News from compositions, the R package

The R-package “compositions”is a tool for advanced compositional analysis. Its basic functionality has seen some conceptual improvement, containing now some facilities to work with and represent ilr bases built from balances, and an elaborated subsys- tem for dealing with several kinds of irregular data: (rounded or structural) zeroes, incomplete observations and outliers. The general approach to these irregularities is based on subcompositions: for an irregular datum, one can distinguish a “regular” sub- composition (where all parts are actually observed and the datum behaves typically) and a “problematic” subcomposition (with those unobserved, zero or rounded parts, or else where the datum shows an erratic or atypical behaviour). Systematic classification schemes are proposed for both outliers and missing values (including zeros) focusing on the nature of irregularities in the datum subcomposition(s). To compute statistics with values missing at random and structural zeros, a projection approach is implemented: a given datum contributes to the estimation of the desired parameters only on the subcompositon where it was observed. For data sets with values below the detection limit, two different approaches are provided: the well-known imputation technique, and also the projection approach. To compute statistics in the presence of outliers, robust statistics are adapted to the characteristics of compositional data, based on the minimum covariance determinant approach. The outlier classification is based on four different models of outlier occur- rence and Monte-Carlo-based tests for their characterization. Furthermore the package provides special plots helping to understand the nature of outliers in the dataset. Keywords: coda-dendrogram, lost values, MAR, missing data, MCD estimator, robustness, rounded zeros

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

A proposal to estimate the motion of an underwater vehicle through visual mosaicking

This thesis proposes a solution to the problem of estimating the motion of an Unmanned Underwater Vehicle (UUV). Our approach is based on the integration of the incremental measurements which are provided by a vision system. When the vehicle is close to the underwater terrain, it constructs a visual map (so called "mosaic") of the area where the mission takes place while, at the same time, it localizes itself on this map, following the Concurrent Mapping and Localization strategy. The proposed methodology to achieve this goal is based on a feature-based mosaicking algorithm. A down-looking camera is attached to the underwater vehicle. As the vehicle moves, a sequence of images of the sea-floor is acquired by the camera. For every image of the sequence, a set of characteristic features is detected by means of a corner detector. Then, their correspondences are found in the next image of the sequence. Solving the correspondence problem in an accurate and reliable way is a difficult task in computer vision. We consider different alternatives to solve this problem by introducing a detailed analysis of the textural characteristics of the image. This is done in two phases: first comparing different texture operators individually, and next selecting those that best characterize the point/matching pair and using them together to obtain a more robust characterization. Various alternatives are also studied to merge the information provided by the individual texture operators. Finally, the best approach in terms of robustness and efficiency is proposed. After the correspondences have been solved, for every pair of consecutive images we obtain a list of image features in the first image and their matchings in the next frame. Our aim is now to recover the apparent motion of the camera from these features. Although an accurate texture analysis is devoted to the matching pro-cedure, some false matches (known as outliers) could still appear among the right correspon-dences. For this reason, a robust estimation technique is used to estimate the planar transformation (homography) which explains the dominant motion of the image. Next, this homography is used to warp the processed image to the common mosaic frame, constructing a composite image formed by every frame of the sequence. With the aim of estimating the position of the vehicle as the mosaic is being constructed, the 3D motion of the vehicle can be computed from the measurements obtained by a sonar altimeter and the incremental motion computed from the homography. Unfortunately, as the mosaic increases in size, image local alignment errors increase the inaccuracies associated to the position of the vehicle. Occasionally, the trajectory described by the vehicle may cross over itself. In this situation new information is available, and the system can readjust the position estimates. Our proposal consists not only in localizing the vehicle, but also in readjusting the trajectory described by the vehicle when crossover information is obtained. This is achieved by implementing an Augmented State Kalman Filter (ASKF). Kalman filtering appears as an adequate framework to deal with position estimates and their associated covariances. Finally, some experimental results are shown. A laboratory setup has been used to analyze and evaluate the accuracy of the mosaicking system. This setup enables a quantitative measurement of the accumulated errors of the mosaics created in the lab. Then, the results obtained from real sea trials using the URIS underwater vehicle are shown.

VLSI architecture for motion estimation in underwater imaging

El treball desenvolupat en aquesta tesi aprofundeix i aporta solucions innovadores en el camp orientat a tractar el problema de la correspondència en imatges subaquàtiques. En aquests entorns, el que realment complica les tasques de processat és la falta de contorns ben definits per culpa d'imatges esborronades; un fet aquest que es deu fonamentalment a il·luminació deficient o a la manca d'uniformitat dels sistemes d'il·luminació artificials. Els objectius aconseguits en aquesta tesi es poden remarcar en dues grans direccions. Per millorar l'algorisme d'estimació de moviment es va proposar un nou mètode que introdueix paràmetres de textura per rebutjar falses correspondències entre parells d'imatges. Un seguit d'assaigs efectuats en imatges submarines reals han estat portats a terme per seleccionar les estratègies més adients. Amb la finalitat d'aconseguir resultats en temps real, es proposa una innovadora arquitectura VLSI per la implementació d'algunes parts de l'algorisme d'estimació de moviment amb alt cost computacional.