| dc.description | Despite the fact that regularization has a long tradition in early vision, most methods tackle the monomodal pixel labeling task, i.e. those applications compute only one model per pixel (the most plausible one). On the other hand, the multimodal regularization problem, in which two or more labels per pixel are computed, has captured less attention to research groups due to the fact that most labeling problems are formulated in order to recover a single model per image position. Although, there are early vision problems that must be solved by specialized multimodal regularization methods, as for instance, problems related with transparencies in images or in cases where the partial volume problem considerably a®ects the model{estimation task. In this thesis, we provide a multimodal regularization framework which is capable of detecting several models at a single image position. Our proposal points out the corresponding labels by means of a set of real{valued memberships. Thus, our solution framework is based on regularization cost functions composed by three terms named data, oriented spatial regularization and intermodel competition. Since the unknown is a ¯eld of real{valued variables, it is possible to apply gradient{based minimization methods with the well{known algorithmic advantages with respect to hard{minimization approaches. Moreover, we introduce the Basis Pursuit method in the context of multi{modal regularization problem. Such an approach is convenient since: it permits us to recover sparse solutions (an important feature in many early vision applications), it is implemented in an e±cient way and it is robust to outliers(due to noise) in the data. We implement our framework in two state{of{the{art challengingproblems: the axon ¯ber estimation in DW{MRI and the transparent optical °ow estimation.We provide solving methods for both problems with algorithmic advantages with respect to state{of{the{art proposals. In particular, we present an e±cient method that overcomes the drawbacks of ¯tting a Gaussian mixture model to the di®usion weighted images for the axon ¯ber estimation. Our spatial and intermodel regularization allows one to eliminate noise and to recover good solutions with a reduced number of images and with low-requirement data. Our formulation has shown a superior performance in experimental comparison with the state of the art method named Q-Ball. For the transparent optical °ow estimation, we provide a novel multimodal regularization framework that improves previous approaches by avoiding combinatorial optimization methods. Moreover, we propose a variant of such a method that is capable of solving transparent the RDK sequences. The performance of the proposal is validated by means of synthetic and real data: quantitative and qualitative results are presented. | |
