Introduction

We live in a world where objects (cars, animals, men, birds, aeroplanes, the Sun, etc.) that surround us are constantly in relative motion. One would like to extract the motion information from the observation of the scene and use it for various purposes, such as detection, tracking and identification. In particular, tracking of multiple objects is of great importance in many real world scenarios. The examples include traffic monitoring, autonomous vehicle navigation, and tracking of ballistic missile warheads. Tracking is a complex problem, often requiring to estimate motion parameters – such as position, velocity – under very challenging situations. Algorithms of this type typically have difficulty in the presence of noise, when the object is obscured, in situations including crossing trajectories, and when highly maneuvering objects are present.

Most motion estimation (ME) techniques such as the ones based on block matching, optical flow, and phase difference [Jah97,280,281] assume that the object is constant from frame to frame. That is, the signature of the object does not change with time. Consequently, these techniques tend to have difficulty handling complex motion, particularly when noise is present.

The time-dependent continuous wavelet transform (CWT) is attractive as a tool for analysis, in that important motion parameters can be compactly and clearly represented.