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Isotropic Quadrature Filter for Motion Estimation Problems

Quadrature filters are a well known means for local spectral analysis of images and to extract relevant structure. Recently, there has been the discovering of an isotropic quadrature filter for images that does not need steering with respect to orientation and provides the user with geometric (local orientation) and structural (local phase) information. Here, we present a further extension of this, an isotropic quadrature filter for 3D data. With only four convolutions we can calculate the local orientation, energy and the phase of locally intrinsically 1D structures in 3D image data. There is a wide variety of useful applications for a filter of this kind. In this paper, we will restrict ourselves to the application of phase-based motion or flow field estimation.