Spatio-Temporal Wavelets for Motion Detection and Target Tracking

摘要

This project has developed a group-theoretic approach to generate new tools of signal processing in order to analyze and track motion. For that purpose, external motion is projected on a sensor array and captured as a spatiotemporal signal to analyze. This research takes into account differential manifolds on which motion takes place and on which the sensor array is deployed. The research has derived the means to generate all the observable kinematics in a spatiotemporal signals. Each particular kinematic is defined by a specific Lie algebra. Each algebra leads to a Lie group, and to the appropriate group representations in the functional space of the signals. These representations lead to the related harmonic analysis. This motion analysis deals with translational, rotational, and deformational motion and all the temporal derivatives. This research has derived the optimal tools to estimate motion, to track moving patterns, to study diffusion and optical flow along motion trajectories. This group-theoretic framework covers determinist and stochastic calculus with Kalman filters, PDE's, ODE's and integral transforms. New algorithms to analyze and track motion have been defined from this theoretical framework and lead to parallelizable implementations based on FFT and dynamic programming.