Accelerated spatio-temporal wavelet transforms: an iterative trajectory estimation

This paper addresses the problem of estimating and analyzing accelerated motion in spatio-temporal discrete signals. It is assumed that the digital signals of interest are acquired from imaging sensors and structured as digital image sequences. The motion trajectories in the signal are two-dimensional spatial projections in time of three-dimensional motions. Consequently, they contain all the orders of acceleration. The purpose of this work is to estimate the trajectory and the motion parameters of selected moving objects in the scene. The final goal is to provide selective reconstructions of accelerated objects of interest. This paper presents the construction of new continuous wavelet transforms that can be tuned to any order of accelerations, we demonstrate their existence and provide the related admissibility conditions. The parameters for analysis that are taken into account in these accelerated wavelet transforms are spatial and temporal translations, velocity, acceleration (second or nth order), spatial scale and spatial rotation. The continuous wavelet functions are finally discretized for signal processing.