Blue-noise multitone dithering.

The introduction of the blue-noise spectra-high-frequency white noise with minimal energy at low frequencies-has had a profound impact on digital halftoning for binary display devices, such as inkjet printers, because it represents an optimal distribution of black and white pixels producing the illusion of a given shade of gray. The blue-noise model, however, does not directly translate to printing with multiple ink intensities. New multilevel printing and display technologies require the development of corresponding quantization algorithms for continuous tone images, namely multitoning. In order to define an optimal distribution of multitone pixels, this paper develops the theory and design of multitone, blue-noise dithering. Here, arbitrary multitone dot patterns are modeled as a layered superposition of stack-constrained binary patterns. Multitone blue-noise exhibits minimum energy at low frequencies and a staircase-like, ascending, spectral pattern at higher frequencies. The optimum spectral profile is described by a set of principal frequencies and amplitudes whose calculation requires the definition of a spectral coherence structure governing the interaction between patterns of dots of different intensities. Efficient algorithms for the generation of multitone, blue-noise dither patterns are also introduced.

A class of authentication digital watermarks for secure multimedia communication.

A new approach to digital signatures for imaging, which adapts well to multimedia communications in lossy channels is introduced. Rather than attaching the signature's bit-string as a file-header, it is invisibly etched into the image using a new watermarking algorithm. The watermark is "nonfragile," tolerating small distortions but not malicious tampering aimed at modifying the image's content. In particular, the rank-order relationship in local areas throughout the lowest level of the DWT is exploited to encode the watermark. An edge-based message digest is used. The signature is in the form of binary data and the wavelet decomposition coefficients are modified according to this binary sequence. The signature is also embedded and tested within the SPIHT compression algorithm. The information capacity is studied and the experimental results confirm a logarithm relation between the bit rate and the quantization level, which is similar to the Shannon's capacity theorem. Experiments are performed to examine the signature's transparency and robustness.

Optimal digital filtering for tremor suppression.

Remote manually operated tasks such as those found in teleoperation, virtual reality, or joystick-based computer access, require the generation of an intermediate electrical signal which is transmitted to the controlled subsystem (robot arm, virtual environment, or a cursor in a computer screen). When human movements are distorted, for instance, by tremor, performance can be improved by digitally filtering the intermediate signal before it reaches the controlled device. This paper introduces a novel tremor filtering framework in which digital equalizers are optimally designed through pursuit tracking task experiments. Due to inherent properties of the man-machine system, the design of tremor suppression equalizers presents two serious problems: 1) performance criteria leading to optimizations that minimize mean-squared error are not efficient for tremor elimination and 2) movement signals show ill-conditioned autocorrelation matrices, which often result in useless or unstable solutions. To address these problems, a new performance indicator in the context of tremor is introduced, and the optimal equalizer according to this new criterion is developed. Ill-conditioning of the autocorrelation matrix is overcome using a novel method which we call pulled-optimization. Experiments performed with artificially induced vibrations and a subject with Parkinson's disease show significant improvement in performance. Additional results, along with MATLAB source code of the algorithms, and a customizable demo for PC joysticks, are available on the Internet at http:¿tremor-suppression.com.

Digital color halftoning with generalized error diffusion and multichannel green-noise masks.

In this paper, we introduce two novel techniques for digital color halftoning with green-noise--stochastic dither patterns generated by homogeneously distributing minority pixel clusters. The first technique employs error diffusion with output-dependent feedback where, unlike monochrome image halftoning, an interference term is added such that the overlapping of pixels of different colors can be regulated for increased color control. The second technique uses a green-noise mask, a dither array designed to create green-noise halftone patterns, which has been constructed to also regulate the overlapping of different colored pixels. As is the case with monochrome image halftoning, both techniques are tunable, allowing for large clusters in printers with high dot-gain characteristics, and small clusters in printers with low dot-gain characteristics.

Order statistic filter banks.

Filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. It is well known, however, that linear filters may have less than satisfactory performance whenever the underlying processes are non-Gaussian. We introduce the nonlinear class of order statistic (OS) filter banks that exploit the spectral characteristics of the input signal as well as its rank-ordering structure. The attained subband signals provide frequency and rank information in a localized time interval. OS filter banks can lead to significant gains over linear filter banks, particularly when the input signals contain abrupt changes and details, as is common with image and video signals. OS filter banks are formed using traditional linear filter banks as fundamental building blocks. It is shown that OS filter banks subsume linear filter banks and that the latter are obtained by simple linear transformations of the former. To illustrate the properties of OS filter banks, we develop simulations showing that the learning characteristics of the LMS algorithm, which are used to optimize the weight taps of OS filters, can be significantly improved by performing the adaptation in the OS subband domain.

Truncation artifacts in tomographic reconstructions from projections.

The artifacts in tomographic reconstructions from truncated sets of projections are analyzed. The shift-variant impulse response of the tomographic system for parallel-beam geometry is derived. A number of propositions are made describing the observed artifacts. A graphical scheme for the prediction of the location and shape of the truncation artifacts is presented and applied to reconstructions from simulated projections. The artifact analysis is applied to images obtained with the commonly used convolution backprojection reconstruction algorithms, and it is extended to reconstructions from fan-beam projections. The analysis is performed for the continuous imaging domain so as to separate the clipping artifacts clearly from those attributed to the digital implementation of the reconstruction algorithms.

Permutation weighted order statistic filter lattices.

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window. Hence, PWOS filters are in essence time-varying WOS filters. By varying the amount of temporal-rank order information used in selecting the output for a given observation window size, we obtain a wide range of filters that are shown to comprise a complete lattice structure. At the simplest level in the lattice, PWOS filters reduce to the well-known WOS filter, but for higher levels in the lattice, the obtained selection filters can model complex nonlinear systems and signal distortions. It is shown that PWOS filters are realizable by a N! piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory. Simulations are included to show the advantages of PWOS filters for the processing of image and video signals.

Inverse halftoning using binary permutation filters.

The problem of reconstructing a continuous-tone image given its ordered dithered halftone or its error-diffused halftone image is considered. We develop a modular class of nonlinear filters that can reconstruct the continuous-tone information preserving image details and edges that provide important visual cues. The proposed nonlinear reconstruction algorithms, denoted as binary permutation filters, are based on the space and rank orderings of the halftone samples provided by the multiset permutation of the "on" pixels in a halftone observation window. For a given window size, we obtain a wide range of filters by varying the amount of space-rank ordering information utilized in the estimate. For image reconstructions from ordered dithered halftones, we develop periodically space-varying filters that can account for the periodical nature of the underlying screening process. A class of suboptimal but simpler space-invariant reconstruction filters are also proposed and tested. Constrained LMS type algorithms are employed for the design of reconstruction filters that minimize the reconstruction mean squared error. We present simulations showing that binary permutation filters are modular, robust to image source characteristics, and that they produce high visual quality image reconstruction.

Synthetic scanner arrays in tomographic reconstructionsfrom fan- and cone-beam projections.

A deterministic method for artifact-free reconstruction from truncated sets of fan-beam projections thatextends the artifact-free zone of fan-beam scanners is presented. Truncated partial sets of projectionsare merged into a complete virtual set of projections before reconstruction through synthetic scannerarrays. The reconstruction from the virtual set of projections yields the artifact-free representation ofthe whole object needed for evaluation of its global structure. The extent of the artifact-free zone in reconstructions from cone-beam projections is evaluated. The concept of synthetic linear and circular scanner arrays for reconstruction from truncated sets of projections is extended to cone-beam geometry. It is shown that linear scanner arrays are not directly applicable to cone-beam geometry but yieldreasonable approximations if the partial sets of projections are resorted into a virtual set of wedge-beam projections before reconstruction. The presented solution constitutes a practical and exact det rministic method of horizontally extending the artifact-free zone in cone-beam geometry. The extension of the vertical limits of the artifact-free zone is discussed. The proposed methods provide a practical low-cost approach to artifact-free reconstruction of large objects. Illustrative examples are provided.