Previously we have shown that error diffusion neural networks (EDNs) find local minima of frequency-weighted error
between a binary halftone output and corresponding smoothly varying input, an ideal framework for solving halftone
problems. An extension of our work to color halftoning employs a three dimensional (3D) interconnect scheme. We cast
color halftoning as four related sub-problems: the first three are to compute good binary halftones for each primary color
and the fourth is to simultaneously minimize frequency-weighted error in the luminosity of the composite result. We
have showed that an EDN with a 3D interconnect scheme can solve all four problems in parallel. This paper shows that
our 3D EDN algorithm not only shapes the error to frequencies to which the Human Visual System (HVS) is least
sensitive but also shapes the error in colors to which the HVS is least sensitive. The correlation among the color planes
by luminosity reduces the formation of high contrast pixels, such as black and white pixels that often constitute color
noise, resulting in a smoother and more homogeneous appearance in a halftone image and a closer resemblance to the
continuous tone image. The texture visibility of color halftone patterns is evaluated in two ways: (1) by computing the
radially averaged power spectrum (2) by computing the visual cost function.
This is a generalization, to color images, of earlier results
on two-dimensional monochromatic halftoning with error diffusion
neural networks (EDNs). Previously, we have shown that EDNs find
local minima of frequency-weighted error between a binary halftone
output and corresponding smoothly varying input, which is an ideal
framework for solving halftone problems. We cast color halftoning
as four related subproblems: the first three are to compute good
binary halftones for each primary color and the fourth is to simultaneously
minimize frequency-weighted error in the luminosity of the
composite result. We show that an EDN with a three-dimensional
(3D) interconnection scheme can solve all four problems in parallel.
The 3D EDN algorithm not only shapes the error to frequencies to
which the human visual system (HVS) is least sensitive but also
shapes the error in colors to which the HVS is least sensitive—
namely it satisfies the minimum brightness variation criterion. The
correlation among the color planes by luminosity reduces the formation
of high contrast pixels, such as black and white pixels that often
constitute color noise, resulting in a smoother and more homogeneous
appearance in a halftone image and a closer
resemblance to the continuous tone image.
Biologically-motivated analog-to-digital (A/D) conversion considers
the charge-fire cycles of neurons in biological systems as binary
oversampled A/D conversion processes. Feedback mechanisms have been
hypothesized that coordinate charge-fire cycles in a manner that
suppresses noise in the signal baseband of the power spectrum of
output spikes, also a central goal of A/D converter design. Biological systems succeed admirably despite the slow and imprecise
characteristics of individual neurons. In A/D converters of very high
speed and precision, where electronic/photonic devices also appear
slow and imprecise, neural architectures offer a path for advancing the performance frontier. In this work, we provide a new analysis
framework and simulation results directed toward that goal.
In previous work we developed a partitioning strategy called constrained framing, which was used to implement an error diffusion neural network for digital image halftoning. The partitioning approach made it possible to implement the original technique in a distributed, parallel fashion. The resulting halftoned images were visually indistinguishable from the non-partitioned approach. Ulichney's halftone metrics of radially averaged power spectra and anisotropy also did not show noticeable differences between the two techniques. Even an intensive application of the power spectra metric (averaging 1000 halftoned images instead of 10) revealed the need for some additional metrics of quality. Taking advantage of a priori knowledge of the partition scheme's geometry, we develop a protocol for evaluating the subtle differences between halftoned images produced using the constrained framing algorithm and the non-tiled halftone. An observed relationship between the new metric and input image grayscale magnitude suggests the existence of normative values which may be used to examine the performance of other halftone algorithms which are applied in a similar segmented fashion.
KEYWORDS: Modulators, Signal to noise ratio, Quantization, Neural networks, Diffusion, Digital filtering, Signal processing, Analog electronics, Interference (communication), Linear filtering
A novel photonic approach to analog-to-digital (A/D) conversion based on temporal and spatial oversampling techniques in conjunction with a smart pixel hardware implementation of a neural algorithm is described. In this approach, the input signal is first sampled at a rate higher than that required by the Nyquist criterion and then presented spatially as the input to the 2D error diffusion neural network consisting of M X N pixels. The neural network processes the input oversampled analog image and produces an M X N pixel binary output image which is an optimum representation of the input analog signal. Upon convergence, the neural network minimizes an energy function representing the frequency-weighted squared error between the input analog image and the output halftoned image. Decimation and low-pass filtering techniques, common to oversampling A/D converters, digitally sum and average the M X N pixel output binary image using high-speed digital electronic circuitry. By employing a 2D smart pixel neural approach to oversampling A/D conversion, each pixel constitutes a simple oversampling modulator thereby producing a distributed A/D architecture. Spectral noise shaping across the array diffuses quantization error thereby improving the signal-to-noise ratio performance. Here, each quantizer within the network is embedded in a fully- connected, distributed mesh feedback loop which spectrally shapes the overall quantization noise significantly reducing the effects of component mismatch typically associated with parallel or channelized A/D approaches. The 2D neural array provides higher aggregate bit rates which can extend the useful bandwidth of oversampling converters.
KEYWORDS: Signal to noise ratio, Diffusion, Modulators, Neural networks, Quantization, Interference (communication), Digital filtering, Error analysis, Digital electronics, Image processing
A novel approach to photonic A/D conversion using a distributed neural network, oversampling techniques, and a smart pixel hardware implementation is described. In this approach, the input signal is first sampled at a rate higher than that required by the Nyquist criterion and then presented spatially as the input to a 2D error diffusion neural network consisting of M X N neurons, each representing a pixel in the image space. The neural network processes the input oversampled analog image and produces an M X N pixel binary or halftoned output image. Decimation and low-pass filtering techniques, common to classical 1D oversampling A/D converters, digitally sum and average the M X N pixel output binary image using high-speed digital electric circuitry. By employing a 2D smart pixel neural approach to oversampling A/D conversion, each pixel constitutes a simple oversampling modulator thereby producing a distributed A/D architecture. Spectral noise shaping across the array diffuses quantization error thereby improving overall signal-to-noise ratio performance. Here, each quantizer within the network is embedded in a fully- connected, distributed mesh feedback loop which spectrally shapes the overall quantization noise thereby significantly reducing the effects of components mismatch typically associated with parallel or channelized A/D approaches. This 2D neural approach provides higher aggregate bit rates which can extend the useful bandwidth of photonic-based, oversampling A/D converters.
In this research, we investigate partitioning schemes for reducing the computational complexity of an error diffusion neural network (EDN) for the application of digital halftoning. We show that by partitioning the original image into k subimages, the time required to perform the halftoning using an EDN is reduced by as much as a factor of k. Motivated by this potential speedup, we introduce three approaches to partitioning with varying degrees of overlap and communication between the partitions. We quantitatively demonstrate that the Constrained Framing approach produces halftoned images whose quality is as good as the quality of halftoned images produced by the EDN without partitioning.
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