M-lattice, a system for signal synthesis and processing based on reaction-diffusion

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 148-154).by Alexander Semyon Sherstinsky.Sc.D

GRADE: Gibbs Reaction and Diffusion Equations

Recently there have been increasing interests in using nonlinear PDEs for applications in computer vision and image processing. In this paper, we propose a general statistical framework for designing a new class of PDEs. For a given application, a Markov random field model $p(I)$ is learned according to the minimax entropy principle so that $p(I)$ should characterize the ensemble of images in our application. $P(I)$ is a Gibbs distribution whose energy terms can be divided into two categories. Subsequently the partial differential equations given by gradient descent on the Gibbs potential are essentially reaction-diffusion equations, where the energy terms in one category produce anisotropic diffusion while the inverted energy terms in the second category produce reaction associated with pattern formation. We call this new class of PDEs the Gibbs Reaction And Diffusion Equations-GRADE and we demonstrate experiments where GRADE are used for texture pattern formation, denoising, image enhancement, and clutter removal.Mathematic

Laser scanner jitter characterization, page content analysis for optimal rendering, and understanding image graininess

In Chapter 1, the electrophotographic (EP) process is widely used in imaging systems such as laser printers and office copiers. In the EP process, laser scanner jitter is a common artifact that mainly appears along the scan direction due to the condition of polygon facets. Prior studies have not focused on the periodic characteristic of laser scanner jitter in terms of the modeling and analysis. This chapter addresses the periodic characteristic of laser scanner jitter in the mathematical model. In the Fourier domain, we derive an analytic expression for laser scanner jitter in general, and extend the expression assuming a sinusoidal displacement. This leads to a simple closed-form expression in terms of Bessel functions of the first kind. We further examine the relationship between the continuous-space halftone image and the periodic laser scanner jitter. The simulation results show that our proposed mathematical model predicts the phenomenon of laser scanner jitter effectively, when compared to the characterization using a test pattern, which consists of a flat field with 25% dot coverage However, there is some mismatches between the analytical spectrum and spectrum of the processed scanned test target. We improve experimental results by directly estimating the displacement instead of assuming a sinusoidal displacement. This gives a better prediction of the phenomenon of laser scanner jitter. ^ In Chapter 2, we describe a segmentation-based object map correction algorithm, which can be integrated in a new imaging pipeline for laser electrophotographic (EP) printers. This new imaging pipeline incorporates the idea of object-oriented halftoning, which applies different halftone screens to different regions of the page, to improve the overall print quality. In particular, smooth areas are halftoned with a low-frequency screen to provide more stable printing; whereas detail areas are halftoned with a high-frequency screen, since this will better reproduce the object detail. In this case, the object detail also serves to mask any print defects that arise from the use of a high frequency screen. These regions are defined by the initial object map, which is translated from the page description language (PDL). However, the information of object type obtained from the PDL may be incorrect. Some smooth areas may be labeled as raster causing them to be halftoned with a high frequency screen, rather than being labeled as vector, which would result in them being rendered with a low frequency screen. To correct the misclassification, we propose an object map correction algorithm that combines information from the incorrect object map with information obtained by segmentation of the continuous-tone RGB rasterized page image. Finally, the rendered image can be halftoned by the object-oriented halftoning approach, based on the corrected object map. Preliminary experimental results indicate the benefits of our algorithm combined with the new imaging pipeline, in terms of correction of misclassification errors. ^ In Chapter 3, we describe a study to understand image graininess. With the emergence of the high-end digital printing technologies, it is of interest to analyze the nature and causes of image graininess in order to understand the factors that prevent high-end digital presses from achieving the same print quality as commercial offset presses. We want to understand how image graininess relates to the halftoning technology and marking technology. This chapter provides three different approaches to understand image graininess. First, we perform a Fourier-based analysis of regular and irregular periodic, clustered-dot halftone textures. With high-end digital printing technology, irregular screens can be considered since they can achieve a better approximation to the screen sets used for commercial offset presses. This is due to the fact that the elements of the periodicity matrix of an irregular screen are rational numbers, rather than integers, which would be the case for a regular screen. From the analytical results, we show that irregular halftone textures generate new frequency components near the spectrum origin; and these frequency components are low enough to be visible to the human viewer. However, regular halftone textures do not have these frequency components. In addition, we provide a metric to measure the nonuniformity of a given halftone texture. The metric indicates that the nonuniformity of irregular halftone textures is higher than the nonuniformity of regular halftone textures. Furthermore, a method to visualize the nonuniformity of given halftone textures is described. The analysis shows that irregular halftone textures are grainier than regular halftone textures. Second, we analyze the regular and irregular periodic, clustered-dot halftone textures by calculating three spatial statistics. First, the disparity between lattice points generated by the periodicity matrix, and centroids of dot clusters are considered. Next, the area of dot clusters in regular and irregular halftone textures is considered. Third, the compactness of dot clusters in the regular and irregular halftone textures is calculated. The disparity of between centroids of irregular dot clusters and lattices points generated by the irregular screen is larger than the disparity of between centroids of regular dot clusters and lattices points generated by the regular screen. Irregular halftone textures have higher variance in the histogram of dot-cluster area. In addition, the compactness measurement shows that irregular dot clusters are less compact than regular dot clusters. But, a clustered-dot halftone algorithm wants to produce clustered-dot as compact as possible. Lastly, we exam the current marking technology by printing the same halftone pattern on different substrates, glossy and polyester media. The experimental results show that the current marking technology provides better print quality on glossy media than on polyester media. With above three different approaches, we conclude that the current halftoning technology introduces image graininess in the spatial domain because of the non-integer elements in the periodicity matrix of the irregular screen and the finite addressability of the marking engine. In addition, the geometric characteristics of irregular dot clusters is more irregular than the geometric characteristics of regular dot clusters. Finally, the marking technology provides inconsistency of print quality between substrates

