Computational Proximity: Excursions In The Topology Of Digital Images (intelligent Systems Reference Library)
by James F. Peters /
2016 / English / PDF
25.7 MB Download
This book introduces computational proximity (CP) as an
algorithmic approach to finding nonempty sets of points
that are either close to each other or far
apart. Typically in computational proximity, the
book starts with some form of proximity space (topological
space equipped with a proximity relation) that has an
inherent geometry. In CP, two types of near sets are
considered, namely, spatially near sets and descriptivelynear
sets. It is shown that connectedness, boundedness, mesh nerves,
convexity, shapes and shape theory are principal topics in the
study of nearness and separation of physical aswell as abstract
sets. CP has a hefty visual content. Applications of CP in
computer vision, multimedia, brain activity, biology, social
networks, and cosmology are included. The book has been
derived from the lectures of the author in a graduate course on
the topology of digital images taught over the past several
years. Many of the students have provided important insights
and valuable suggestions. The topics in this monograph
introduce many forms of proximities with a computational
flavour (especially, what has become known as the strong
contact relation), many nuances of topological spaces, and
point-free geometry.
This book introduces computational proximity (CP) as an
algorithmic approach to finding nonempty sets of points
that are either close to each other or far
apart. Typically in computational proximity, the
book starts with some form of proximity space (topological
space equipped with a proximity relation) that has an
inherent geometry. In CP, two types of near sets are
considered, namely, spatially near sets and descriptivelynear
sets. It is shown that connectedness, boundedness, mesh nerves,
convexity, shapes and shape theory are principal topics in the
study of nearness and separation of physical aswell as abstract
sets. CP has a hefty visual content. Applications of CP in
computer vision, multimedia, brain activity, biology, social
networks, and cosmology are included. The book has been
derived from the lectures of the author in a graduate course on
the topology of digital images taught over the past several
years. Many of the students have provided important insights
and valuable suggestions. The topics in this monograph
introduce many forms of proximities with a computational
flavour (especially, what has become known as the strong
contact relation), many nuances of topological spaces, and
point-free geometry.