Size homotopy groups for computation of natural size distances

1999/01/01 by Patrizio Frosini, Michele Mulazzani · 85 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Digital Image Processing Techniques #Homotopy and Cohomology in Algebraic Topology #Mathematics #Homotopy group #Homotopy #Parametric statistics #Group (periodic table) #Combinatorics #Computation #Manifold (fluid mechanics) #Natural number #Function (biology) #Pure mathematics #Algorithm #Statistics #Physics #Biology

paper · pdf · doi:10.36045/bbms/1103065863

published in Bulletin of the Belgian Mathematical Society - Simon Stevin 6(3)

openalex publication_date 1999/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

For every manifold M endowed with a structure described by a function from M to the vector space R k , a parametric family of groups, called size homotopy groups, is introduced and studied.Some lower bounds for natural size distances are obtained in this way.

Citations

• A distance for similarity classes of submanifolds of a Euclidean space
• Optimal approximations by piecewise smooth functions and associated variational problems

Cited by

• Topological data analysis [wikipedia]