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Digital Functions and Data Reconstruction - Digital-Discrete Methods (Hardcover, 2013 ed.)
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Digital Functions and Data Reconstruction - Digital-Discrete Methods (Hardcover, 2013 ed.)
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Digital Functions and Data Reconstruction: Digital-Discrete Methods
provides a solid foundation to the theory of digital functions and
its applications to image data analysis, digital object
deformation, and data reconstruction. This new method has a unique
feature in that it is mainly built on discrete mathematics with
connections to classical methods in mathematics and computer
sciences. Digitally continuous functions and gradually varied
functions were developed in the late 1980s. A. Rosenfeld (1986)
proposed digitally continuous functions for digital image analysis,
especially to describe the "continuous" component in a digital
image, which usually indicates an object. L. Chen (1989) invented
gradually varied functions to interpolate a digital surface when
the boundary appears to be continuous. In theory, digitally
continuous functions are very similar to gradually varied
functions. Gradually varied functions are more general in terms of
being functions of real numbers; digitally continuous functions are
easily extended to the mapping from one digital space to another.
This will be the first book about digital functions, which is an
important modern research area for digital images and digitalized
data processing, and provides an introduction and comprehensive
coverage of digital function methods. Digital Functions and Data
Reconstruction: Digital-Discrete Methods offers scientists and
engineers who deal with digital data a highly accessible,
practical, and mathematically sound introduction to the powerful
theories of digital topology and functional analysis, while
avoiding the more abstruse aspects of these topics.
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