Size function - Wikipedia

Abstraction: Topological shape descriptors counting connected components via measuring functions

Key points:

• Size functions are shape descriptors from the half-plane to natural numbers, counting connected components of a topological space relative to a measuring function; used in pattern recognition and topology
• Introduced by Patrizio Frosini (with Claudia Landi and others) in size theory; the size function is the rank of the 0th persistent homology group
• Invariant under any transformation that preserves the measuring function, making them adaptable to different applications by changing the measuring function
• Algebraic representation via cornerpoints and cornerlines in the real plane encodes discontinuities and values concisely; enables similarity measures via the matching distance
• Extended to algebraic topology through size homotopy groups and the size functor, closely related to persistent homology theory

Connections: Patrizio Frosini · Topological Data Analysis · Persistent Homology · Size Theory · Pattern Recognition

Source: https://en.wikipedia.org/wiki/Size_function