Bayesian Dictionary Learning for Single and Coupled Feature Spaces

Over-complete bases offer the flexibility to represent much wider range of signals with more elementary basis atoms than signal dimension. The use of over-complete dictionaries for sparse representation has been a new trend recently and has increasingly become recognized as providing high performance for applications such as denoise, image super-resolution, inpaiting, compression, blind source separation and linear unmixing. This dissertation studies the dictionary learning for single or coupled feature spaces and its application in image restoration tasks. A Bayesian strategy using a beta process prior is applied to solve both problems. Firstly, we illustrate how to generalize the existing beta process dictionary learning method (BP) to learn dictionary for single feature space. The advantage of this approach is that the number of dictionary atoms and their relative importance may be inferred non-parametrically. Next, we propose a new beta process joint dictionary learning method (BP-JDL) for coupled feature spaces, where the learned dictionaries also reflect the relationship between the two spaces. Compared to previous couple feature spaces dictionary learning algorithms, our algorithm not only provides dictionaries that customized to each feature space, but also adds more consistent and accurate mapping between the two feature spaces. This is due to the unique property of the beta process model that the sparse representation can be decomposed to values and dictionary atom indicators. The proposed algorithm is able to learn sparse representations that correspond to the same dictionary atoms with the same sparsity but different values in coupled feature spaces, thus bringing consistent and accurate mapping between coupled feature spaces. Two applications, single image super-resolution and inverse halftoning, are chosen to evaluate the performance of the proposed Bayesian approach. In both cases, the Bayesian approach, either for single feature space or coupled feature spaces, outperforms state-of-the-art methods in comparative domains

Visual-Based error diffusion for printers

An approach for halftoning is presented that incorporates a printer model and also explicitly uses the human visual model. Conventional methods, such as clustered-dot screening or dispersed-dot screening, do not solve the gray-level distortion of printers and just implicitly use the eye as a lowpass filter. Error diffusion accounts for errors when processing subsequent pixels to minimize the overall mean-square errors. Recently developed model-based halftoning technique eliminates the effect of printer luminance distortion, but this method does not consider the filtering action of the eye, that is, some artifacts of standard error diffusion still exist when the printing resolution and view distance change. Another visual error diffusion method incorporates the human visual filter into error diffusion and results in improved noise characteristics and better resolution for structured image regions, but gray levels are still distorted. Experiments prove that human viewers judge the quality of a halftoning image based mainly on the region which exhibits the worst local error, and low-frequency distortions introduced by the halftoning process are responsible for more visually annoying artifacts in the halftone image than high-frequency distortion. Consequently, we adjust the correction factors of the feedback filter by local characteristics and adjust the dot patterns for some gray levels to minimize the visual blurred local error. Based on the human visual model, we obtain the visual-based error diffusion algorithm, and further we will also incorporate the printer model to correct the printing distortion. The artifacts connected with standard error diffusion are expected to be eliminated or decreased and therefore better print quality should be achieved. In addition to qualitative analysis, we also introduce a subjective evaluation of algorithms. The tests show that the algorithms developed here have improved the performance of error diffusion for printers

Taming Reversible Halftoning via Predictive Luminance

Traditional halftoning usually drops colors when dithering images with binary dots, which makes it difficult to recover the original color information. We proposed a novel halftoning technique that converts a color image into a binary halftone with full restorability to its original version. Our novel base halftoning technique consists of two convolutional neural networks (CNNs) to produce the reversible halftone patterns, and a noise incentive block (NIB) to mitigate the flatness degradation issue of CNNs. Furthermore, to tackle the conflicts between the blue-noise quality and restoration accuracy in our novel base method, we proposed a predictor-embedded approach to offload predictable information from the network, which in our case is the luminance information resembling from the halftone pattern. Such an approach allows the network to gain more flexibility to produce halftones with better blue-noise quality without compromising the restoration quality. Detailed studies on the multiple-stage training method and loss weightings have been conducted. We have compared our predictor-embedded method and our novel method regarding spectrum analysis on halftone, halftone accuracy, restoration accuracy, and the data embedding studies. Our entropy evaluation evidences our halftone contains less encoding information than our novel base method. The experiments show our predictor-embedded method gains more flexibility to improve the blue-noise quality of halftones and maintains a comparable restoration quality with a higher tolerance for disturbances.Comment: to be published in IEEE Transactions on Visualization and Computer Graphic

Virtuális világok szimulációja és megjelenítése = Simulation-Rendering in Virtual Reality Systems

