Title :
Spatio-temporal continuous wavelets for the analysis of motion on manifolds
Author :
Leduc, Jean-Pierre ; Corbett, Jonathan R.
Author_Institution :
Dept. of Math., Washington Univ., St. Louis, MO, USA
Abstract :
This paper presents kinematical Lie algebras and Lie groups that describe motion on differentiable spatiotemporal manifolds. Motion is assumed to be translational and rotational with position, velocity and acceleration. The general kinematical groups that are derived have action that depends up the local chart and the local curvature. Squared integrable representations of these Lie groups define continuous wavelet transforms. General conditions of admissibility are presented with an example on space of constant curvature. The wavelet construction matches perfectly to differential geometry “a la Cartan” and mechanics on manifolds. Applications concern optimum control, general relativity and quantum mechanics
Keywords :
Lie algebras; Lie groups; image representation; image sequences; motion estimation; wavelet transforms; Lie groups; acceleration; admissibility conditions; differentiable spatiotemporal manifolds; differential geometry; digital image sequences; general relativity; kinematical Lie algebras; kinematical groups; local chart; local curvature; motion analysis; motion parameters estimation; optimum control; position; quantum mechanics; rotational motion; spatio-temporal continuous wavelets; squared integrable representations; translational motion; velocity; wavelet construction; Acceleration; Algebra; Cameras; Continuous wavelet transforms; Kinematics; Mathematics; Motion analysis; Sensor arrays; Wavelet analysis; Wavelet transforms;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1998. Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Pittsburgh, PA
Print_ISBN :
0-7803-5073-1
DOI :
10.1109/TFSA.1998.721360