Generalized Semimagic Squares for Digital Halftoning

Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m-by-n board (with wrap-around) so that each k-by-l region holds the same sum. For one of the cases where this is impossible, we give a heuristic method to find a matrix with small discrepancy.Comment: 6 pages, 6 figure

固定パラメータ問題に対する高速算法に基づく計算困難問題の解決

金沢大学 / 北陸先端科学技術大学院大学本研究の目的は、最近の計算機環境の下で固定パラメータ問題を高速に解決するための方法論を確立することである。そのために、単なるプログラムテクニックとして解析に反映されなかった側面を数学的に厳密に評価し、従来の解析方法とは全く異なる立場から計算の効率評価を行うことであった。今年度は、トライセクター曲線に関する研究に時間を割いた.平面上に与えられた2点に対する2等分線は容易に計算できるが,2点間に等距離の曲線を描くのは困難である.正確には,任意の精度で近似解を得ることはできるが,正確に曲線上の点を求めることは不可能(代数的でない)であることが予想される.本研究では,そのような曲線が常に存在し,ユニークに定まることを数学的にかつ構成的に証明した.それ以外にも様々な興味深い構造的な性質を明らかにした.この研究の成果は,5月に開かれた理論計算機科学では最高峰の国際会議であるSTOCにおいて発表すると共に,Advances in Mathematicsという数学ではトップクラスのジャーナルにも論文を発表した.非常に基本的な問題でありながら,これまでに全く類似の研究がなかったということはむしろ驚きである.計算幾何学においてボロノイ図は重要な研究課題のひとつである.本研究では,従来のボロノイ図の概念を一般化して,三角形に関する評価尺度に基づいた様々なボロノイ図を定義したが,特に角度ボロノイ図に興味をもち,その構造と複雑さに関する研究を行った.具体的には,線分の集合が与えられたとき,どの線分に対して定義される視角が最も小さいかという関係で平面を分割したものである.この研究では,角度ボロノイ図が通常のボロノイ図と極めて異なる性質をもつことを証明し,さらに最小の視角を最大にする点を効率よく求めるためのアルゴリズムを示している.この結果にっいては,7月に開かれたボロノイ図に関する国際ワークショップにおいて報告した.現在は,そのジャーナルバージョンを執筆中であり,近い将来にジャーナル誌に投稿をする予定である.The purpose of this research is to establish methodology for solving fixed parameter problems in an efficient way under latest computer environment. For the purpose we mathematically evaluate some aspects of programming which has not been reflected to analysis as just simple programming techniques and then analyze computational performance from a completely different standpoint from the existing ones.In this year we spent much time for the study of distance trisector curves. Given two points in the plane, it is easy to draw perpendicular bisector, but it is hard to draw two curves equidistant from each other. More exactly, we can approximate points on the curves at any precision, but it is impossible to compute their coordinates exactly without any error. In fact we conjecture that the curves are non-algebraic. In this research we proved that such curves exist and they are unique, mathematically in a constructive manner. We also found many interesting properties of the curves. The resu lts were presented at an international symposium STOC, one of the top conference in the world in this area and also published in a top mathematical journal, Advances in Mathematics. It is rather surprising that it is quite simple and fundamental problem while there is no study on the curves. We also applied the idea to Voronoi diagrams, which is one of the most important research topics in computational geometry. In this research we defined various Voronoi diagrams based on criteria on goodness of triangles by generalizing the traditional Voronoi diagrams. More concretely, given a set of line segments in the plane, an angular Voronoi diagram is a partition of the plane into regions by the relation on which line segment gives the smallest visual angle. We have shown that this Voronoi diagram has properties which are quite different from those of the exisiting ones. We also gave an efficient algorithm for finding a point that maximizes the smallest visual angle. The results were presented at an international symposium on Voronoi diagrams We are now preparing journal version of those papers to submit them to international journals.研究課題/領域番号:15300003, 研究期間(年度):2003 - 2006出典：「固定パラメータ問題に対する高速算法に基づく計算困難問題の解決」研究成果報告書　課題番号15300003（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-15300003/153000032006kenkyu_seika_hokoku_gaiyo/）を加工して作

A note on the regularity of matrices with uniform polynomial entries

In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized Vandermonde matrices and Schur polynomials that are discussed in detail

幾つかの画像関連問題の計算複雑度の解析と効率的な解決法の提案

金沢大学 / 北陸先端科学技術大学院大学研究課題/領域番号:16092209, 研究期間(年度):2004 - 2007出典：「幾つかの画像関連問題の計算複雑度の解析と効率的な解決法の提案」研究成果報告書　課題番号16092209（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-16092209/）を加工して作

