Integrated shape-sensitive functional metrics
Metric Geometry
2022-09-26 v1 Applications
Abstract
This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the L_p distance in general function spaces. Selecting d as the Hausdorff or Fr\'echet distances, we introduce integrated shape-sensitive versions of these supremum-based metrics. The new metrics allow for finer analyses in functional settings, not attainable applying the non-integrated versions directly. Moreover, convergent discrete approximations make computations feasible in practice.
Cite
@article{arxiv.2107.08917,
title = {Integrated shape-sensitive functional metrics},
author = {Sami Helander and Petra Laketa and Pauliina Ilmonen and Stanislav Nagy and Germain Van Bever and Lauri Viitasaari},
journal= {arXiv preprint arXiv:2107.08917},
year = {2022}
}