An important task in brain connectivity research is the classification of patients from healthy subjects. In this work, we present a two-step mathematical framework allowing to discriminate between two groups of people with an application to multiple sclerosis. The proposed approach exploits the properties of the connectivity matrices determined using the covariances between signals of a fixed set of brain areas. These positive semi-definite matrices lay on a Riemannian manifold, allowing to use a geodesic distance defined on this space. In order to generate a vector representation useful for classification purpose, but still preserving the network structures, we encoded the data exploiting the network attractors determined by a geodesic clustering of connectivity matrices. Then clustering centroids were used as a dictionary allowing to encode subject’s connectivity matrices as a vector of geodesic distances. A Linear Support Vector Machine was then used to perform classification between subjects. To demonstrate the advantage of using geodesic metrics in this framework, we conducted the same analysis using Euclidean metric. Experimental results validate the fact that employing geodesic metric in this framework leads to a higher classification performance, whereas with Euclidean metric performance was suboptimal.

In this paper, we tackle the task of automatically analyzing 3D volumetric scans obtained from computed tomography (CT) devices. In particular, we address a particular task for which data is very limited: the segmentation of ancient Egyptian mummies CT scans. We aim at digitally unwrapping the mummy and identify different segments such as body, bandages and jewelry. The problem is complex because of the lack of annotated data for the different semantic regions to segment, thus discouraging the use of strongly supervised approaches. We, therefore, propose a weakly supervised and efficient interactive segmentation method to solve this challenging problem. After segmenting the wrapped mummy from its exterior region using histogram analysis and template matching, we first design a voxel distance measure to find an approximate solution for the body and bandage segments. Here, we use geodesic distances since voxel features as well as spatial relationship among voxels is incorporated in this measure. Next, we refine the solution using a GrabCut based segmentation together with a tracking method on the slices of the scan that assigns labels to different regions in the volume, using limited supervision in the form of scribbles drawn by the user. The efficiency of the proposed method is demonstrated using visualizations and validated through quantitative measures and qualitative unwrapping of the mummy.