Dithering by Differences of Convex Functions

Motivated by a recent halftoning method which is based on electrostatic principles, we analyse a halftoning framework where one minimizes a functional consisting of the difference of two convex functions (DC). One of them describes attracting forces caused by the image gray values, the other one enforces repulsion between points. In one dimension, the minimizers of our functional can be computed analytically and have the following desired properties: the points are pairwise distinct, lie within the image frame and can be placed at grid points. In the two-dimensional setting, we prove some useful properties of our functional like its coercivity and suggest to compute a minimizer by a forward-backward splitting algorithm. We show that the sequence produced by such an algorithm converges to a critical point of our functional. Furthermore, we suggest to compute the special sums occurring in each iteration step by a fast summation technique based on the fast Fourier transform at non-equispaced knots which requires only Ο(m log(m)) arithmetic operations for m points. Finally, we present numerical results showing the excellent performance of our DC dithering method

Structure-aware halftoning

our result faithfully preserves the texture details as well as the local tone. All images have the same resolution of 445×377. This paper presents an optimization-based halftoning technique that preserves the structure and tone similarities between the original and the halftone images. By optimizing an objective function consisting of both the structure and the tone metrics, the generated halftone images preserve visually sensitive texture details as well as the local tone. It possesses the blue-noise property and does not introduce annoying patterns. Unlike the existing edge-enhancement halftoning, the proposed method does not suffer from the deficiencies of edge detector. Our method is tested on various types of images. In multiple experiments and the user study, our method consistently obtains the best scores among all tested methods.

Energy-Based Evaluation of Digital Halftones

The purpose of this study was to determine the validity of the energy measure developed by Geist, Reynolds, and Suggs, when used as an evaluator of digitally half-toned images. The energy measure was found to be a valid, useful tool for the evaluation of binary digital halftone quality. Data resulting from the analysis and visual comparison of fifteen different halftones supports this conclusion. Using linear regression, the coefficient of correlation between the energy measure and visual quality ratings was -0.606 using all images, and -0.936 using average results for each halftone method. These figures indicate the strong relationship between image energy and image quality. Although the energy measure was found to be accurate for different halftones of the same continuous-tone image, there is an inherent difficulty when comparing the quality of halftones of different image content. Geist, Reynold, and Suggs\u27 algorithm does not produce values within a fixed range. A simple approximation for normalizing the energy values is proposed and used for the study, but further development is needed to obtain absolute quality rankings using this technique

The modelling of natural imperfections and an improved space filling curve halftoning technique.

by Tien-tsin Wong.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 72-79).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- The Modelling of Natural Imperfections --- p.1Chapter 1.2 --- Improved Clustered-dot Space Filling Curve Halftoning Technique --- p.2Chapter 1.3 --- Structure of the Thesis --- p.3Chapter 2 --- The Modelling of Natural Imperfections --- p.4Chapter 2.1 --- Introduction --- p.4Chapter 2.2 --- Related Work --- p.6Chapter 2.2.1 --- Texture Mapping --- p.6Chapter 2.2.2 --- Blinn's Dusty Surfaces --- p.7Chapter 2.2.3 --- Imperfection Rule-based Systems --- p.7Chapter 2.3 --- Natural Surface Imperfections --- p.8Chapter 2.3.1 --- Dust Accumulation --- p.8Chapter 2.3.2 --- Scratching --- p.10Chapter 2.3.3 --- Rusting --- p.10Chapter 2.3.4 --- Mould --- p.11Chapter 2.4 --- New Modelling Framework for Natural Imperfections --- p.13Chapter 2.4.1 --- Calculation of Tendency --- p.13Chapter 2.4.2 --- Generation of Chaotic Pattern --- p.19Chapter 2.5 --- Modelling of Dust Accumulation --- p.21Chapter 2.5.1 --- Predicted Tendency of Dust Accumulation --- p.22Chapter 2.5.2 --- External Factors --- p.24Chapter 2.5.3 --- Generation of Fuzzy Dust Layer --- p.30Chapter 2.5.4 --- Implementation Issues --- p.31Chapter 2.6 --- Modelling of Scratching --- p.31Chapter 2.6.1 --- External Factor --- p.32Chapter 2.6.2 --- Generation of Chaotic Scratch Patterns --- p.35Chapter 2.6.3 --- Implementation Issues --- p.36Chapter 3 --- An Improved Space Filling Curve Halftoning Technique --- p.39Chapter 3.1 --- Introduction --- p.39Chapter 3.2 --- Review on Some Halftoning Techniques --- p.41Chapter 3.2.1 --- Ordered Dither --- p.41Chapter 3.2.2 --- Error Diffusion and Dither with Blue Noise --- p.42Chapter 3.2.3 --- Dot Diffusion --- p.43Chapter 3.2.4 --- Halftoning Along Space Filling Traversal --- p.43Chapter 3.2.5 --- Space Diffusion --- p.46Chapter 3.3 --- Improvements on the Clustered-Dot Space Filling Halftoning Method --- p.47Chapter 3.3.1 --- Selective Precipitation --- p.47Chapter 3.3.2 --- Adaptive Clustering --- p.50Chapter 3.4 --- Comparison With Other Methods --- p.57Chapter 3.4.1 --- Low Resolution Observations --- p.57Chapter 3.4.2 --- High Resolution Printing Results --- p.58Chapter 3.4.3 --- Analytical Comparison --- p.58Chapter 4 --- Conclusion and Future Work --- p.69Chapter 4.1 --- The Modelling of Natural Imperfections --- p.69Chapter 4.2 --- An Improved Space Filling Curve Halftoning Technique --- p.71Bibliography --- p.7

