928 research outputs found
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
Bayes-optimal inverse halftoning and statistical mechanics of the Q-Ising model
On the basis of statistical mechanics of the Q-Ising model, we formulate the
Bayesian inference to the problem of inverse halftoning, which is the inverse
process of representing gray-scales in images by means of black and white dots.
Using Monte Carlo simulations, we investigate statistical properties of the
inverse process, especially, we reveal the condition of the Bayes-optimal
solution for which the mean-square error takes its minimum. The numerical
result is qualitatively confirmed by analysis of the infinite-range model. As
demonstrations of our approach, we apply the method to retrieve a grayscale
image, such as standard image `Lenna', from the halftoned version. We find that
the Bayes-optimal solution gives a fine restored grayscale image which is very
close to the original.Comment: 13pages, 12figures, using elsart.cl
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
Backward Diffusion Methods for Digital Halftoning
We examine using discrete backward diffusion to produce digital halftones.
The noise introduced by the discrete approximation to backwards diffusion forces
the intensity away from uniform values, so that rounding each pixel to black or
white can produce a pleasing halftone. We formulate our method by considering
the Human Visual System norm and approximating the inverse of the blurring
operator. We also investigate several possible mobility functions for use in a
nonlinear backward diffusion equation for higher quality results
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