Planar projection: Difference between revisions

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In size theory, a size pair is a pair $(M, φ)$ , where $M$ is a compact topological space and $φ : M \to ℝ^{k}$ is a continuous function^[1]^[2] .^[3] The function $φ$ is called a measuring function. The topological space $M$ is usually assumed to be also a locally connected and Hausdorff space.

References

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↑ Patrizio Frosini, Claudia Landi, Size theory as a topological tool for computer vision, Pattern Recognition And Image Analysis, 9(4):596-603, 1999.
↑ Patrizio Frosini, Michele Mulazzani, Size homotopy groups for computation of natural size distances, Bulletin of the Belgian Mathematical Society - Simon Stevin, 6:455-464, 1999.
↑ 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.

[FroLa99-1] Patrizio Frosini, Claudia Landi, Size theory as a topological tool for computer vision, Pattern Recognition And Image Analysis, 9(4):596-603, 1999.

[2] Patrizio Frosini, Michele Mulazzani, Size homotopy groups for computation of natural size distances, Bulletin of the Belgian Mathematical Society - Simon Stevin, 6:455-464, 1999.

[3] 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.

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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,
+''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]]

Planar projection: Difference between revisions

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