Victor Ostromoukhov

Fast hierarchical importance sampling with blue noise properties

This paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and these numbers are used to threshold the samples against the local value of the importance density. Pre-computed correction vectors, obtained using relaxation, are used to improve the spectral characteristics of the sampling pattern. The technique is deterministic and very fast; the sampling time grows linearly with the required number of samples. We illustrate our technique with importance-based environment mapping, but the technique is versatile enough to be used in a large variety of computer graphics applications, such as light transport calculations, digital halftoning, geometry processing, and various rendering techniques.

A simple and efficient error-diffusion algorithm

In this contribution, we introduce a new error-diffusion scheme that produces higher quality results. The algorithm is faster than the universally used Floyd-Steinberg algorithm, while maintaining its original simplicity. The efficiency of our algorithm is based on a deliberately restricted choice of the distribution coefficients. Its pleasing nearly artifact-free behavior is due to the off-line minimization process applied to the basic algorithms parameters (distribution coefficients). This minimization brings the Fourier spectra of the selected key intensity levels as close as possible to the corresponding “blue noise” spectra. The continuity of the algorithms behavior across the full range of intensity levels is achieved thanks to smooth interpolation between the distribution coefficients corresponding to key levels. This algorithm is applicable in a wide range of computer graphics applications, where a color quantization algorithm with good visual properties is needed.

Rotated dispersed dither: a new technique for digital halftoning

Rotated dispersed-dot dither is proposed as a new dither technique for digital halftoning. It is based on the discrete one-to-one rotation of a Bayer dispersed-dot dither array. Discrete rotation has the effect of rotating and splitting a significant part of the frequency impulses present in Bayers halftone arrays into many low-amplitude distributed impulses. The halftone patterns produced by the rotated dither method therefore incorporate fewer disturbing artifacts than the horizontal and vertical components present in most of Bayers halftone patterns. In grayscale wedges produced by rotated dither, texture changes at consecutive gray levels are much smoother than in error diffusion or in Bayers 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. Besides their use in black and white printing, rotated dither halftoning techniques have also been successfully applied to in-phase color reproduction on ink-jet printers.

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 engravers work.

Sampling with polyominoes

We present a new general-purpose method for fast hierarchical importance sampling with blue-noise properties. Our approach is based on self-similar tiling of the plane or the surface of a sphere with rectifiable polyominoes. Sampling points are associated with polyominoes, one point per polyomino. Each polyomino is recursively subdivided until the desired local density of samples is reached. A numerical code generated during the subdivision process is used for thresholding to accept or reject the sample. The exact position of the sampling point within the polyomino is determined according to a structural index, which indicates the polyominos local neighborhood. The variety of structural indices and associated sampling point positions are computed during the offline optimization process, and tabulated. Consequently, the sampling itself is extremely fast. The method allows both deterministic and pseudo-non-deterministic sampling. It can be successfully applied in a large variety of graphical applications, where fast sampling with good spectral and visual properties is required. The prime application is rendering.

Blue noise through optimal transport

We present a fast, scalable algorithm to generate high-quality blue noise point distributions of arbitrary density functions. At its core is a novel formulation of the recently-introduced concept of capacity-constrained Voronoi tessellation as an optimal transport problem. This insight leads to a continuous formulation able to enforce the capacity constraints exactly, unlike previous work. We exploit the variational nature of this formulation to design an efficient optimization technique of point distributions via constrained minimization in the space of power diagrams. Our mathematical, algorithmic, and practical contributions lead to high-quality blue noise point sets with improved spectral and spatial properties.

Reproducing color images using custom inks

This dissertation investigates the general problem of reproducing color images on an off-set printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing with inks other than the standard process colors (cyan, magenta, yellow, and black), particularly as the number of inks increases. These challenges include the development of gamut mapping strategies, efficient ink selection strategies, and robust methods for computing color separations in situations that may be either overconstrained or underconstrained. In addition, the demands of high-quality color printing require an accurate physical model of the colors that result from overprinting multiple inks using halftoning, including the effects of trapping, dot gain, and the interreflection of light between ink layers. As we explore these issues, we present new algorithms and physical models that together comprise a system capable of choosing optimal inks for an image and generating the appropriate color separations. Finally, we present some printed examples demonstrating the promise of our techniques.

Spectral analysis and minimization of moire patterns in color separation

Undesired moire patterns may appear in color printing for various reasons. One of the most important reasons is interference between the superposed halftone screens of the different primary colors, due to an improper alignment of their frequencies or orientations. We explain the superposition moire phenomenon using a spectral model that is based of Fourier analysis. After examining the basic case of cosinusoidal grating superpositions we advance, step by step, through the cases of binary gratings, square grids, and dot screens, and discuss the implications on moires between halftone screens in color separation. Then, based on these results, we focus on the moire phenomenon from a different angle , the dynamic point of view: We introduce the noire parameter space and show how changes in the parameters of the superposed layers vary the moire patterns in the superposition. This leads us to an algorithm for moire minimization that provides stable moire-free screen combinations for color separation.

Artistic screening

Artistic screening is a new image reproduction technique incorporating freely created artistic screen elements for generating halftones. Fixed predefined dot contours associated with given intensity levels determine the screen dot shape’s growing behavior. Screen dot contours associated with each intensity level are obtained by interpolation between the fixed predefined dot contours. A user-defined mapping transforms screen elements from screen element definition space to screen element rendition space. This mapping can be tuned to produce various effects such as dilatations, contractions and nonlinear deformations of the screen element grid. Discrete screen elements associated with all desired intensity levels are obtained by rasterizing the interpolated screen dot shapes in the screen element rendition space. Since both the image to be reproduced and the screen shapes can be designed independently, the design freedom offered to artists is very great. The interaction between the image to be reproduced and the screen shapes enables the creation of graphic designs of high artistic quality. Artistic screening is particularly well suited for the reproduction of images on large posters. When looked at from a short distance, the poster’s screening layer may deliver its own message. Furthermore, thanks to artistic screening, both full size and microscopic letters can be incorporated into the image reproduction process. In order to avoid counterfeiting, banknotes may comprise grayscale images with intensity levels produced by microletters of varying size and shape.

Decoupling Strokes and High-Level Attributes for Interactive Traditional Drawing

We present an interactive system, which allows the user to produce drawings in a variety of traditional styles. It takes as input an image and performs semi-automatic tonal modeling. Our system shifts tedious technical aspects to the computer side, while providing the user with freedom on the creative and aesthetic side. The user has low-level control over stroke placement, and high-level control over the tone, smudging and amount of detail. The drawing is rendered in real-time. The basic component is a thresholding model of strokes that can simulate a large class of styles (e.g. pencil, charcoal, engraving). It provides a controllable simulation of the variation of pencil pressure or stroke thickness traditionally used in tonal modeling. We introduce a novel fast equilibration approach for the resulting thresholding structure. The user can specify smudging and control the amount of detail over each part of the drawing.