CaltechTHESIS: Book Chapter
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https://resolver.caltech.edu/CaltechTHESIS:02222011-105108216
Year: 2001
DOI: 10.7907/561b-d051
In this work, we first discuss the image halftoning problem. Halftoning is the rendition of
continuous-tone pictures on displays that are capable of producing only two levels. There
are several well-known algorithms for half toning. The dot diffusion method for digital
half toning has the advantage of pixel-level parallelism unlike the error diffusion method,
which is a popular half toning method. The image quality offered by error diffusion is
still regarded as superior to most of the other known methods. We show how the image
quality obtained using the dot diffusion method can be improved by optimization of the
so-called class matrix. By taking the human visual characteristics into account we show
that such optimization consistently results in images comparable to error diffusion, without
sacrificing the pixel-level parallelism. The dot diffusion algorithm will be discussed and
by modifying the algorithm, embedded multiresolution property will be added. Later,
we introduce LUT (Look Up Table) based half toning and tree-structured LUT (TLUT)
halftoning. We demonstrate how error diffusion characteristics can be achieved with this
method. Afterwards, our algorithm will be trained on halftones obtained by Direct Binary
Search (DBS) which is an algorithm with high computational complexity. The complexity
of TLUT halftoning is higher than that of error diffusion but much lower than that of the
DBS algorithm. Thus, halftone image quality between that of error diffusion and DBS will
be achieved depending on the size of tree structure in TLUT algorithm.
We also discuss the inverse halftoning problem. Inverse halftoning is the reconstruction
of a continuous tone image from its halftoned version. We propose two methods for
inverse half toning of dot diffused images. The first one uses Projection Onto Convex Sets
(POCS) and the second one uses wavelets. We then propose a novel and fast method for
inverse halftoning called the Look Up Table (LUT) Method. The LUT for inverse halftoning
is obtained from the histogram gathered from a few sample halftone images and the
corresponding original images. For each pixel, the algorithm looks at the pixel's neighborhood
(template) and depending upon the distribution of pixels in the template, it assigns
a contone value from a precomputed LUT. The method is extremely fast (no filtering is
required) and the image quality achieved is comparable to the best methods known for inverse halftoning. The LUT inverse half toning method does not depend on the specific
properties of the half toning method, and can be applied to any method. An algorithm for
template selection for LUT inverse half toning is introduced. We also extend LUT inverse
halftoning to color halftones.
The next topic is image watermarking and effects of halftoning on watermarked images.
Watermarking is the process of embedding a secret signal into a host signal in order to
verify ownership or authenticity. We discuss the effects of applying inverse half toning before
detection of watermark in half toned images and offer methods to improve watermark
detection from halftoned images.
Finally, we consider the optimal histogram modification with MSE metric and optimal
codebook selection problem. Watermarking with histogram modification is one of the few
watermarking methods which is robust to rotation and scaling. We formulate histogram
modification problem as finding a transformation such that the error between the input and
the output signal is minimized and the output signal has the desired histogram. It turns
out that this problem is equivalent to the integer linear programming problem. Then, we
formulate the problem of finding the optimal code book where the codewords can come from
a finite set. The equivalent problem again turns out to be a linear integer programming
problem and the solution is guaranteed to be globally optimal.https://resolver.caltech.edu/CaltechTHESIS:02222011-105108216