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Geometry of Digital Spaces (Applied and Numerical Harmonic Analysis)



Rok: 1998
ISBN: 9780817638979
OKCZID: 110370332

Citace (dle ČSN ISO 690):
HERMAN, Gabor T. Geometry of Digital Spaces. [1st ed.]. Boston: Birkhäuser, 1998. viii, x, 216 s., příl. Applied and numerical harmonic analysis / John J. Benedetto.


Anotace

 

There are many areas of science and engineering where multidimensional discrete data are collected and analyzed, e.g., neuroscience, medical imaging, industrial inspection, geoscience, and fluid dynamics to name a few. In attempting to design and to prove the validity of computational procedures for visualization and analysis of the information in such data, the need for a mathematical theory of surfaces, objects and their boundaries in discrete spaces becomes essential. Such a theory, the geometry of digital spaces, is the subject matter of this important new book. Self-contained, accessible, and mathematically precise, this book serves as an introduction to this field, providing information that can be used immediately in the discussion of properties of practical algorithms in digital spaces. The approach used in Geometry of Digital Spaces is strongly application oriented. It presents problems of visualization and analysis of multidimensional data sets. The primary areas of mathematics used are graph theory and topology. Scientists and professionals from diverse backgrounds will find the discussions clear and accessible because all concepts and methods are carefully introduced, defined and illustrated with examples. Features and Topics: * emphasizes 3D surface detection and Jordan properties in discrete spaces * covers graph traversal algorithms, digital spaces and topological issues * focuses on applications * includes chapter exercise sets and numerous worked examples Geometry of Digital Spaces is a new text/reference that is an essential resource for mathematicians, computer scientists, and electrical engineers working in areas of digital geometry and topology, image processing, medical imaging and computer graphics. Any scientist or engineer who uses computer algorithms for processing multidimensional data will benefit form using this book. It is also an excellent self-study resource for practitioners and professionals.


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