Convex Dynamics and Applications

This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. \textit{Digital halftoning} is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A corollary of the theorem is that for \textit{error diffusion}, one of the methods of digital halftoning, averages of colors of the printed dots converge to averages of the colors taken from the same dots of the actual images. Digital printing is a special case of a much wider class of scheduling problems to which the theorem applies. Convex dynamics has roots in classical areas of mathematics such as symbolic dynamics, Diophantine approximation, and the theory of uniform distributions.Comment: LaTex with 9 PostScript figure

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

Clustered-dot periodic halftone screen design and ICC profile color table compression

This dissertation studies image quality problems associated with rendering images in devices like printing or displaying. It mainly includes two parts: clustered-dot periodic halftone screen design, and color table compression. Screening is a widely used halftoning method. As a consequence of the lower resolution of digital presses and printers, the number of printer-addressable dots or holes in each microcell may be too few to provide the requisite number of tone lev- els between paper white and full colorant coverage. To address this limitation, the microcells can be grouped into supercells. The challenge is then to determine the desired supercell shape and the order in which dots are added to the microcell. Using DBS to determine this order results in a very homogeneous halftone pattern. To simplify the design and implementation of supercell halftone screens, it is common to repeat the supercell to yield a periodically repeating rectangular block called the basic screen block (BSB). While applying DBS to design a dot-cluster growth order- ing for the entire BSB is simpler to implement than is the application of DBS to the single non-rectangular supercell, it is computationally very inefficient. To achieve a more efficient way to apply DBS to determine the microcell sequence, we describe a procedure for design of high-quality regular screens using the non-rectangular super- cell. A novel concept the Elementary Periodicity Set is proposed to characterize how a supercell is developed. After a supercell is set, we use DBS to determine the micro-cell sequence within the supercell. We derive the DBS equations for this situation, and show that it is more efficient to implement. Then, we mainly focus on the regular and irregular screen design. With digital printing systems, the achievable screen angles and frequencies are limited by the finite addressability of the marking engine. In order for such screens to generate dot clusters in which each cluster is identical, the elements of the periodicity matrix must be integer-valued, when expressed in units of printer-addressable pixels. Good approximation of the screen sets result in better printing quality. So to achieve a better approximation to the screen sets used for commercial offset printing, irregular screens can be used. With an irregular screen, the elements of the periodicity matrix are rational numbers. In this section, first we propose a procedure to generate regular screens starting from midtone level. And then we describe a procedure for design of high-quality irregular screens based on the regular screen design method. We then propose an algorithm to determine how to add dots from midtone to shadow and how to remove dots from midtone to highlight. We present experimental results illustrating the quality of the halftones resulting from our design procedure by comparing images halftoned with irregular screens using our approach and a template-based approach. We also present the evaluation of the smoothness and improvement of the proposed methods. In the next part, we study another quality problem: ICC profile color table compression. ICC profiles are widely used to provide transformations between different color spaces in different devices. The color look-up tables (CLUTs) in the profiles will increase the file sizes when embedded in color documents. In this chapter, we discuss compression methods that decrease the storage cost of the CLUTs. For DCT compression method, a compressed color table includes quantized DCT coefficients for the color table, the additional nodes with large color difference, and the coefficients bit assignment table. For wavelet-based compression method, a compressed color table includes output of the wavelet encoding method, and the additional nodes with large color difference. These methods support lossy table compression to minimize the network traffic and delay, and also achieves relatively small maximum color difference

Optimized image Embedding in QR Code with Secure Wireless Network

QR pictures familiar a modified procedure with insert QR codes into shading pictures with constrained probability of distinguishing proof oversight. Quick response (QR) codes have immediately ascended as a comprehensively used stock after and conspicuous evidence procedure in transport, collecting, and retail business ventures. QR codes are used as a part of a variety of employments, for instance, begin phone calls,download singular card information, getting to destinations, post information to casual groups, impersonate recordings or open substance documents. To direct the visual winding of the QR picture, the figuring utilizes half molding cloak for the decision of changed pixels and nonlinear programming systems to locally propel brilliance levels. A tractable model for the probability of error is made and models of the human visual system are considered in the quality metric used to propel the radiance levels of the QR image.Experimental results exhibit the exquisite defilement of the unwinding rate and the perceptual quality as a limit the embedding parameters

