| The motion estimation between images is an ever increasing necessity in digital image processing. This problem, also called image registration, consists of finding the best spatial correspondence between two images.; This Ph.D. Thesis tackles the non-rigid motion estimation problem between images, with the proposal of a novel image registration method that consists of two clear stages: in the first one a fuzzy spatial correspondence between both images is drawn, and in the second stage the explicit spatial correspondence is obtained from the previous result by means of Tikhonov regularization.; In the first processing phase, the possible spatial correspondences, characterized over convex parametric models, are drawn. Such models define the region of spatial correspondence of high likelihood, being able to represent different geometries, like points and curves. In contrast to feature based methods, the proposed strategy does not extract features from images nor uses segmentation techniques, but it reminds broadly speaking to area based methods, although the correspondence is obtained from a difference-correlation-based similarity measure.; In the second phase, the final motion vectors, which relates in an explicit manner both images, are obtained. The use of Tikhonov regularization results from considering that the actual spatial correspondence is a continuous and smooth map. The ad hoc regularization method yields to an iterative process, which converges to a continuous, smooth solution and in agreement with the spatial constraints imposed by the parametric models. This regularization mechanism is related to the theory of deformable models, allowing setting the curvature or smoothness constraints of the spatial correspondence map a priori.; Since the parametric models are convex, the final result corresponds to the global minimum of the functional. The absence of local minima is an advantage that, in contrast, is not own of other non-parametric or energy minimization methods, such as elastic registration, fluid registration, diffusion registration, etc. Additionally, the extension of the global method to the three-dimensional scenario (3D), or volume registration, has been carried out. This extension includes the proposal of new parametric models (point, curve, surface and its combination) and the techniques of projection on these models. |
