This book analyzes techniques that use the direct and inverse fuzzy
transform for image processing and data analysis. The book is
divided into two parts, the first of which describes methods and
techniques that use the bi-dimensional fuzzy transform method in
image analysis. In turn, the second describes approaches that use
the multidimensional fuzzy transform method in data analysis. An
F-transform in one variable is defined as an operator which
transforms a continuous function f on the real interval [a,b] in an
n-dimensional vector by using n-assigned fuzzy sets A1, ... , An
which constitute a fuzzy partition of [a,b]. Then, an inverse
F-transform is defined in order to convert the n-dimensional vector
output in a continuous function that equals f up to an arbitrary
quantity . We may limit this concept to the finite case by defining
the discrete F-transform of a function f in one variable, even if
it is not known a priori. A simple extension of this concept to
functions in two variables allows it to be used for the
coding/decoding and processing of images. Moreover, an extended
version with multidimensional functions can be used to address a
host of topics in data analysis, including the analysis of large
and very large datasets. Over the past decade, many researchers
have proposed applications of fuzzy transform techniques for
various image processing topics, such as image coding/decoding,
image reduction, image segmentation, image watermarking and image
fusion; and for such data analysis problems as regression analysis,
classification, association rule extraction, time series analysis,
forecasting, and spatial data analysis. The robustness, ease of
use, and low computational complexity of fuzzy transforms make them
a powerful fuzzy approximation tool suitable for many computer
science applications. This book presents methods and techniques
based on the use of fuzzy transforms in various applications of
image processing and data analysis, including image segmentation,
image tamper detection, forecasting, and classification,
highlighting the benefits they offer compared with traditional
methods. Emphasis is placed on applications of fuzzy transforms to
innovative problems, such as massive data mining, and image and
video security in social networks based on the application of
advanced fragile watermarking systems. This book is aimed at
researchers, students, computer scientists and IT developers to
acquire the knowledge and skills necessary to apply and implement
fuzzy transforms-based techniques in image and data analysis
applications.
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