Contributions of Lattice Computing to Medical Image Processing

This Thesis is developed along two main axis: The exploration of new computational solutions based on the novel paradigm of Lattice Computing. The application to medical image data in order to obtain new image processing methods, or computed aided diagnosis systems based on image biomarkers. The proposal of Lattice Computing encompasses all computational constructions involving the use of Lattice Theory results and/or operators. In this Thesis, this ambitious scope is reduced to three fields of development of algorithms: Lattice Associative Memories, Dendritic Computing, and Multivariate Mathematical Morphology. Specifically, Lattice Auto-Associative Memories play a role in the development of a Lattice Independent Component Analysis (LICA) proposed as a lattice based alternative to the well known Independent Component Analysis (ICA) approach, and in the definition of a reduced ordering in an approach to define a Multivariate Mathematical Morphology. These issues have been tackled in this Thesis from an application point of view: the diverse tools are applied to several kinds of medical image data. From the medical image processing point of view, the Thesis works on features of anatomical MRI for computer aided diagnosis of Alzheimer’s disease, on resting state fMRI of Schizophrenia patients, and on CTA data for Abdominal Aortic Aneurysm.