Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective

In this report, we revisit the work of Pilleboue et al. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a more general theory. We review the related representation theory and show how it can be used to derive a closed-form solution

Reproduction couleur par trames irrégulières et semi-régulières

In the printing industry, one of the most common methods for reproducing halftone images using bilevel printing devices is clustered-dot ordered dithering. The images produced using this method are quite faithful to the original and are visually pleasing. Nevertheless, only rational angles are attainable with clustered-dot dithering, due to the discrete nature of the grids. This phenomenon can become detrimental in the case of four-color printing, when different screen angles and maybe even different screen frequencies are used for separate color planes, thus producing a so-called Moiré phenomenon. Another important drawback, the so-called banding or contouring effect, is related to the limited area of basic screen elements used in traditional dithering. In order to deal with these problems, we have developed, within the scope of our research, several new techniques for digital halftoning: (1) pseudo-random halftone screening, (2) a new method for generating clustered-dot halftone images having a number of reproducible gray or colour levels which is independent of the screen element size (CombiScreen), (3) rotated clustered-dot dithering, based on discrete one-to-one rotation, and (4) rotated dispersed-dot dither. A new method of pseudo-random halftone screening is described. It starts by obtaining the quasi-random distribution of tile centers according to some well-defined spectral characteristics. We then obtain the desired tesselation of the output device space by applying the Voronoi polygonization process. Then, an analytic black-dot curve is calculated according to the resampled input signal level and the area of each given tile. This analytic curve is scan-converted to obtain the blackened pixels. In the second approach, we associate threshold values to all pixels inside every tile according to some specially tailored analytic spot function. Then, the standard threshold comparison process is applied. Unlike known error-diffusion techniques, the pseudo-random halftone screening technique can be applied to a high resolution printing process. The characteristic screen element size can be properly chosen so as to ensure the best trade-off between the printing process constraints and the most precise printing. The described halftone algorithm seems to be appropriate for high-resolution color and black&white devices (above 1000 dpi). A new method (CombiScreen) is proposed for generating clustered-dot halftone images on raster printing devices having a number of reproducible gray or colour levels which is independent of the screen element size. The dither tiles generated by this method may contain several screen elements having any rational orientation and size. Threshold values are distributed among the cells of the dither tile so as to produce a large range of gray values, while at the same time preserving the clustered-dot behavior of individual screen elements. When rendering images at smoothly increasing intensity levels, this new method generates few contouring effects and other visible artifacts. The method works equally well for quadratic, rectangular, parallelogram and hexagonally shaped screen elements. Resulting dither tiles are generally either of parallelogram or of hexagonal shape. Since CombiScreen enables the screen dot frequency or orientation to be chosen independently of the number of gray levels, it has proven to be specially effective when printing at resolutions between 150 to 600 dpi with ink jet printers and at resolutions between 300 and 1200 dpi with xerographic printers. A new operator of discrete one-to-one rotation is described. It offers means previously unknown in the art for generating rotated screens which approximate irrational angles with high-precision, producing much less disturbing interferences and artifacts than other methods. Therefore, a carefully prepared dither tile incorporating screen elements with the desired period, initial orientation, and dither threshold values defining their screen dot shape growth behavior can be rotated by discrete one-to-one rotation and keep the desired screen element period, the number of cells per screen element and the threshold values associated with each screen element cell, thereby preserving the screen dot shape growth behavior of the original dither tile. Several different discrete one-to-one rotation variants are described: a small angle rotation technique valid for a subset of rational rotation angles, a rigid band technique and a technique based on discrete shearing transformations. The high-quality of the so rotated dither tile is due to the fact that discrete one-to-one rotation preserves the exact number of elementary cells per screen element and their exact dither threshold values. The described method provides a new range of solutions for obtaining high-quality digital angled halftone screens. High-quality solutions can be found for generating three digital angled halftone screens, each 30° apart from each other, as known from traditional photographic colour screening techniques. Further solutions minimizing Moiré effects may be obtained by halftone screens whose first order frequency component vectors sum up to zero. This new method has turned out to be particularly effective when printing with color ink jet printers at resolutions between 150 and 800 dpi as well as with xerographic printers at resolutions between 300 and 1200 dpi. Rotated dispersed-dot dither is based on the discrete one-to-one rotation of a Bayer dispersed-dot dither array. The halftone patterns produced by the rotated dither method therefore incorporate fewer disturbing artifacts than the horizontal and vertical components present in most of Bayer's halftone patterns. In grayscale wedges produced by rotated dither, texture changes at consecutive gray levels are much smoother than in error diffusion or in Bayer's dispersed-dot dither methods, thereby avoiding contouring effects. Due to its semi-clustering behavior at mid-tones, rotated dispersed-dot dither exhibits an improved tone reproduction behavior on printers having a significant dot gain, while maintaining the high detail rendition capabilities of dispersed-dot halftoning algorithms. This technique has successfully been applied to in-phase color reproduction on ink-jet printers as well as to black and white reproduction on laser printers

