Abstract
Image registration is the problem of determining a geometric transformation to properly align the images of concern. This thesis presents a class of transformations – continuous piecewise affine transformations (abbreviated as CPA-transformations) – and its associated design methodologies for 2-D registration problem, by knowing the correspondence of point features as common information in the images to be registered. In our approach, both of theoretical and practical aspects are considered. With emphasis on an axiomatic theoretical development, two important properties – the invertibility and transitivity properties – are raised and proved under some mild conditions. In practical aspect, the CPA-transformation design problem is formulated as a least-squares optimization problem with linear constraints so that well-developed computational algorithms in mathematical programming can be applied directly. Furthermore, several experimental simulations are given in this thesis to demonstrate the contribution and applicability of our approach.