Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table

Software libre para alcanzar la colaboración en un SIG Corporativo. El caso de la Confederación Hidrográfica del Duero

La Confederación Hidrográfica del Duero (CHDuero), organismo de cuenca dependiente del Ministerio de Medio Ambiente, y Medio Rural y Marino, tiene una voluntad política manifiesta por acercar a todos los actores implicados la gestión del agua. Para ello, y desde el año 2006, se ha estado desarrollando una plataforma SIG siguiendo los principios de la directiva INSPIRE [1] y utilizando componentes libres e interoperables para el desarrollo de la funcionalidad necesaria. No sólo se utilizan componentes de software libre que implementan de forma probada normas y especificaciones como las del Open Geospatial Consortium (OGC) [2] o la serie de normas ISO 19100 sino que también se siguen las recomendaciones de distintos grupos de trabajo relacionados con los SIG como los de la Infraestructura de Datos Espaciales de España (IDEE) [3] o los del Sistema de Información Europeo del Agua WISE [4]. Así, la plataforma SIG de la CHDuero, que surgió inicialmente para satisfacer las necesidades de la Oficina de Planificación Hidrológica se está consolidando como un punto común de acceso a datos dentro de la CHDuero. Se trata de una plataforma normalizada para el intercambio de información con Portugal que facilita la información y la participación pública, participa como nodo de la IDEE y sirve como eje de colaboración con la Comisión Europea y algunos Estados Miembros para el desarrollo e implementación del nodo del Sistema de Información Europeo del Agua (WISE)

Recovering Euclidean deformable models from stereo-motion

In this paper we present a novel structure from motion (SfM) approach able to infer 3D deformable models from uncalibrated stereo images. Using a stereo setup dramatically improves the 3D model estimation when the observed 3D shape is mostly deforming without undergoing strong rigid motion. Our approach first calibrates the stereo system automatically and then computes a single metric rigid structure for each frame. Afterwards, these 3D shapes are aligned to a reference view using a RANSAC method in order to compute the mean shape of the object and to select the subset of points on the object which have remained rigid throughout the sequence without deforming. The selected rigid points are then used to compute frame-wise shape registration and to extract the motion parameters robustly from frame to frame. Finally, all this information is used in a global optimization stage with bundle adjustment which allows to refine the frame-wise initial solution and also to recover the non-rigid 3D model. We show results on synthetic and real data that prove the performance of the proposed method even when there is no rigid motion in the original sequence

Visualitzation and processing of diffusion tensor MRI

Diffusion Tensor Imaging (DTI) is a new magnetic resonance imaging modality capable of producing quantitative maps of microscopic natural displacements of water molecules that occur in brain tissues as part of the physical diffusion process. This technique has become a powerful tool in the investigation of brain structure and function because it allows for in vivo measurements of white matter fiber orientation. The application of DTI in clinical practice requires specialized processing and visualization techniques to extract and represent acquired information in a comprehensible manner. Tracking techniques are used to infer patterns of continuity in the brain by following in a step-wise mode the path of a set of particles dropped into a vector field. In this way, white matter fiber maps can be obtained.