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

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

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