Digital halftoning is a crucial technique used in digital printers to convert a continuoustone image into a pattern of black and white dots. Halftoning is used since printers have a limited availability of inks and cannot reproduce all the color intensities in a continuous image. Error Diffusion is an algorithm in halftoning that iteratively quantizes pixels in a neighborhood dependent fashion. This thesis focuses on the development and design of a parallel scalable hardware architecture for high performance implementation of a high quality Stacked Error Diffusion algorithm. The algorithm is described in ‘C’ and requires a significant processing time when implemented on a conventional CPU. Thus, a new hardware processor architecture is developed to implement the algorithm and is implemented to and tested on a Xilinx Virtex 5 FPGA chip. There is an extraordinary decrease in the run time of the algorithm when run on the newly proposed parallel architecture implemented to FPGA technology compared to execution on a single CPU. The new parallel architecture is described using the Verilog Hardware Description Language. Post-synthesis and post-implementation, performance based Hardware Description Language (HDL), simulation validation of the new parallel architecture is achieved via use of the ModelSim CAD simulation tool.

Triangle mesh models of images are studied. Through exploration, a computational framework for mesh generation based on data-dependent triangulations (DDTs) and two specific mesh-generation methods derived from this framework are proposed. In earlier work, Yang et al. proposed a highly-effective technique for generating triangle-mesh models of images, known as the error diffusion (ED) method. Unfortunately, the ED method, which chooses triangulation connectivity via a Delaunay triangulation, typically yields triangulations in which many (triangulation) edges crosscut image edges (i.e., discontinuities in the image), leading to increased approximation error. In this thesis, we propose a computational framework for mesh generation that modifies the ED method to use DDTs in conjunction with the Lawson local optimization procedure (LOP) and has several free parameters. Based on experimentation, we recommend two particular choices for these parameters, yielding two specific mesh-generation methods, known as MED1 and MED2, which make different trade offs between approximation quality and computational cost. Through the use of DDTs and the LOP, triangulation connectivity can be chosen optimally so as to minimize approximation error. As part of our work, two novel optimality criteria for the LOP are proposed, both of which are shown to outperform other well known criteria from the literature. Through experimental results, our MED1 and MED2 methods are shown to yield image approximations of substantially higher quality than those obtained with the ED method, at a relatively modest computational cost. For example, in terms of peak-signal-to-noise ratio, our MED1 and MED2 methods outperform the ED method, on average, by 3.26 and 3.81 dB, respectively. / Graduate

In this thesis, we propose a general computational framework for generating mesh models of single-component (e.g., grayscale) and multi-component (e.g., RGB color) images. This framework builds on ideas from the previously-proposed GPRFSED method for single-component images to produce a framework that can handle images with any arbitrary number of components. The key ideas embodied in our framework are Floyd-Steinberg error diffusion and greedy-point removal. Our framework has several free parameters and the effect of the choices of these parameters is studied. Based on experimentation, we recommend two specific sets of parameter choices, yielding two highly effective single/multi-component mesh-generation methods, known as MED and MGPRFS. These two methods make different trade offs between mesh quality and computational cost. The MGPRFS method is able to produce high quality meshes at a reasonable computational cost, while the MED method trades off some mesh quality for a reduction in computational cost relative to the MGPRFS method. To evaluate the performance of our proposed methods, we compared them to three highly-effective previously-proposed single-component mesh generators for both grayscale and color images. In particular, our evaluation considered the following previously-proposed methods: the error diffusion (ED) method of Yang et al., the greedy-point-removal from-subset (GPRFSED) method of Adams, and the greedy-point removal (GPR) method of Demaret and Iske. Since these methods cannot directly handle color images, color images were handled through conversion to grayscale as a preprocessing step, and then as a postprocessing step after mesh generation, the grayscale sample values in the generated mesh were replaced by their corresponding color values. These color-capable versions of ED, GPRFSED, and GPR are henceforth referred to as CED, CGPRFSED, and CGPR, respectively. Experimental results show that our MGPRFS method yields meshes of higher quality than the CGPRFSED and GPRFSED methods by up to 7.05 dB and 2.88 dB respectively, with nearly the same computational cost. Moreover, the MGPRFS method outperforms the CGPR and GPR methods in mesh quality by up to 7.08 dB and 0.42 dB respectively, with about 5 to 40 times less computational cost. Lastly, our MED method yields meshes of higher quality than the CED and ED methods by up to 7.08 and 4.72 dB respectively, where all three of these methods have a similar computational cost. / Graduate

Dans ce mémoire nous allons présenter une méthode de diffusion d’erreur originale qui peut reconstruire des images en demi-ton qui plaisent à l’œil. Cette méthode préserve des détails fins et des structures visuellement identifiables présentes dans l’image originale. Nous allons tout d’abord présenter et analyser quelques travaux précédents afin de montrer certains problèmes principaux du rendu en demi-ton, et nous allons expliquer pourquoi nous avons décidé d’utiliser un algorithme de diffusion d’erreur pour résoudre ces problèmes. Puis nous allons présenter la méthode proposée qui est conceptuellement simple et efficace. L’image originale est analysée, et son contenu fréquentiel est détecté. Les composantes principales du contenu fréquentiel (la fréquence, l’orientation et le contraste) sont utilisées comme des indices dans un tableau de recherche afin de modifier la méthode de diffusion d’erreur standard. Le tableau de recherche est établi dans un étape de pré-calcul et la modification est composée par la modulation de seuil et la variation des coefficients de diffusion. Ensuite le système en entier est calibré de façon à ce que ces images reconstruites soient visuellement proches d’images originales (des aplats d’intensité constante, des aplats contenant des ondes sinusoïdales avec des fréquences, des orientations et des constrastes différents). Finalement nous allons comparer et analyser des résultats obtenus par la méthode proposée et des travaux précédents, et démontrer que la méthode proposée est capable de reconstruire des images en demi-ton de haute qualité (qui préservent des structures) avec un traitement de temps très faible. / In this work we present an original error-diffusion method which produces visually pleasant halftone images while preserving fine details and visually identifiable structures present in original images. We first present and analyze the previous work to show the major problems in halftoning, and explain why we decided to use an error diffusion algorithm to solve the problems. Then we present our method which is conceptually simple and computationally efficient. The source image is analyzed, and its local frequency content is detected. The main components of the frequency content (main frequency, orientation, and contrast) serve as lookup table indices in a pre-computed database of modifications to a standard error diffusion. The modifications comprise threshold modulation and variation of error-diffusion coefficients. The whole system is calibrated in such a way that the produced halftone images are visually close to original images (patches of constant intensity, patches containing sinu- soidal waves of different frequencies/orientations/contrasts, as well as natural images of different origins). Finally, we compare and analyze the results obtained by our method and previous work, and show that our method can produre high-quality halftone image (which is struc- ture aware) within very short time.

Dans ce mémoire nous allons présenter une méthode de diffusion d’erreur originale qui peut reconstruire des images en demi-ton qui plaisent à l’œil. Cette méthode préserve des détails fins et des structures visuellement identifiables présentes dans l’image originale. Nous allons tout d’abord présenter et analyser quelques travaux précédents afin de montrer certains problèmes principaux du rendu en demi-ton, et nous allons expliquer pourquoi nous avons décidé d’utiliser un algorithme de diffusion d’erreur pour résoudre ces problèmes. Puis nous allons présenter la méthode proposée qui est conceptuellement simple et efficace. L’image originale est analysée, et son contenu fréquentiel est détecté. Les composantes principales du contenu fréquentiel (la fréquence, l’orientation et le contraste) sont utilisées comme des indices dans un tableau de recherche afin de modifier la méthode de diffusion d’erreur standard. Le tableau de recherche est établi dans un étape de pré-calcul et la modification est composée par la modulation de seuil et la variation des coefficients de diffusion. Ensuite le système en entier est calibré de façon à ce que ces images reconstruites soient visuellement proches d’images originales (des aplats d’intensité constante, des aplats contenant des ondes sinusoïdales avec des fréquences, des orientations et des constrastes différents). Finalement nous allons comparer et analyser des résultats obtenus par la méthode proposée et des travaux précédents, et démontrer que la méthode proposée est capable de reconstruire des images en demi-ton de haute qualité (qui préservent des structures) avec un traitement de temps très faible. / In this work we present an original error-diffusion method which produces visually pleasant halftone images while preserving fine details and visually identifiable structures present in original images. We first present and analyze the previous work to show the major problems in halftoning, and explain why we decided to use an error diffusion algorithm to solve the problems. Then we present our method which is conceptually simple and computationally efficient. The source image is analyzed, and its local frequency content is detected. The main components of the frequency content (main frequency, orientation, and contrast) serve as lookup table indices in a pre-computed database of modifications to a standard error diffusion. The modifications comprise threshold modulation and variation of error-diffusion coefficients. The whole system is calibrated in such a way that the produced halftone images are visually close to original images (patches of constant intensity, patches containing sinu- soidal waves of different frequencies/orientations/contrasts, as well as natural images of different origins). Finally, we compare and analyze the results obtained by our method and previous work, and show that our method can produre high-quality halftone image (which is struc- ture aware) within very short time.