A point calculus for interlevel set homology

作者：Bendich Paul; Cabello Sergio^*; Edel**runner Herbert

来源：Pattern Recognition Letters, 2012, 33(11): 1436-1444.

DOI：10.1016/j.patrec.2011.10.007

• Continuous functions
• Interlevel sets
• Homology
• Vector spaces
• Persistence diagrams
• Exact sequences

The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology.

• 出版日期2012-8-1