Rotational wavelet transforms for motion analysis, estimation and tracking

This paper addresses the problem of estimating, analyzing and tracking objects moving with spatio-temporal rotational motion (i.e. the angular velocity of spinning or orbiting motions). It is assumed that the digital signals of interest are acquired from a camera and structured as digital image sequences. The trajectories in the signal are two-dimensional spatial projections in time of motion taking place in a three-dimensional space. The purpose of this work is to focus on the rotational motion, i.e. estimate the angular velocity and acceleration. In natural scenes, rotational motion usually evolves on a trajectory and then composes with translational or accelerated motion. This paper shows that the trajectory parameters and the rotational parameters can be efficiently estimated and tracked either simultaneously or separately. The final goal of this work is to provide selective reconstructions of moving objects of interest. This paper constructs new continuous wavelet transforms that can be tuned to both translational and rotational motion. The parameters of analysis that are taken into account in these rotational wavelet transforms are space and time position, velocity, spatial scale, angular orientation and angular velocity. The continuous wavelet functions are finally discretized for signal processing. The link between rotational motion, symmetry and critical sampling is also presented. Simulations have been performed with estimation, detection and tracking on natural scenes.