E. Ju. Zubkova, L. P. Košeleva, G. A. Kuznecova, A. I. Minjuk, L. A. Rogovaja, eds., Sovetskaja žizn´, 1945-1953

C’est « le quotidien soviétique, la vie de tous les jours des gens ordinaires » (p. 5), qui fait l’objet de ce recueil de documents. Objet familier pour Elena Zubkova, qui lui a déjà consacré plusieurs études, mais objet nouveau, d’après les auteurs, pour un recueil de ce type. En effet, refléter le quotidien d’une époque à travers des documents d’archives est une tâche délicate qui peut se heurter à un certain nombre de problèmes épistémologiques. Premièrement, un tel projet suppose une visé..

Lada Vladimirovna Silina, Nastroenija sovetskogo studenčestva, 1945-1964

Le titre de l’ouvrage semble l’inscrire d’emblée dans le courant de l’historiographie actuelle, et ce pour plusieurs raisons. Axé sur un groupe de population défini et facile à cerner, ce travail fait partie des études sur le quotidien, sur le vécu d’individus ordinaires, qui permettent de compléter les travaux d’histoire politique. Cette démarche implique également une ouverture de l’histoire à des méthodes empruntées à d’autres sciences sociales. Le terme d’« état d’esprit » va également da..

Chromaticity Gamut Enhancement by Heptatone Multi-Color Printing

The present paper studies the chromaticity gamut of multi-color printing processes. Heptatone (7-color) printing - the most promising variant of multi-color printing - offers a significantly larger gamut than a conventional CMYK printing process, approaching CRT and film gamuts. The behavior of the process in the device-independent CIE-XYZ and CIE-L*u*v* colorimetric spaces is explored using the compound Neugebauer model developped for this purpose. A simple and straightforward Moiri-free separation process is proposed. The strong point of the proposed separation process is the fact that only 3 different screen layers are needed for any odd number of basic colors including black

Pseudo-Random Halftone Screening for Colour and Black&White Printing

The idea of using pseudo-random spatial structures in graphic arts (color and black & white rendering algorithms) was suggested by psychologists and biologists about ten years ago. They observed that some natural pseudo-random structures such as the spatial distribution of receptors in the human retina play an important part in the perceptual process. Our modelization of pseudo-random spatial structures resembles the retinal mosaic. It starts by obtaining the quasi-random distribution of tile centers according to some well-defined spectral characteristics. We then obtain the desired tesselation of the output device space by applying the Voronoi polygonization process. Two slightly different approaches to the output image computation are being explored. In the first approach, an analytic black-dot curve is calculated according to the resampled input signal level and the area of each given tile. This analytic curve is scan-converted to obtain the blackened pixels. In the second approach, we associate threshold values to all pixels inside every tile according to some specially tailored analytic spot function. Then, the standard threshold comparison process is applied

Digital facial engraving

This contribution introduces the basic techniques for digital facial engraving, which imitates traditional copperplate engraving. Inspired by traditional techniques, we first establish a set of basic rules thanks to which separate engraving layers are built on the top of the original photo. Separate layers are merged according to simple merging rules and according to range shift/scale masks specially introduced for this purpose. We illustrate the introduced technique by a set of black/white and color engravings, showing different features such as engraving-specific image enhancements, mixing different regular engraving lines with mezzotint, irregular perturbations of engraving lines etc. We introduce the notion of engraving style which comprises a set of separate engraving layers together with a set of associated range shift/scale masks. The engraving style helps to port the look and feel of one engraving to another. Once different libraries of pre-defined mappable engraving styles and an appropriate user interface are added to the basic system, producing a decent gravure starting from a simple digital photo will be a matter of seconds. The engraving technique described in this contribution opens new perspectives for digital art, adding unprecedented power and precision to the engraver's work

Efficient product sampling using hierarchical thresholding

We present an efficient method for importance sampling the product of multiple functions. Our algorithm computes a quick approximation of the product on the fly, based on hierarchical representations of the local maxima and averages of the individual terms. Samples are generated by exploiting the hierarchical properties of many low-discrepancy sequences, and thresholded against the estimated product. We evaluate direct illumination by sampling the triple product of environment map lighting, surface reflectance, and a visibility function estimated per pixel. Our results show considerable noise reduction compared to existing state-of-the-art methods using only the product of lighting and BRD