Simulation of an electrophotographic halftone reproduction

The robustness of three digital halftoning techniques are simulated for a hypothetical electrophotographic laser printer subjected to dynamic environmental conditions over a copy run of one thousand images. Mathematical electrophotographic models have primarily concentrated on solid area reproductions under time-invariant conditions. The models used in this study predict the behavior of complex image distributions at various stages in the electrophotographic process. The system model is divided into seven subsystems: Halftoning, Laser Exposure, Photoconductor Discharge, Toner Development, Transfer, Fusing, and Image Display. Spread functions associated with laser spot intensity, charge migration, and toner transfer and fusing are used to predict the electrophotographic system response for continuous and halftone reproduction. Many digital halftoning techniques have been developed for converting from continuous-tone to binary (halftone) images. The general objective of halftoning is to approximate the intermediate gray levels of continuous tone images with a binary (black-and-white) imaging system. Three major halftoning techniques currently used are Ordered-Dither, Cluster-Dot, and Error Diffusion. These halftoning algorithms are included in the simulation model. Simulation in electrophotography can be used to better understand the relationship between electrophotographic parameters and image quality, and to observe the effects of time-variant degradation on electrophotographic parameters and materials. Simulation programs, written in FORTRAN and SLAM (Simulation Language Alternative Modeling), have been developed to investigate the effects of system degradation on halftone image quality. The programs have been designed for continuous simulation to characterize the behavior or condition of the electrophotographic system. The simulation language provides the necessary algorithms for obtaining values for the variables described by the time-variant equations, maintaining a history of values during the simulation run, and reporting statistical information on time-dependent variables. Electrophotographic variables associated with laser intensity, initial photoconductor surface voltage, and residual voltage are degraded over a simulated run of one thousand copies. These results are employed to predict the degraded electrophotographic system response and to investigate the behavior of the various halftone techniques under dynamic system conditions. Two techniques have been applied to characterize halftone image quality: Tone Reproduction Curves are used to characterize and record the tone reproduction capability of an electrophotographic system over a simulated copy run. Density measurements are collected and statistical inferences drawn using SLAM. Typically the sharpness of an image is characterized by a system modulation transfer function (MTF). The mathematical models used to describe the subsystem transforms of an electrophotographic system involve non-linear functions. One means for predicting this non-linear system response is to use a Chirp function as the input to the model and then to compare the reproduced modulation to that of the original. Since the imaging system is non-linear, the system response cannot be described by an MTF, but rather an Input Response Function. This function was used to characterize the robustness of halftone patterns at various frequencies. Simulated images were also generated throughout the simulation run and used to evaluate image sharpness and resolution. The data, generated from each of the electrophotographic simulation models, clearly indicates that image stability and image sharpness is not influenced by dot orientation, but rather by the type of halftoning operation used. Error-Diffusion is significantly more variable than Clustered-Dot and Dispersed-Dot at low to mid densities. However, Error-Diffusion is significantly less variable than the ordered dither patterns at high densities. Also, images generated from Error-Diffusion are sharper than those generated using Clustered-Dot and Dispersed-Dot techniques, but the resolution capability of each of the techniques remained the same and degraded equally for each simulation run

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Dithering by Differences of Convex Functions

Motivated by a recent halftoning method which is based on electrostatic principles, we analyse a halftoning framework where one minimizes a functional consisting of the difference of two convex functions (DC). One of them describes attracting forces caused by the image gray values, the other one enforces repulsion between points. In one dimension, the minimizers of our functional can be computed analytically and have the following desired properties: the points are pairwise distinct, lie within the image frame and can be placed at grid points. In the two-dimensional setting, we prove some useful properties of our functional like its coercivity and suggest to compute a minimizer by a forward-backward splitting algorithm. We show that the sequence produced by such an algorithm converges to a critical point of our functional. Furthermore, we suggest to compute the special sums occurring in each iteration step by a fast summation technique based on the fast Fourier transform at non-equispaced knots which requires only Ο(m log(m)) arithmetic operations for m points. Finally, we present numerical results showing the excellent performance of our DC dithering method

A projection method on measures sets

We consider the problem of projecting a probability measure π on a set MN of Radon measures. The projection is defined as a solution of the following variational problem: inf µ∈M N h (µ − π) 2 2 , where h ∈ L 2 (Ω) is a kernel, Ω ⊂ R d and denotes the convolution operator. To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with N dots) or continuous line drawing (representing an image with a continuous line). We provide a necessary and sufficient condition on the sequence (MN) N ∈N that ensures weak convergence of the projections (µ * N) N ∈N to π. We then provide a numerical algorithm to solve a discretized version of the problem and show several illustrations related to computer-assisted synthesis of artistic paintings/drawings

Towards the Control of Electrophotographic-based 3-Dimensional Printing: Image-Based Sensing and Modeling of Surface Defects

Electro-Photography (EP) has been used for decades for fast, cheap, and reliable printing in offices and homes around the world. It has been shown that extending the use of EP for 3D printing is feasible; multiple layered prints are already commercially available (color laser printers) but only for a very limited number of layers. Many of the advantages of laser printing make EP 3D printing desirable including: speed, reliability, selective coloring, ability to print a thermoplastic, possibilities for multi-material printing, ability to print materials not amenable to liquid ink formulations. However, many challenges remain before EP-based 3D printing can be commercially viable. A limiting factor in using the same system architecture as a traditional laser printer is that as the thickness of the part increases, material deposition becomes more difficult with each layer since the increased thickness reduces the field strength. Different system configurations have been proposed where the layer is printed on intermediate stations and are subsequently transferred to the work piece. Layer registration and uniform transfer from the intermediate station become crucial factors in this architecture. At the Print Research and Imaging Systems Modeling (PRISM) Lab preliminary tests have confirmed the feasibility of using EP for Additive Manufacturing (AM). However, similar issues were encountered to those reported in literature as the number of layers increased, resulting in non-uniform brittle 3D structures. The defects were present but not obvious at each layer, and as the part built up, the defects add up and became more obvious. The process, as in many printers, did not include a control system for the ultimate system output (print), and the actuation method (electrostatic charge) is not entirely well characterized or sensed to be used in a control system. This research intends to help the development of a model and an image-based sensing system that can be used for control of material deposition defects for an EP 3D printing process. This research leverages from the expertise at RIT and the Rochester area in Printing, Electrophotography, Rapid Prototyping, Control, and Imaging Sciences

Digital Color Imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided

A projection algorithm on measures sets

We consider the problem of projecting a probability measure $\pi$ on a set $\mathcal{M}_N$ of Radon measures. The projection is defined as a solution of the following variational problem:\begin{equation*}\inf_{\mu\in \mathcal{M}_N} \|h\star (\mu - \pi)\|_2^2,\end{equation*}where $h\in L^2(\Omega)$ is a kernel, $\Omega\subset \R^d$ and $\star$ denotes the convolution operator.To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with $N$ dots) or continuous line drawing (representing an image with a continuous line).We provide a necessary and sufficient condition on the sequence $(\mathcal{M}_N)_{N\in \N}$ that ensures weak convergence of the projections $(\mu^*_N)_{N\in \N}$ to $\pi$.We then provide a numerical algorithm to solve a discretized version of the problem and show several illustrations related to computer-assisted synthesis of artistic paintings/drawings