to determine whether the object has approaching or receding motion or when the object changes its direction of motion. This inference can be used in qualitative computer vision