Spatial domain methods for orientation and velocity estimation

Abstract: In this thesis, novel methods for estimation of orientation and velocity are presented. The methods are designed exclusively in the spatial domain.Two important concepts in the use of the spatial domain for signal processing is projections into subspaces, e.g. the subspace of second degree polynomials, and representations by frames, e.g. wavelets. It is shown how these concepts can be unified in a least squares framework for representation of finite dimensional vectors by bases, frames, subspace bases, and subspace frames.This framework is used to give a new derivation of Normalized Convolution, a method for signal analysis that takes uncertainty in signal values into account and also allows for spatial localization of the analysis functions.With the help of Normalized Convolution, a novel method for orientation estimation is developed. The method is based on projection onto second degree polynomials and the estimates are represented by orientation tensors. A new concept for orientation representation, orientation functionals, is introduced and it is shown that orientation tensors can be considered a special case of this representation. A very efficient implementation of the estimation method is presented and by evaluation on a test sequence it is demonstrated that the method performs excellently.Considering an image sequence as a spatiotemporal volume, velocity can be estimated from the orientations present in the volume. Two novel methods for velocity estimation are presented, with the common idea to combine the orientation tensors over some region for estimation of the velocity fkield according to a motion model, e.g. affine motion. The first method involves a simultaneous segmentation and velocity estimation algorithm to obtain appropriate regions. The second method is designed for computational efficiency and uses local neighborhoods instead of trying to obtain regions with coherent motion. By evaluation on the Yosemite sequence, it is shown that both methods give substantially more accurate results than previously published methods.