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

Improved methods and system for watermarking halftone images

Watermarking is becoming increasingly important for content control and authentication. Watermarking seamlessly embeds data in media that provide additional information about that media. Unfortunately, watermarking schemes that have been developed for continuous tone images cannot be directly applied to halftone images. Many of the existing watermarking methods require characteristics that are implicit in continuous tone images, but are absent from halftone images. With this in mind, it seems reasonable to develop watermarking techniques specific to halftones that are equipped to work in the binary image domain. In this thesis, existing techniques for halftone watermarking are reviewed and improvements are developed to increase performance and overcome their limitations. Post-halftone watermarking methods work on existing halftones. Data Hiding Cell Parity (DHCP) embeds data in the parity domain instead of individual pixels. Data Hiding Mask Toggling (DHMT) works by encoding two bits in the 2x2 neighborhood of a pseudorandom location. Dispersed Pseudorandom Generator (DPRG), on the other hand, is a preprocessing step that takes place before image halftoning. DPRG disperses the watermark embedding locations to achieve better visual results. Using the Modified Peak Signal-to-Noise Ratio (MPSNR) metric, the proposed techniques outperform existing methods by up to 5-20%, depending on the image type and method considered. Field programmable gate arrays (FPGAs) are ideal for solutions that require the flexibility of software, while retaining the performance of hardware. Using VHDL, an FPGA based halftone watermarking engine was designed and implemented for the Xilinx Virtex XCV300. This system was designed for watermarking pre-existing halftones and halftones obtained from grayscale images. This design utilizes 99% of the available FPGA resources and runs at 33 MHz. Such a design could be applied to a scanner or printer at the hardware level without adversely affecting performance

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

Innovations in the Analysis of Chandra-ACIS Observations

As members of the instrument team for the Advanced CCD Imaging Spectrometer (ACIS) on NASA's Chandra X-ray Observatory and as Chandra General Observers, we have developed a wide variety of data analysis methods that we believe are useful to the Chandra community, and have constructed a significant body of publicly-available software (the ACIS Extract package) addressing important ACIS data and science analysis tasks. This paper seeks to describe these data analysis methods for two purposes: to document the data analysis work performed in our own science projects, and to help other ACIS observers judge whether these methods may be useful in their own projects (regardless of what tools and procedures they choose to implement those methods). The ACIS data analysis recommendations we offer here address much of the workflow in a typical ACIS project, including data preparation, point source detection via both wavelet decomposition and image reconstruction, masking point sources, identification of diffuse structures, event extraction for both point and diffuse sources, merging extractions from multiple observations, nonparametric broad-band photometry, analysis of low-count spectra, and automation of these tasks. Many of the innovations presented here arise from several, often interwoven, complications that are found in many Chandra projects: large numbers of point sources (hundreds to several thousand), faint point sources, misaligned multiple observations of an astronomical field, point source crowding, and scientifically relevant diffuse emission.Comment: Accepted by the ApJ, 2010 Mar 10 (\#343576) 39 pages, 16 figure

High Redshift Supernovae in the Hubble Deep Field

Two supernovae detected in the Hubble Deep Field using the original December 1995 epoch and data from a shorter (63000 s in F814W) December 1997 visit with HST are discussed. The supernovae (SNe) are both associated with distinct galaxies at redshifts of 0.95 (spectroscopic) from Cohen etal. (1996) and 1.32 (photometric) from the work of Fernandez-Soto, Lanzetta, and Yahil (1998). These redshifts are near, in the case of 0.95, and well beyond for 1.32 the greatest distance reported previously for SNe. We show that our observations are sensitive to SNe to z < 1.8 in either epoch for an event near peak brightness. Detailed simulations are discussed that quantify the level at which false events from our search phase would start to to arise, and the completeness of our search as a function of both SN brightness and host galaxy redshift. The number of Type Ia and Type II SNe expected as a function of redshift in the two HDF epochs are discussed in relation to several published predictions and our own detailed calculations. A mean detection frequency of one SN per epoch for the small HDF area is consistent with expectations from current theory.Comment: 62 pages, 17 figures, ApJ 1999 in pres

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