ABSTRACT
Following a general procedure developed previously [Ann. Henri Poincaré 1, 685 (2000)], here we construct Wigner functions on a phase space related to the similitude group in two dimensions. Since the group space in this case is topologically homeomorphic to the phase space in question, the Wigner functions so constructed may also be considered as being functions on the group space itself. Previously the similitude group was used to construct wavelets for two-dimensional image analysis; we discuss here the connection between the wavelet transform and the Wigner function.
ABSTRACT
This paper presents a novel motion parameter estimation (ME) algorithm based on the spatio-temporal continuous wavelet transform (CWT). The multidimensional nature of the CWT allows for the definition of a multitude of energy densities by integrating over a subset of the CWT parameter space. Three energy densities are used to estimate motion parameters by sequentially optimizing a state vector composed of velocity, position, and size parameters. This optimization is performed on a frame-by-frame basis allowing the algorithm to track moving objects. The ME algorithm is designed to address real world challenges encountered in the defense industry and traffic monitoring scenarios, such as attaining robust performance in noise and handling obscuration and crossing object trajectories.
