Clasificación Automática de Sujetos con Deterioro Cognitivo Leve mediante la Caracterización Fractal 3D en Imágenes Cerebrales de Resonancia Magnética

Sixty brain volumes were analyzed from separate magnetic resonance images in two populations: healthy control subjects and subjects with mild cognitive impairment. For each element, the Box Counting algorithm was applied to obtain the characterization of the 3D Fractal Dimension that it presented. In addition, other morphological indices of volume, discrete compactness and surrounding area were added. Finally, a classification strategy is implemented using the Gaussian Process with a radial-based Kernel to compare the correct discrimination in the populations studied. The classifier model after the validation process gave a 60% success rate for the fractal dimension and for the morphological indices. The highest hit rate was when both metrics were combined with 80%. With these results, it is believed that the fractal index could become a biomarker for the prediagnosis of Alzheimer's disease, although for this, more studies are needed in the future.

Automatic Representation and Segmentation of Video Sequences via a Novel Framework Based on the nD-EVM and Kohonen Networks

Recently in the Computer Vision field, a subject of interest, at least in almost every video application based on scene content, is video segmentation. Some of these applications are indexing, surveillance, medical imaging, event analysis, and computer-guided surgery, for naming some of them. To achieve their goals, these applications need meaningful information about a video sequence, in order to understand the events in its corresponding scene. Therefore, we need semantic information which can be obtained from objects of interest that are present in the scene. In order to recognize objects we need to compute features which aid the finding of similarities and dissimilarities, among other characteristics. For this reason, one of the most important tasks for video and image processing is segmentation. The segmentation process consists in separating data into groups that share similar features. Based on this, in this work we propose a novel framework for video representation and segmentation. The main workflow of this framework is given by the processing of an input frame sequence in order to obtain, as output, a segmented version. For video representation we use the Extreme Vertices Model in the n-Dimensional Space while we use the Discrete Compactness descriptor as feature and Kohonen Self-Organizing Maps for segmentation purposes.

Novel Discrete Compactness-Based Training for Vector Quantization Networks: Enhancing Automatic Brain Tissue Classification

An approach for nonsupervised segmentation of Computed Tomography (CT) brain slices which is based on the use of Vector Quantization Networks (VQNs) is described. Images are segmented via a VQN in such way that tissue is characterized according to its geometrical and topological neighborhood. The main contribution rises from the proposal of a similarity metric which is based on the application of Discrete Compactness (DC) which is a factor that provides information about the shape of an object. One of its main strengths lies in the sense of its low sensitivity to variations, due to noise or capture defects, in the shape of an object. We will present, compare, and discuss some examples of segmentation networks trained under Kohonen’s original algorithm and also under our similarity metric. Some experiments are established in order to measure the effectiveness and robustness, under our application of interest, of the proposed networks and similarity metric.

On 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems

We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete W1,p compactness, discrete compactness in space and in time) for the so-called Discrete Duality Finite Volume (DDFV) schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [IMA J. Numer. Anal., 32 (2012), pp. 1574–1603]. Some of our results are new, such as a general time-compactness result based upon the idea of Kruzhkov (1969); others generalize the ideas known for the 2D DDFV schemes or for traditional two-point-flux finite volume schemes. We illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray–Lions kind, and provide numerical results for this example.

Computing the Discrete Compactness of Orthogonal Pseudo-Polytopes via Their D-EVM Representation

This work is devoted to present a methodology for the computation of Discrete Compactness in -dimensional orthogonal pseudo-polytopes. The proposed procedures take in account compactness' definitions originally presented for the 2D and 3D cases and extend them directly for considering the D case. There are introduced efficient algorithms for computing discrete compactness which are based on an orthogonal polytopes representation scheme known as the Extreme Vertices Model in the -Dimensional Space (D-EVM). It will be shown the potential of the application of Discrete Compactness in higher-dimensional contexts by applying it, through EVM-based algorithms, in the classification of video sequences, associated to the monitoring of a volcano's activity, which are expressed as 4D orthogonal polytopes in the space-color-time geometry.