A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis and Its Application to the Analysis of Motion

Abstract : This research presents a multiresolution wavelet analysis tool for analyzing motion in time sequential imagery. A theoretical framework is developed for constructing an L2(R) wavelet multiresolution analysis from three non-identical spatial and temporal L2(R) wavelet multiresolution analyses. This framework provides the flexibility to tailor the spatio-temporal frequency characteristics of the three dimensional wavelet filter to match the frequency behavior of the analyzed signal. An unconventional, discrete multiresolution wavelet decomposition algorithm is developed which yields a rich set of independent spatio-temporally oriented frequency channels for analyzing, the size and speed characteristics of moving objects. Unlike conventional wavelet decomposition methods, this algorithm provides independent zoom-in and zoom-out capability in space and time. Symmetric 3D filters produced by the unconventional decomposition process are combined with the properties of the Hilbert transform to produce a bank of directionally selective wavelet filters. Multiple directionally selective wavelet filters are integrated to form a multiresolution vector wavelet motion sensor capable of unambiguously computing the optical flow of a 3D image sequence. A unique flow restoration methodology is presented which incorporates a modified version of Grossberg's gated dipole filter in a cooperative-competitive flow restoration methodology that reinforces consistent flow behavior and removes flow inconsistencies. Finally, several digital and optical parallel architectures arc investigated for their ability to speed up the 3D wavelet decomposition process.