IRAbMC: Image Recommendation with Absorbing Markov Chain

Image Recommendation is an important feature for search engine as tremendous amount images are available online. It is necessary to retrieve relevant images to meet user's requirement. In this paper, we present an algorithm Image Recommendation with Absorbing Markov Chain (IRAbMC) to retrieve relevant images for user input query. Images are ranked by calculating keyword relevance probability between annotated keywords from log and keywords of user input query. Absorbing Markov chain is used to calculate keyword relevance. Experiments results show that the IRAbMC algorithm outperforms Markovian Semantic Indexing (MSI) method with improved relevance score of retrieved ranked images

Hardware-accelerated algorithms in visual computing

This thesis presents new parallel algorithms which accelerate computer vision methods by the use of graphics processors (GPUs) and evaluates them with respect to their speed, scalability, and the quality of their results. It covers the fields of homogeneous and anisotropic diffusion processes, diffusion image inpainting, optic flow, and halftoning. In this turn, it compares different solvers for homogeneous diffusion and presents a novel \u27extended\u27 box filter. Moreover, it suggests to use the fast explicit diffusion scheme (FED) as an efficient and flexible solver for nonlinear and in particular for anisotropic parabolic diffusion problems on graphics hardware. For elliptic diffusion-like processes, it recommends to use cascadic FED or Fast Jacobi schemes. The presented optic flow algorithm represents one of the fastest yet very accurate techniques. Finally, it presents a novel halftoning scheme which yields state-of-the-art results for many applications in image processing and computer graphics.Diese Arbeit präsentiert neue parallele Algorithmen zur Beschleunigung von Methoden in der Bildinformatik mittels Grafikprozessoren (GPUs), und evaluiert diese im Hinblick auf Geschwindigkeit, Skalierungsverhalten, und Qualität der Resultate. Sie behandelt dabei die Gebiete der homogenen und anisotropen Diffusionsprozesse, Inpainting (Bildvervollständigung) mittels Diffusion, die Bestimmung des optischen Flusses, sowie Halbtonverfahren. Dabei werden verschiedene Löser für homogene Diffusion verglichen und ein neuer \u27erweiterter\u27 Mittelwertfilter präsentiert. Ferner wird vorgeschlagen, das schnelle explizite Diffusionsschema (FED) als effizienten und flexiblen Löser für parabolische nichtlineare und speziell anisotrope Diffusionsprozesse auf Grafikprozessoren einzusetzen. Für elliptische diffusionsartige Prozesse wird hingegen empfohlen, kaskadierte FED- oder schnelle Jacobi-Verfahren einzusetzen. Der vorgestellte Algorithmus zur Berechnung des optischen Flusses stellt eines der schnellsten und dennoch äußerst genauen Verfahren dar. Schließlich wird ein neues Halbtonverfahren präsentiert, das in vielen Bereichen der Bildverarbeitung und Computergrafik Ergebnisse produziert, die den Stand der Technik repräsentieren

Discretization and Bayesian modeling in inverse problems and imaging

In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented