The authors present a group-theoretic method, which exploits the properties of motion parameters to be structured in Lie algebras and Lie groups and leads to motion-tuned continuous spatiotemporal wavelets and Kalman filters. From the use of square-integrable group representation, the continuous wavelet tansforms (CWTs) bring optimum motion measurement with minimum mean squared error (MMSE), selective tracking with Kalman filters, and selective reconstruction of moving objects with frame properties. For that purpose, the spatiotemporal CWTs are parameterized with motion parameters that can be either local (velocity) or global (acceleration) on the trajectory. These CWTs, which are numerically computed in the Fourier domain, bring nice properties for signal analysis, such as matched filtering, MMSE estimation, signal denoising, and robustness to noise and motion jitter. The spatiotemporal interpolation property of the CWT solves the multiple-trajectory crossing problems. Kalman filters and dynamic programming bring all the algorithmic properties that allow motion tracking to take place as in any optimum control problem. The study of the Lagrangians in the least action principle shows how to select the kind of motions to track. The paper presents simulations on synthetic scenes including noise and motion jitter.