Motion trajectories

In this paper, we present a simple algorithm for selecting and linking interesting ow vectors across a sequence of frames for computing motion trajectories. We track tokens which have both interesting pixel gray values in the spatial domain and in the optical ow eld in the temporal domain. This and operation eeectively remove some redundant trajectories. Due to errors introduced during the computation of optical ow, and the linking of such ow vectors across a sequence of frames, the resultant trajectories are not always smooth. We discuss a Kalman ltering based approach for smoothing the trajectories. Isolating the trajectories into sets belonging to individual objects is an important rst step that should be taken before any type of shape or motion interpretation can be done. Therefore, we also discuss a simple algorithm for segmenting motion trajectories. When motion trajectories belonging to a single translating object are extended, they intersect at a single point called the Focus Of Expansion (FOE). If the motions of objects are assumed to be independent, each FOE represents one object. Therefore, FOE can be used to segment trajectories belonging to individual objects. We present a simple but highly robust algorithm for partitioning motion trajectories, which does not require the exact location of FOE, but uses some useful properties of FOE. We have applied our method for computing and segmenting motion trajectories to a number of real sequences, and have obtained very encouraging results.