A compositional data analysis package for R providing multiple approaches

”compositions” is a new R-package for the analysis of compositional and positive data.It contains four classes corresponding to the four different types of compositional andpositive geometry (including the Aitchison geometry). It provides means for computation,plotting and high-level multivariate statistical analysis in all four geometries.These geometries are treated in an fully analogous way, based on the principle of workingin coordinates, and the object-oriented programming paradigm of R. In this way,called functions automatically select the most appropriate type of analysis as a functionof the geometry. The graphical capabilities include ternary diagrams and tetrahedrons,various compositional plots (boxplots, barplots, piecharts) and extensive graphical toolsfor principal components. Afterwards, ortion and proportion lines, straight lines andellipses in all geometries can be added to plots. The package is accompanied by ahands-on-introduction, documentation for every function, demos of the graphical capabilitiesand plenty of usage examples. It allows direct and parallel computation inall four vector spaces and provides the beginner with a copy-and-paste style of dataanalysis, while letting advanced users keep the functionality and customizability theydemand of R, as well as all necessary tools to add own analysis routines. A completeexample is included in the appendix

Colour image processing

In the context of the round table the following topics related to image colour processing will be discussed: historical point of view. Studies of Aguilonius, Gerritsen, Newton and Maxwell. CIE standard (Commission International de lpsilaEclaraige). Colour models. RGB, HIS, etc. Colour segmentation based on HSI model. Industrial applications. Summary and discussion. At the end, video images showing the robustness of colour in front of B/W images will be presented

Dam wall detection and tracking using a Mechanically Scanned Imaging Sonar

In dam inspection tasks, an underwater robot has to grab images while surveying the wall meanwhile maintaining a certain distance and relative orientation. This paper proposes the use of an MSIS (mechanically scanned imaging sonar) for relative positioning of a robot with respect to the wall. An imaging sonar gathers polar image scans from which depth images (range & bearing) are generated. Depth scans are first processed to extract a line corresponding to the wall (with the Hough transform), which is then tracked by means of an EKF (Extended Kalman Filter) using a static motion model and an implicit measurement equation associating the sensed points to the candidate line. The line estimate is referenced to the robot fixed frame and represented in polar coordinates (rho&thetas) which directly corresponds to the actual distance and relative orientation of the robot with respect to the wall. The proposed system has been tested in simulation as well as in water tank conditions

Improving Clustering Algorithms for Image Segmentation using Contour and Region Information

In image segmentation, clustering algorithms are very popular because they are intuitive and, some of them, easy to implement. For instance, the k-means is one of the most used in the literature, and many authors successfully compare their new proposal with the results achieved by the k-means. However, it is well known that clustering image segmentation has many problems. For instance, the number of regions of the image has to be known a priori, as well as different initial seed placement (initial clusters) could produce different segmentation results. Most of these algorithms could be slightly improved by considering the coordinates of the image as features in the clustering process (to take spatial region information into account). In this paper we propose a significant improvement of clustering algorithms for image segmentation. The method is qualitatively and quantitative evaluated over a set of synthetic and real images, and compared with classical clustering approaches. Results demonstrate the validity of this new approach

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay