Voronoi tessellation quality: applications in digital image analysis
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Date
2016
Authors
A-iyeh, Enoch
Journal Title
Journal ISSN
Volume Title
Publisher
A-iyeh E., Peters, J.F, Proximal Groupoid Patterns in Digital Images, Computing Research Repository: Computer Vision and Pattern Recognition, 2016
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.
Description
Keywords
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
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
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
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