Perceptually inspired image estimation and enhancement

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2009.Includes bibliographical references (p. 137-144).In this thesis, we present three image estimation and enhancement algorithms inspired by human vision. In the first part of the thesis, we propose an algorithm for mapping one image to another based on the statistics of a training set. Many vision problems can be cast as image mapping problems, such as, estimating reflectance from luminance, estimating shape from shading, separating signal and noise, etc. Such problems are typically under-constrained, and yet humans are remarkably good at solving them. Classic computational theories about the ability of the human visual system to solve such under-constrained problems attribute this feat to the use of some intuitive regularities of the world, e.g., surfaces tend to be piecewise constant. In recent years, there has been considerable interest in deriving more sophisticated statistical constraints from natural images, but because of the high-dimensional nature of images, representing and utilizing the learned models remains a challenge. Our techniques produce models that are very easy to store and to query. We show these techniques to be effective for a number of applications: removing noise from images, estimating a sharp image from a blurry one, decomposing an image into reflectance and illumination, and interpreting lightness illusions. In the second part of the thesis, we present an algorithm for compressing the dynamic range of an image while retaining important visual detail. The human visual system confronts a serious challenge with dynamic range, in that the physical world has an extremely high dynamic range, while neurons have low dynamic ranges.(cont.) The human visual system performs dynamic range compression by applying automatic gain control, in both the retina and the visual cortex. Taking inspiration from that, we designed techniques that involve multi-scale subband transforms and smooth gain control on subband coefficients, and resemble the contrast gain control mechanism in the visual cortex. We show our techniques to be successful in producing dynamic-range-compressed images without compromising the visibility of detail or introducing artifacts. We also show that the techniques can be adapted for the related problem of "companding", in which a high dynamic range image is converted to a low dynamic range image and saved using fewer bits, and later expanded back to high dynamic range with minimal loss of visual quality. In the third part of the thesis, we propose a technique that enables a user to easily localize image and video editing by drawing a small number of rough scribbles. Image segmentation, usually treated as an unsupervised clustering problem, is extremely difficult to solve. With a minimal degree of user supervision, however, we are able to generate selection masks with good quality. Our technique learns a classifier using the user-scribbled pixels as training examples, and uses the classifier to classify the rest of the pixels into distinct classes. It then uses the classification results as per-pixel data terms, combines them with a smoothness term that respects color discontinuities, and generates better results than state-of-art algorithms for interactive segmentation.by Yuanzhen Li.Ph.D

The contour tree image encoding technique and file format

The process of contourization is presented which converts a raster image into a discrete set of plateaux or contours. These contours can be grouped into a hierarchical structure, defining total spatial inclusion, called a contour tree. A contour coder has been developed which fully describes these contours in a compact and efficient manner and is the basis for an image compression method. Simplification of the contour tree has been undertaken by merging contour tree nodes thus lowering the contour tree's entropy. This can be exploited by the contour coder to increase the image compression ratio. By applying general and simple rules derived from physiological experiments on the human vision system, lossy image compression can be achieved which minimises noticeable artifacts in the simplified image. The contour merging technique offers a complementary lossy compression system to the QDCT (Quantised Discrete Cosine Transform). The artifacts introduced by the two methods are very different; QDCT produces a general blurring and adds extra highlights in the form of overshoots, whereas contour merging sharpens edges, reduces highlights and introduces a degree of false contouring. A format based on the contourization technique which caters for most image types is defined, called the contour tree image format. Image operations directly on this compressed format have been studied which for certain manipulations can offer significant operational speed increases over using a standard raster image format. A couple of examples of operations specific to the contour tree format are presented showing some of the features of the new format.Science and Engineering Research Counci

Enhancing Mesh Deformation Realism: Dynamic Mesostructure Detailing and Procedural Microstructure Synthesis

Propomos uma solução para gerar dados de mapas de relevo dinâmicos para simular deformações em superfícies macias, com foco na pele humana. A solução incorpora a simulação de rugas ao nível mesoestrutural e utiliza texturas procedurais para adicionar detalhes de microestrutura estáticos. Oferece flexibilidade além da pele humana, permitindo a geração de padrões que imitam deformações em outros materiais macios, como couro, durante a animação. As soluções existentes para simular rugas e pistas de deformação frequentemente dependem de hardware especializado, que é dispendioso e de difícil acesso. Além disso, depender exclusivamente de dados capturados limita a direção artística e dificulta a adaptação a mudanças. Em contraste, a solução proposta permite a síntese dinâmica de texturas que se adaptam às deformações subjacentes da malha de forma fisicamente plausível. Vários métodos foram explorados para sintetizar rugas diretamente na geometria, mas sofrem de limitações como auto-interseções e maiores requisitos de armazenamento. A intervenção manual de artistas na criação de mapas de rugas e mapas de tensão permite controle, mas pode ser limitada em deformações complexas ou onde maior realismo seja necessário. O nosso trabalho destaca o potencial dos métodos procedimentais para aprimorar a geração de padrões de deformação dinâmica, incluindo rugas, com maior controle criativo e sem depender de dados capturados. A incorporação de padrões procedimentais estáticos melhora o realismo, e a abordagem pode ser estendida além da pele para outros materiais macios.We propose a solution for generating dynamic heightmap data to simulate deformations for soft surfaces, with a focus on human skin. The solution incorporates mesostructure-level wrinkles and utilizes procedural textures to add static microstructure details. It offers flexibility beyond human skin, enabling the generation of patterns mimicking deformations in other soft materials, such as leater, during animation. Existing solutions for simulating wrinkles and deformation cues often rely on specialized hardware, which is costly and not easily accessible. Moreover, relying solely on captured data limits artistic direction and hinders adaptability to changes. In contrast, our proposed solution provides dynamic texture synthesis that adapts to underlying mesh deformations. Various methods have been explored to synthesize wrinkles directly to the geometry, but they suffer from limitations such as self-intersections and increased storage requirements. Manual intervention by artists using wrinkle maps and tension maps provides control but may be limited to the physics-based simulations. Our research presents the potential of procedural methods to enhance the generation of dynamic deformation patterns, including wrinkles, with greater creative control and without reliance on captured data. Incorporating static procedural patterns improves realism, and the approach can be extended to other soft-materials beyond skin

