Video dithering

In this work, we present mathematical and artistic techniques for the easy creation of artistic screening animations in video resolution by extending the artistic screening technique of adapting various patterns as screen dots for generating halftones. For video dithering, three different animations are needed. One is for screen dots which is a simple black and white animation; another is for the goal (or perceived) animation on the screen; and the other animation is for controlling the color and the size of screen dots. By combining three different animations with video dithering techniques, two animations appear simultaneously on the result video screen and provide complex and unique animation. Our techniques assure creating of aesthetic looking movies by providing frame to frame coherence and avoiding spatial and temporal aliasing that can be caused by low quality of video images. We shows how this technique is a powerful and effective way to create artistic results, by demonstrating variety of video dithering

Digital halftoning and the physical reconstruction function

Originally presented as author's thesis (Ph. D.--Massachusetts Institute of Technology), 1986.Bibliography: p. 397-405."This work has been supported by the Digital Equipement Corporation."by Robert A. Ulichney

Video dithering

In this work, we present mathematical and artistic techniques for the easy creation of artistic screening animations in video resolution by extending the artistic screening technique of adapting various patterns as screen dots for generating halftones. For video dithering, three different animations are needed. One is for screen dots which is a simple black and white animation; another is for the goal (or perceived) animation on the screen; and the other animation is for controlling the color and the size of screen dots. By combining three different animations with video dithering techniques, two animations appear simultaneously on the result video screen and provide complex and unique animation. Our techniques assure creating of aesthetic looking movies by providing frame to frame coherence and avoiding spatial and temporal aliasing that can be caused by low quality of video images. We shows how this technique is a powerful and effective way to create artistic results, by demonstrating variety of video dithering

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

An importance driven genetic algorithm for the halftoning process

Most evolutionary approaches to halftoning techniques have been concerned with the paramount goal of halftoning: achieving an accurate reproduction of local grayscale intensities while avoiding the introduction of artifacts. A secondary concern in halftoning has been the preservation of edges in the halftoned image. In this paper, we will introduce a new evolutionary approach through the use of an importance function. This approach has at least two main characteristics. First, it can produce results similar to many other halftoning techniques. Second, if the chosen importance function is accordingly changed, areas of the image with high variance can be highlighted.III Workshop de Computación Gráfica, Imágenes y Visualización (WCGIV)Red de Universidades con Carreras en Informática (RedUNCI

Halftoning by rotating non-Bayer dispersed dither arrays

We propose a new operator for creating rotated dither threshold arrays. This new discrete one- to-one rotation operator is briefly explained. We analyze its application to different dispersed- dot dither arrays such as hexagonal dispersed dither arrays and 3X3 matrix-based Bayer- expanded dither arrays and compare the results with the ones obtained by rotating standard Bayer dither arrays. We show that the rotation operator introduced new lower-frequency components that, for example in the case of rotated dispersed-dot Bayer dither, produces a slight clustering effect, improving the tone reproduction behavior of the halftone patterns. In other cases, such as hexagonal dispersed dither, these new lower frequency components are responsible for strong interferences in the rotated halftone array. When applied to 3x3 matrix- based Bayer-expanded dither arrays, the rotation operator induces sequences of short horizontal and vertical patterns that have very good tone reproduction behavior in the dark tones. Besides their used in black and white printing, rotated dispersed-dot dither halftoning techniques have also been successfully applied to in-phase color reproduction on inkjet printers

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods