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

• Size theory
• Size function
• Size functor
• Size homotopy group
• Natural pseudodistance