Flat panel display signal processing

Televisions (TVs) have shown considerable technological progress since their introduction almost a century ago. Starting out as small, dim and monochrome screens in wooden cabinets, TVs have evolved to large, bright and colorful displays in plastic boxes. It took until the turn of the century, however, for the TV to become like a ‘picture on the wall’. This happened when the bulky Cathode Ray Tube (CRT) was replaced with thin and light-weight Flat Panel Displays (FPDs), such as Liquid Crystal Displays (LCDs) or Plasma Display Panels (PDPs). However, the TV system and transmission formats are still strongly coupled to the CRT technology, whereas FPDs use very different principles to convert the electronic video signal to visible images. These differences result in image artifacts that the CRT never had, but at the same time provide opportunities to improve FPD image quality beyond that of the CRT. This thesis presents an analysis of the properties of flat panel displays, their relation to image quality, and video signal processing algorithms to improve the quality of the displayed images. To analyze different types of displays, the display signal chain is described using basic principles common to all displays. The main function of a display is to create visible images (light) from an electronic signal (video), requiring display chain functions like opto-electronic effect, spatial and temporal addressing and reconstruction, and color synthesis. The properties of these functions are used to describe CRT, LCDs, and PDPs, showing that these displays perform the same functions, using different implementations. These differences have a number of consequences, that are further investigated in this thesis. Spatial and temporal aspects, corresponding to ‘static’ and ‘dynamic’ resolution respectively, are covered in detail. Moreover, video signal processing is an essential part of the display signal chain for FPDs, because the display format will in general no longer match the source format. In this thesis, it is investigated how specific FPD properties, especially related to spatial and temporal addressing and reconstruction, affect the video signal processing chain. A model of the display signal chain is presented, and applied to analyze FPD spatial properties in relation to static resolution. In particular, the effect of the color subpixels, that enable color image reproduction in FPDs, is analyzed. The perceived display resolution is strongly influenced by the color subpixel arrangement. When taken into account in the signal chain, this improves the perceived resolution on FPDs, which clearly outperform CRTs in this respect. The cause and effect of this improvement, also for alternative subpixel arrangements, is studied using the display signal model. However, the resolution increase cannot be achieved without video processing. This processing is efficiently combined with image scaling, which is always required in the FPD display signal chain, resulting in an algorithm called ‘subpixel image scaling’. A comparison of the effects of subpixel scaling on several subpixel arrangements shows that the largest increase in perceived resolution is found for two-dimensional subpixel arrangements. FPDs outperform CRTs with respect to static resolution, but not with respect to ‘dynamic resolution’, i.e. the perceived resolution of moving images. Life-like reproduction of moving images is an important requirement for a TV display, but the temporal properties of FPDs cause artifacts in moving images (‘motion artifacts’), that are not found in CRTs. A model of the temporal aspects of the display signal chain is used to analyze dynamic resolution and motion artifacts on several display types, in particular LCD and PDP. Furthermore, video signal processing algorithms are developed that can reduce motion artifacts and increase the dynamic resolution. The occurrence of motion artifacts is explained by the fact that the human visual system tracks moving objects. This converts temporal effects on the display into perceived spatial effects, that can appear in very different ways. The analysis shows how addressing mismatches in the chain cause motion-dependent misalignment of image data, e.g. resulting in the ‘dynamic false contour’ artifact in PDPs. Also, non-ideal temporal reconstruction results in ‘motion blur’, i.e. a loss of sharpness of moving images, which is typical for LCDs. The relation between motion blur, dynamic resolution, and temporal properties of LCDs is analyzed using the display signal model in the temporal (frequency) domain. The concepts of temporal aperture, motion aperture and temporal display bandwidth are introduced, which enable characterization of motion blur in a simple and direct way. This is applied to compare several motion blur reduction methods, based on modified display design and driving. This thesis further describes the development of several video processing algorithms that can reduce motion artifacts. It is shown that the motion of objects in the image plays an essential role in these algorithms, i.e. they require motion estimation and compensation techniques. In LCDs, video processing for motion artifact reduction involves a compensation for the temporal reconstruction characteristics of the display, leading to the ‘motion compensated inverse filtering’ algorithm. The display chain model is used to analyze this algorithm, and several methods to increase its performance are presented. In PDPs, motion artifact reduction can be achieved with ‘motion compensated subfield generation’, for which an advanced algorithm is presented