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In [[size theory]], a '''size pair''' is a pair <math>(M,\varphi)</math>, where <math>M\ </math> is a compact [[topological space]] and <math>\varphi:M\to \mathbb{R}^k</math> is a [[continuous function]]<ref name="FroLa99">Patrizio Frosini, Claudia Landi, ''Size theory as a topological tool for computer vision'', Pattern Recognition And Image Analysis, 9(4):596-603, 1999.</ref><ref>Patrizio Frosini, Michele Mulazzani,
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''Size homotopy groups for computation of natural size distances'',
Bulletin of the Belgian Mathematical Society - Simon Stevin, 6:455-464, 1999.</ref>
.<ref>Françoise Dibos, Patrizio Frosini, Denis Pasquignon,
''The use of size functions for comparison of shapes through differential invariants'',
Journal of Mathematical Imaging and Vision, 21(2):107-118, 2004.</ref>
The function <math>\varphi</math> is called a ''[[measuring function]]''. The topological space <math>M\ </math> is usually assumed to be also a [[locally connected]] and [[Hausdorff space]].
 
==References==
 
{{reflist}}
 
==See also==
* [[Size theory]]
* [[Size function]]
* [[Size functor]]
* [[Size homotopy group]]
* [[Natural pseudodistance]]
 
[[Category:Differential geometry]]
[[Category:Topology]]

Latest revision as of 04:11, 17 September 2014

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