# Digital Functions and Data Reconstruction Digital-Discrete Methods

## Synopsis

Digital Functions and Data Reconstruction Digital-Discrete Methods by Li Chen

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.

## Reviews

The main topic of the book is data reconstruction, i.e. curve or surface fitting

to a given digital function. This is important for various engineering

applications, especially image processing... The present book focuses on the

concept of a gradually varied function (GVF) and its applications... The author

discusses in 11.3 the `natural
continuity and smoothness. According to him,

such notions are not absolute as in the conventional theory in pure mathematics,

but rather depend on the scale to be considered. This is an interesting opinion

...

This is a huge collection of the author's works on the practical applications of

gradually varied functions. It is also a nice textbook for curve/surface

fitting. (S. Hitotumatu, Mathematical Review, MR3013361)

The book under review provides an introduction and comprehensive

survey of digital function methods and their applications to image data analysis

is mainly written for graduate students in computer science and for researchers

who are interested in digital geometry, computer graphics, and data

reconstruction... Without any doubt, this book will be a valuable source of

information on digital functions and its applications. (Manfred Tasche,

Zentralblatt MATH, Zbl 06102122)

## Book Info

#### Publication date

28th January 2015

#### Author

Li Chen

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#### Publisher

Springer-Verlag New York Inc.

Paperback
208 pages

#### Categories

Computer vision
Imaging systems & technology
Discrete mathematics

#### ISBN

9781489994950

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