000 03720nam a22004695i 4500
001 978-3-319-30262-1
003 DE-He213
005 20200420221255.0
007 cr nn 008mamaa
008 160419s2016 gw | s |||| 0|eng d
020 _a9783319302621
_9978-3-319-30262-1
024 7 _a10.1007/978-3-319-30262-1
_2doi
050 4 _aQ342
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aPeters, James F.
_eauthor.
245 1 0 _aComputational Proximity
_h[electronic resource] :
_bExcursions in the Topology of Digital Images /
_cby James F. Peters.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXXVIII, 433 p. 254 illus., 39 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aIntelligent Systems Reference Library,
_x1868-4394 ;
_v102
505 0 _aComputational Proximity -- Proximities Revisited -- Distance and Proximally Continuous.-Image Geometry and Nearness Expressions for Image and Scene Analysis -- Homotopic Maps, Shapes and Borsuk-Ulam Theorem -- Visibility, Hausdorffness, Algebra and Separation Spaces -- Strongly Near Sets and Overlapping Dirichlet Tessellation Regions -- Proximal Manifolds.-Watershed, Smirnov Measure, Fuzzy Proximity and Sorted Near Sets -- Strong Connectedness Revisited -- Helly's Theorem and Strongly Proximal Helly Theorem -- Nerves and Strongly Near Nerves -- Connnectedness Patterns -- Nerve Patterns- Appendix A: Mathematica and Matlab Scripts -- Appendix B: Kuratowski Closure Axioms -- Appendix C: Sets. A Topological Perspective -- Appendix D: Basics of Proximities -- Appendix E: Set Theory Axioms, Operations and Symbols -- Appendix F: Topology of Digital Images.
520 _aThis 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.
650 0 _aEngineering.
650 0 _aArtificial intelligence.
650 0 _aComputational intelligence.
650 1 4 _aEngineering.
650 2 4 _aComputational Intelligence.
650 2 4 _aArtificial Intelligence (incl. Robotics).
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319302607
830 0 _aIntelligent Systems Reference Library,
_x1868-4394 ;
_v102
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-30262-1
912 _aZDB-2-ENG
942 _cEBK
999 _c52834
_d52834