Mutual visibility by luminous robots without collisions

We consider the Mutual Visibility problem for anonymous dimensionless robots with obstructed visibility moving in a plane: starting from distinct locations, the robots must reach, without colliding, a configuration where no three of them are collinear. We study this problem in the luminous robots model, in which each robot has a visible light that can assume colors from a fixed set. Among other results, we prove that Mutual Visibility can be solved in SSynch with 2 colors and in ASynch with 3 colors. If an adversary can interrupt and stop a robot moving to its computed destination, Mutual Visibility is still solvable in SSynch with 3 colors and, if the robots agree on the direction of one axis, also in ASynch. As a byproduct, we provide the first obstructed-visibility solutions to two classical problems for oblivious robots: collision-less convergence to a point (also known as near-gathering) and circle formation

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Image Processing and Pattern Recognition Applied to Soil Structure

This thesis represents a collaborative research between the Department of Electronics & Electrical Engineering and the Department of Civil Engineering, University of Glasgow. The project was initially aimed at development of some theories and techniques of image processing and pattern recognition for the study of soil microstructures. More specifically, the aim was to study the shapes, orientations, and arrangements of soil particles and voids (i.e. pores): these three are very important properties, which are used both for description, recognition and classification of soils, and also for studying the relationships between the soil structures and physical, chemical, geological, geographical, and environmental changes. The work presented here was based principally on a need for analysing the structure of soil as recorded in two-dimensional images which might be conventional photographs, optical micrographs, or electron-micrographs. In this thesis, first a brief review of image processing and pattern recognition and their previous application in the study of soil microstructures is given. Then a convex hull based shape description and classification for soil particles is presented. A new algorithm, SPCH, is proposed for finding the convex hull of either a binary object or a cluster of points in a plane. This algorithm is efficient and reliable. Features of pattern vectors for shape description and classification are obtained from the convex hull and the object. These features are invariant with respect to coordinate rotation, translation, and scaling. The objects can then be classified by any standard feature-space method: here minimum-distance classification was used. Next the orientation analysis of soil particles is described. A new method, Directed Vein, is proposed for the analysis. Another three methods: Convex Hull, Principal Components, and Moments, are also presented. Comparison of the four methods shows that the Directed Vein method appears the fastest; but it also has the special property of estimating an 'internal preferred orientation' whereas the other methods estimate an 'elongation direction'. Fourth, the roundness/sharpness analysis of soil particles is presented. Three new algorithms, referred to as the Centre, Gradient Centre, and Radius methods, all based on the Circular Hough Transform, are proposed. Two traditional Circular Hough Transform algorithms are presented as well. The three new methods were successfully applied to the measurement of the roundness (sharpness of comers) of two-dimensional particles. The five methods were compared from the points of view of memory requirement, speed, and accuracy; and the Radius method appears to be the best for the special topic of sharpness/roundness analysis. Finally the analysis and classification of aggregates of objects is introduced. A new method. Extended Linear Hough Transform, is proposed. In this method, the orientations and locations of the objects are mapped into extended Hough space. The arrangements of the objects within an aggregate are then determined by analysing the data distributions in this space. The aggregates can then be classified using a tree classifier. Taken together, the methods developed or tested here provide a useful toolkit for analysing the shapes, orientation, and aggregation of particles such as those seen in two-dimensional images of soil structure at various scales

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Development of the VHP-Female Full-Body Computational Model and Its Applications for Biomedical Electromagnetic Modeling

Computational modeling offers better insight into a wide range of bioelectrical and biomechanical problems with improved tools for the design of medical devices and the diagnosis of pathologies. Electromagnetic modeling at low and high frequencies is particularly necessary. Modeling electromagnetic, structural, thermal, and acoustic response of the human body to different internal and external stimuli is limited by the availability of numerically efficient computational human models. This study describes the development to date of a computational full-body human model - Visible Human Project (VHP) - Female Model. Its unique feature is full compatibility both with MATLAB and specialized FEM computational software packages such as ANSYS HFSS/Maxwell 3D. This study also describes progress made to date in using the newly developed tools for segmentation. A visualization tool is implemented within MATLAB and is based on customized version of the constrained 2D Delaunay triangulation method for intersecting objects. This thesis applies a VHP - Female Model to a specific application, transcranial Direct Current Stimulation (tDCS). Transcranial Direct Current Stimulation has been beneficial in the stimulation of cortical activity and treatment of neurological disorders in humans. The placement of electrodes, which is cephalic versus extracephalic montages, is studied for optimal targeting of currents for a given functional area. Given the difficulty of obtaining in vivo measurements of current density, modeling of conventional and alternative electrode montages via the FEM has been utilized to provide insight into the tDCS montage performance. An insight into future work and potential areas of research, such as study of bone quality have been presented too