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Blind deconvolution is a classical image processing problem which
has been investigated by a large number of researchers over the
last four decades. The purpose of this monograph is not to propose
yet another method for blind image restoration. Rather the basic
issue of deconvolvability has been explored from a theoretical view
point. Some authors claim very good results while quite a few claim
that blind restoration does not work. The authors clearly detail
when such methods are expected to work and when they will not. In
order to avoid the assumptions needed for convergence analysis in
the Fourier domain, the authors use a general method of convergence
analysis used for alternate minimization based on three point and
four point properties of the points in the image space. The authors
prove that all points in the image space satisfy the three point
property and also derive the conditions under which four point
property is satisfied. This provides the conditions under which
alternate minimization for blind deconvolution converges with a
quadratic prior. Since the convergence properties depend on the
chosen priors, one should design priors that avoid trivial
solutions. Hence, a sparsity based solution is also provided for
blind deconvolution, by using image priors having a cost that
increases with the amount of blur, which is another way to prevent
trivial solutions in joint estimation. This book will be a highly
useful resource to the researchers and academicians in the specific
area of blind deconvolution.
Blind deconvolution is a classical image processing problem which
has been investigated by a large number of researchers over the
last four decades. The purpose of this monograph is not to propose
yet another method for blind image restoration. Rather the basic
issue of deconvolvability has been explored from a theoretical view
point. Some authors claim very good results while quite a few claim
that blind restoration does not work. The authors clearly detail
when such methods are expected to work and when they will not. In
order to avoid the assumptions needed for convergence analysis in
the Fourier domain, the authors use a general method of convergence
analysis used for alternate minimization based on three point and
four point properties of the points in the image space. The authors
prove that all points in the image space satisfy the three point
property and also derive the conditions under which four point
property is satisfied. This provides the conditions under which
alternate minimization for blind deconvolution converges with a
quadratic prior. Since the convergence properties depend on the
chosen priors, one should design priors that avoid trivial
solutions. Hence, a sparsity based solution is also provided for
blind deconvolution, by using image priors having a cost that
increases with the amount of blur, which is another way to prevent
trivial solutions in joint estimation. This book will be a highly
useful resource to the researchers and academicians in the specific
area of blind deconvolution.
This book presents and analyzes methods to perform image
co-segmentation. In this book, the authors describe efficient
solutions to this problem ensuring robustness and accuracy, and
provide theoretical analysis for the same. Six different methods
for image co-segmentation are presented. These methods use concepts
from statistical mode detection, subgraph matching, latent class
graph, region growing, graph CNN, conditional encoder-decoder
network, meta-learning, conditional variational encoder-decoder,
and attention mechanisms. The authors have included several block
diagrams and illustrative examples for the ease of readers. This
book is a highly useful resource to researchers and academicians
not only in the specific area of image co-segmentation but also in
related areas of image processing, graph neural networks,
statistical learning, and few-shot learning.
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