The aim of the thesis is the classification of magnetic resonance images by Deep Learning models. The goal was to predict Alzheimer's disease on the dataset created by Alzheimer's Disease Neuroimaging Initiative (ADNI). To prepare the dataset, we built two processing pipelines, which align, normalise and remove irrelevant features from brain scans. We used the processed scans for a 2D and 3D dataset. We designed a few models based on convolutional and previously proposed architectures. Although, many studies published astonishing results on ADNI classification, the results of our experiments do not support previous research in this area. Contrary to what was previously thought, we found that the accuracy strongly depends on the dataset splitting. If we split the dataset by patients, not by scans, the accuracy drops significantly. We presented an overview of several previously published architectures and our experiments showing results of these architectures on the datasets generated by random splitting or subject-based splitting. We also pointed out how the dataset splitting choice changes the performance of our models. The work is a natural extension of study [Fung et al., 2019]. 1

Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing. This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications.