A distance for similarity classes of submanifolds of a Euclidean space

1990/12/01 by Patrizio Frosini · 6 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #3D Shape Modeling and Analysis #Geometric Analysis and Curvature Flows #Mathematics #Euclidean distance #Similarity (geometry) #Euclidean space #Seven-dimensional space #Quotient #Pure mathematics #Space (punctuation) #Metric (unit) #Euclidean distance matrix #Euclidean geometry #Metric space #Set (abstract data type) #Geometry #Artificial intelligence #Image (mathematics) #Computer science

paper · pdf · doi:10.1017/s0004972700028574

openalex publication_date 1990/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

A distance is defined on the quotient of the set of submanifolds of a Euclidean space, with respect to similarity. It is then related to a previously defined function which captures the metric behaviour of paths.

Citations

• Lectures on Quasiconformal Mappings
• Uniformization, Moduli, and Kleinian Groups†

Cited by

• Retrieval of trademark images by means of size functions
• Size functions for comparing 3D models
• One-dimensional reduction of multidimensional persistent homology
• Size homotopy groups for computation of natural size distances
• Gromov‐Hausdorff Stable Signatures for Shapes using Persistence
• Topological data analysis [wikipedia]