Accurate and Computational: A review of color reproduction in Full-color 3D printing

As functional 3D printing becomes more popular with industrial manufacturing applications, it is time to start discussing high-fidelity appearance reproduction of 3D objects, particularly in faithful colors. To date, there is only limited research on accurate color reproduction and on universal color reproduction method for different color 3D printing materials. To systematically understand colorization principles and color transmission in color 3D printing, an exhaustive literature review is stated to show the state of the art of color reproduction methods for full-color 3D printing, such as optical parameter modeling, colorimetric difference evaluation, computer aided colorization and voxel droplet jetting. Meanwhile, the challenges in developing an accurate color reproduction framework suitable for different printing materials are fully analyzed in this literature review. In full-color 3D printing, coloring, rendering and acquisition constitute the core issues for accurate color reproduction, and their specific concepts are explained in concrete examples. Finally, the future perspectives of a universal color reproduction framework for accurate full-color 3D printing are discussed, which can overcome the limitations of printing materials, combined with computational boundary contoning

Prior Learning and Gibbs Reaction-Diffusion

This article addresses two important themes in early visual computation: it presents a novel theory for learning the universal statistics of natural images, and, it proposes a general framework of designing reaction-diffusion equations for image processing. We studied the statistics of natural images including the scale invariant properties, then generic prior models were learned to duplicate the observed statistics, based on minimax entropy theory. The resulting Gibbs distributions have potentials of the form U(I; Λ, S)=Σα=1kΣx,yλ (α)((F(α)*I)(x,y)) with S={F(1) , F(2),...,F(K)} being a set of filters and Λ={λ(1)(),λ(2)(),...,λ (K)()} the potential functions. The learned Gibbs distributions confirm and improve the form of existing prior models such as line-process, but, in contrast to all previous models, inverted potentials were found to be necessary. We find that the partial differential equations given by gradient descent on U(I; Λ, S) are essentially reaction-diffusion equations, where the usual energy terms produce anisotropic diffusion, while the inverted energy terms produce reaction associated with pattern formation, enhancing preferred image features. We illustrate how these models can be used for texture pattern rendering, denoising, image enhancement, and clutter removal by careful choice of both prior and data models of this type, incorporating the appropriate featuresMathematic

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

Shaped Pupil Lyot Coronagraphs: High-Contrast Solutions for Restricted Focal Planes

Coronagraphs of the apodized pupil and shaped pupil varieties use the Fraunhofer diffraction properties of amplitude masks to create regions of high contrast in the vicinity of a target star. Here we present a hybrid coronagraph architecture in which a binary, hard-edged shaped pupil mask replaces the gray, smooth apodizer of the apodized pupil Lyot coronagraph (APLC). For any contrast and bandwidth goal in this configuration, as long as the prescribed region of contrast is restricted to a finite area in the image, a shaped pupil is the apodizer with the highest transmission. We relate the starlight cancellation mechanism to that of the conventional APLC. We introduce a new class of solutions in which the amplitude profile of the Lyot stop, instead of being fixed as a padded replica of the telescope aperture, is jointly optimized with the apodizer. Finally, we describe shaped pupil Lyot coronagraph (SPLC) designs for the baseline architecture of the Wide-Field Infrared Survey Telescope-Astrophysics Focused Telescope Assets (WFIRST-AFTA) coronagraph. These SPLCs help to enable two scientific objectives of the WFIRST-AFTA mission: (1) broadband spectroscopy to characterize exoplanet atmospheres in reflected starlight and (2) debris disk imaging.Comment: 41 pages, 15 figures; published in the JATIS special section on WFIRST-AFTA coronagraph