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dc.contributor.supervisor Peters, James F. (Electrical and Computer Engineering) en_US
dc.contributor.author A-iyeh, Enoch
dc.date.accessioned 2017-01-19T20:27:38Z
dc.date.available 2017-01-19T20:27:38Z
dc.date.issued A-iyeh, E., Peters, J.F, Rényi Entropy in Measuring Information Levels in Voronoï Tessellation Cells with Application in Digital Image Analysis, Vol. 6, no. 1, pp. 77-95, 2016, Theory and Applications of Mathematics and Computer Science en_US
dc.identifier.citation A-iyeh, E., Peters, J.F, Measure of Tessellation Quality of Voronoï Meshes, Vol. 5, no. 2, pp. 158-185, 2015, Theory and Applications of Mathematics and Computer Science en_US
dc.identifier.citation A-iyeh, E., Peters, J.F, Gini index-based digital image complementing in the study of medical images, Intelligent Decision Technologies, Vol. 9, no. 2, pp. 209-218, 2015, IOS press en_US
dc.identifier.uri http://hdl.handle.net/1993/32055
dc.description.abstract A measure of the quality of Voronoi tessellations resulting from various mesh generators founded on feature-driven models is introduced in this work. A planar tessellation covers an image with polygons of various shapes and sizes. Tessellations have potential utility due to their geometry and the opportunity to derive useful information from them for object recognition, image processing and classification. Problem domains including images are generally feature-endowed, non-random domains. Generators modeled otherwise may easily guarantee quality of meshes but certainly bear no reference to features of the meshed problem domain. They are therefore unsuitable in point pattern identification, characterization and subsequently the study of meshed regions. We therefore found generators on features of the problem domain. This provides a basis for element quality studies and improvement based on quality criteria. The resulting polygonal meshes tessellating an n-dimensional digital image into convex regions are of varying element qualities. Given several types of mesh generating sets, a measure of overall solution quality is introduced to determine their effectiveness. Given a tessellation of general and mixed shapes, this presents a challenge in quality improvement. The Centroidal Voronoi Tessellation (CVT) technique is developed for quality improvement and guarantees of mixed, general-shaped elements and to preserve the validity of the tessellations. Mesh quality indicators and entropies introduced are useful for pattern studies, analysis, recognition and assessing information. Computed features of tessellated spaces are explored for image information content assessment and cell processing to expose detail using information theoretic methods. Tessellated spaces also furnish information on pattern structure and organization through their quality distributions. Mathematical and theoretical results obtained from these spaces help in understanding Voronoi diagrams as well as for their successful applications. Voronoi diagrams expose neighbourhood relations between pattern units. Given this realization, the foundation of near sets is developed for further applications. en_US
dc.publisher A-iyeh E., Peters, J.F, Proximal Groupoid Patterns in Digital Images, Computing Research Repository: Computer Vision and Pattern Recognition, 2016 en_US
dc.rights info:eu-repo/semantics/openAccess
dc.subject Algorithms, centroids, centroidal Voronoi tessellation, cell processing, classification, corners, cell, convex, digital image, diagrams, dominant generators, edges, entropy, energy, features, generators, generation, geometry, Gini index, groupoid, image processing, information, improvement, index, keypoints, lemma, mesh, motifs, near, neighbourliness, Poisson-Voronoi, proximity, pattern, polygons, quality, recognition, spaces, sites, sets, tessellation, theorem, topology, Voronoi en_US
dc.title Voronoi tessellation quality: applications in digital image analysis en_US
dc.type info:eu-repo/semantics/doctoralThesis
dc.type doctoral thesis en_US
dc.degree.discipline Electrical and Computer Engineering en_US
dc.contributor.examiningcommittee Alfa, Attahiru (Electrical and Computer Engineering) McNeill, Dean (Electrical and Computer Engineering) Tachie, Mark (Mechanical Engineering) Hassanien, Aboul E. (Information and Technology Department, Cairo University) en_US
dc.degree.level Doctor of Philosophy (Ph.D.) en_US
dc.description.note February 2017 en_US


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