Size function: Difference between revisions

Revision as of 16:29, 17 November 2015

Revision as of 16:32, 17 November 2015

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<math>\{p\in M:\varphi(p)\le y\}</math> that contain at least one point at which the [[measuring function]] (a [[continuous function]] from a [[topological space]] <math>M\ </math> to <math>\mathbb{R}^k\ </math>

<ref name="FroLa99">Patrizio Frosini and Claudia Landi, ''Size Theory as a Topological Tool for Computer Vision'', Pattern Recognition And Image Analysis, 9(4):596–603, 1999.</ref>

<ref name="FroMu99">Patrizio Frosini, and Michele Mulazzani, ''Size homotopy groups for computation of natural size distances'', [[Bulletin of the Belgian Mathematical Society]], 6:455–464 1999.</ref>) <math>\varphi</math> takes a value smaller than or equal to <math>x\ </math>

.<ref name="dAFrLa06">Michele d'Amico, Patrizio Frosini, Claudia Landi, ''Using matching distance in Size Theory: a survey'', International Journal of Imaging Systems and Technology, 16(5):154–161, 2006.</ref> The concept of size function can be easily extended to the case of a measuring function <math>\varphi:M\to \mathbb{R}^k</math>, where <math>\mathbb{R}^k</math> is endowed with the usual partial order

.<ref name="BiCeFr08">Silvia Biasotti, Andrea Cerri, Patrizio Frosini, Claudia Landi, ''Multidimensional size functions for shape comparison'', Journal of Mathematical Imaging and Vision 32:161–179, 2008.</ref>