New methods for digital halftoning and inverse halftoning

Halftoning is the rendition of continuous-tone pictures on bi-level displays. Here we first review some of the halftoning algorithms which have a direct bearing on our paper and then describe some of the more recent advances in the field. Dot diffusion halftoning has the advantage of pixel-level parallelism, unlike the popular error diffusion halftoning method. We first review the dot diffusion algorithm and describe a recent method to improve its image quality by taking advantage of the Human Visual System function. Then we discuss the inverse halftoning problem: The reconstruction of a continuous tone image from its halftone. We briefly review the methods for inverse halftoning, and discuss the advantages of a recent algorithm, namely, the Look Up Table (LUT)Method. This method is extremely fast and achieves image quality comparable to that of the best known methods. It can be applied to any halftoning scheme. We then introduce LUT based halftoning and tree-structured LUT (TLUT)halftoning. We demonstrate how halftone image quality in between that of error diffusion and Direct Binary Search (DBS)can be achieved depending on the size of tree structure in TLUT algorithm while keeping the complexity of the algorithm much lower than that of DBS

Studies on Imaging System and Machine Learning: 3D Halftoning and Human Facial Landmark Localization

In this dissertation, studies on digital halftoning and human facial landmark localization will be discussed. 3D printing is becoming increasingly popular around the world today. By utilizing 3D printing technology, customized products can be manufactured much more quickly and efficiently with much less cost. However, 3D printing still suffers from low-quality surface reproduction compared with 2D printing. One approach to improve it is to develop an advanced halftoning algorithm for 3D printing. In this presentation, we will describe a novel method to 3D halftoning that can cooperate with 3D printing technology in order to generate a high-quality surface reproduction. In the second part of this report, a new method named direct element swap to create a threshold matrix for halftoning is proposed. This method directly swaps the elements in a threshold matrix to find the best element arrangement by minimizing a designated perceived error metric. Through experimental results, the new method yields halftone quality that is competitive with the conventional level-by-level matrix design method. Besides, by using direct element swap method, for the first time, threshold matrix can be designed through being trained with real images. In the second part of the dissertation, a novel facial landmark detection system is presented. Facial landmark detection plays a critical role in many face analysis tasks. However, it still remains a very challenging problem. The challenges come from the large variations of face appearance caused by different illuminations, different facial expressions, different yaw, pitch and roll angles of heads and different image qualities. To tackle this problem, a novel coarse-to-fine cascaded convolutional neural network system for robust facial landmark detection of faces in the wild is presented. The experiment result shows our method outperforms other state-of-the-art methods on public test datasets. Besides, a frontal and profile landmark localization system is proposed and designed. By using a frontal/profile face classifier, either frontal landmark configuration or profile landmark configuration is employed in the facial landmark prediction based on the input face yaw angle

Design of Farthest-Point Masks for Image Halftoning

In an earlier paper, we briefly presented a new halftoning algorithm called farthest-point halftoning. In the present paper, this method is analyzed in detail, and a novel dispersion measure is defined to improve the simplicity and flexibility of the result. This new stochastic screen algorithm is loosely based on Kang's dispersed-dot ordered dither halftone array construction technique used as part of his microcluster halftoning method. Our new halftoning algorithm uses pixelwise measures of dispersion based on one proposed by Kang which is here modified to be more effective. In addition, our method exploits the concept of farthest-point sampling (FPS), introduced as a progressive irregular sampling method by Eldar et al. but uses a more efficient implementation of FPS in the construction of the dot profiles. The technique we propose is compared to other state-of-the-art dither-based halftoning methods in both qualitative and quantitative manners