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.
