Chromaticity of Certain Bipartite Graphs

Since the introduction of the concepts of chromatically unique graphs and chromatically equivalent graphs, numerous families of such graphs have been obtained. The purpose of this thesis is to continue with the search of families of chromatically unique bipartite graphs. In Chapters 1 and 2, we define the concept of graph colouring, the associated chromatic polynomial and some properties of a chromatic polynomial. We also give some necessary conditions for graphs that are chromatically unique or chromatically equivalent. We end this chapter by stating some known results on the chromaticity of bipartite graphs, denoted as K(p,q)

Hector, a fast simulator for the transport of particles in beamlines

Computing the trajectories of particles in generic beamlines is an important ingredient of experimental particle physics, in particular regarding near-beam detectors. A new tool, Hector, has been built for such calculations, using the transfer matrix approach and energy corrections. The limiting aperture effects are also taken into account. As an illustration, the tool was used to simulate the LHC beamlines, in particular around the high luminosity interaction points (IPs), and validated with results of the Mad-X simulator. The LHC beam profiles, trajectories and beta functions are presented. Assuming certain forward proton detector scenarios around the IP5, acceptance plots, irradiation doses and chromaticity grids are produced. Furthermore, the reconstruction of proton kinematic variables at the IP (energy and angle) is studied as well as the impact of the misalignment of beamline elements.Comment: 40 pages, 20 figures; added references, corrected typos ; submitted to JINS

Chromaticity Of Certain K4-Homeomorphs

The chromaticity of graphs is the term used referring to the question of chromatic equivalence and chromatic uniqueness of graphs. Since the arousal of the interest on the chromatically equivalent and chromatically unique graphs, various concepts and results under the said areas of research have been discovered and many families of such graphs have been obtained. The purpose of this thesis is to contribute new results on the chromatic equivalence and chromatic uniqueness of graphs, specifically, K4-homeomorphs

Colour Constancy: Cues, Priors and Development

Colour is crucial for detecting, recognising, and interacting with objects. However, the reflected wavelength of light ("colour") varies vastly depending on the illumination. Whilst adults can judge colours as relatively invariant under changing illuminations (colour constancy), much remains unknown, which this thesis aims to resolve. Firstly, previous studies have shown adults can use certain cues to estimate surface colour. However, one proposed cue - specular highlights - has been little researched so this is explored here. Secondly, the existing data on a daylight prior for colour constancy remain inconclusive so we aimed to further investigate this. Finally, no studies have investigated the development of colour constancy during childhood so the third aim is to determine at what age colour constancy becomes adult-like. In the introduction, existing research is discussed, including cues to the illuminant, daylight priors, and the development of perceptual constancies. The second chapter contains three experiments conducted to determine whether adults can use a specular highlight cue and/ or daylight prior to aid colour constancy. Results showed adults can use specular highlights when other cues are weakened. Evidence for a daylight prior was weak. In the third chapter the development of colour constancy during childhood was investigated by developing a novel child-friendly task. Children had higher constancy than adults, and evidence for a daylight prior was mixed. The final experimental chapter used the task developed in Chapter 3 to ask whether children can use specular highlights as a cue for colour constancy. Testing was halted early due to the coronavirus pandemic, yet the data obtained suggest that children are negatively impacted by specular highlights. Finally, in the general discussion, the results of the six experiments are brought together to draw conclusions regarding the use of cues and priors, and the development of colour constancy. Implications and future directions for research are discussed

Detecting salient cues through illumination-invariant color ratios

This work presents a novel technique for embedding color constancy into a saliency-based system for detecting potential landmarks in outdoor environments. Since multiscale color opponencies are among the ingredients determining saliency, the idea is to make such opponencies directly invariant to illumination variations, rather than enforcing the invariance of colors themselves. The new technique is compared against the alternative approach of preprocessing the images with a color constancy procedure before entering the saliency system. The first procedure used in the experimental comparison is the well-known image conversion to chromaticity space, and the second one is based on successive lighting intensity and illuminant color normalizations. The proposed technique offers significant advantages over the preceding two ones since, at a lower computational cost, it exhibits higher stability in front of illumination variations and even of slight viewpoint changes, resulting in a better correspondence of visual saliency to potential landmark elements.This work was supported by the project 'Sistema reconfigurable para la navegación basada en visión de robots caminantes y rodantes en entornos naturales.' (00). The authors would like to the support obtained from the Forschungszentrum Informatik and Institut für Prozessrechentechnik, Automation und Robotik , Karlsruhe University, Germany. This work is partially supported by the Spanish Science and Technology Directorate, in the scope of the project “Reconfigurable system for vision-based navigation of legged and wheeled robots in natural environments (SIRVENT)”, grant DPI2003-05193-C02-01.Peer Reviewe

Total variation regularization for manifold-valued data

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer

Parametric studies on pattern recognition mechanisms in human vision

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