1. A Navier-Stokes egyenletek Lagrange-i és Euler-i nézőpontjának masszívan párhuzamos architektúrán végrehajtható hatékony megoldási algoritmusa folyadékszimulációhoz. A folyadék szabályozása, azaz előírt sűrűségfüggvény felé terelése. 2. Formális nyelvek, L-rendszerek párhuzamos kiértékelési algoritmusa és alkalmazás ""végtelen"" városok és növények szimulációjára. 3. Térfogati modellekben a fényterjedés szimuláció szabad úthossz mintavételezésének hatékony megoldása, amely heterogén közegben extrém nagy felbontásokra (pl. 32 ezer köbös) is működik. 4. Térfogati modellek véges elemes megoldásához az iterációt gyorsító kezdeti becslő kialakítása. 5. A fotonterjedés szimulációjának felhasználása inverz feladatokban, pozitron emissziós tomográfiához rekonstrukciós eljárások kidolgozása. 6. A Koksma-Hlawka egyenlőtlenség általánosítása nem egyenletes minták esetére és ez alapján delta-szigma modulációs módszer kidolgozása fontosság szerinti mintavételezéshez. 7. Az ambiens takarási módszer új geometriai értelmezésének megalkotása és új, hatékony módszerek kidolgozása. 8. Out-of-core vizualizáció sugárkövetés alapon, több száz millió háromszögből álló modellek interaktív bejárása. 9. Az NPR algoritmusoknál a 3D konzisztencia biztosítása, és animációs algoritmusok létrehozása. | 1. Algorithms for the solution of the Navier-Stokes equations of fluids on massively parallel hardware, taking both the Eulerian and Lagrangian viewpoints. Solution of the fluid control problem. 2. Parallel evaluation of L-systems and its application to procedural infinite virtual worlds. 3. Free path sampling method for high resolution, heterogeneous participating media. 4. Bootstrapping the iterative solver of finite element approaches for light transport in participating media. 5. Development of a parallel solver for the photon transport problem and its application in positron emission tomography. 6. Generalization of Koksma-Hlawka inequality and the development of a delta-sigma type importance sampling. 7. New geometric interpretation for ambient occlusion and novel computation algorithms. 8. Out-of-core visualization methods based on ray tracing. 9. Solution of the 3D consistency problem of NPR and extension to animation sequences

Threshold modulation in 1-D error diffusion

Error diffusion (ED) is widely used in digital imaging as a binarization process which preserves fine detail and results in pleasant images. The process resembles the human visual system in that it exhibits an intrinsic edge enhancement An additional extrinsic edge enhancement can be controlled by varying the threshold. None of these characteristics has yet been fully explained due to the lack of a suitable mathematical model of the algorithm. The extrinsic sharpening introduced in 1-D error diffusion is the subject of this thesis. An available pulse density modulation(PDM) model generated from a frequency modulation is used to gain a better understanding of variables in ED. As a result, threshold variation fits the model as an additional phase modulation. Equivalent images are obtained by applying ED with threshold modulation or by preprocessing an image with an appropriate convolution mask and subsequently running standard ED

Perceptual Error Optimization for {Monte Carlo} Rendering

Realistic image synthesis involves computing high-dimensional light transport integrals which in practice are numerically estimated using Monte Carlo integration. The error of this estimation manifests itself in the image as visually displeasing aliasing or noise. To ameliorate this, we develop a theoretical framework for optimizing screen-space error distribution. Our model is flexible and works for arbitrary target error power spectra. We focus on perceptual error optimization by leveraging models of the human visual system's (HVS) point spread function (PSF) from halftoning literature. This results in a specific optimization problem whose solution distributes the error as visually pleasing blue noise in image space. We develop a set of algorithms that provide a trade-off between quality and speed, showing substantial improvements over prior state of the art. We perform evaluations using both quantitative and perceptual error metrics to support our analysis, and provide extensive supplemental material to help evaluate the perceptual improvements achieved by our methods

Digital halftoning and the physical reconstruction function

Originally presented as author's thesis (Ph. D.--Massachusetts Institute of Technology), 1986.Bibliography: p. 397-405."This work has been supported by the Digital Equipement Corporation."by Robert A. Ulichney

Perceptual error optimization for Monte Carlo rendering

Realistic image synthesis involves computing high-dimensional light transport integrals which in practice are numerically estimated using Monte Carlo integration. The error of this estimation manifests itself in the image as visually displeasing aliasing or noise. To ameliorate this, we develop a theoretical framework for optimizing screen-space error distribution. Our model is flexible and works for arbitrary target error power spectra. We focus on perceptual error optimization by leveraging models of the human visual system's (HVS) point spread function (PSF) from halftoning literature. This results in a specific optimization problem whose solution distributes the error as visually pleasing blue noise in image space. We develop a set of algorithms that provide a trade-off between quality and speed, showing substantial improvements over prior state of the art. We perform evaluations using both quantitative and perceptual error metrics to support our analysis, and provide extensive supplemental material to help evaluate the perceptual improvements achieved by our methods

Rethinking PRL: A Multiscale Progressively Residual Learning Network for Inverse Halftoning

Image inverse halftoning is a classic image restoration task, aiming to recover continuous-tone images from halftone images with only bilevel pixels. Because the halftone images lose much of the original image content, inverse halftoning is a classic ill-problem. Although existing inverse halftoning algorithms achieve good performance, their results lose image details and features. Therefore, it is still a challenge to recover high-quality continuous-tone images. In this paper, we propose an end-to-end multiscale progressively residual learning network (MSPRL), which has a UNet architecture and takes multiscale input images. To make full use of different input image information, we design a shallow feature extraction module to capture similar features between images of different scales. We systematically study the performance of different methods and compare them with our proposed method. In addition, we employ different training strategies to optimize the model, which is important for optimizing the training process and improving performance. Extensive experiments demonstrate that our MSPRL model obtains considerable performance gains in detail restoration