Size pair

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

References

  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 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.

See also

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