Single and Multiple Motion Field Estimation

Abstract: This thesis presents a framework for estimation of motion fields both for single and multiple layers. All the methods have in common that they generate or use constraints on the local motion. Motion constraints are represented by vectors whose directions describe one component of the local motion and whose magnitude indicate confidence.Two novel methods for estimating these motion constraints are presented. Both methods take two images as input and apply orientation sensitive quadrature filters. One method is similar to a gradient method applied on the phase from the complex filter outputs. The other method is based on novel results using canonical correlation presented in this thesis.Parametric models, e.g. affine or FEM, are used to estimate motion from constraints on local motion. In order to estimate smooth fields for models with many parameters, cost functions on deformations are introduced.Motions of transparent multiple layers are estimated by implicit or explicit clustering of motion constraints into groups. General issues and difficulties in analysis of multiple motions are described. An extension of the known EM algorithm is presented together with experimental results on multiple transparent layers with affine motions. Good accuracy in estimation allows reconstruction of layers using a backprojection algorithm. As an alternative to the EM algorithm, this thesis also introduces a method based on higher order tensors.A result with potential applicatications in a number of diffeerent research fields is the extension of canonical correlation to handle complex variables. Correlation is maximized using a novel method that can handle singular covariance matrices.