Integrated shape-sensitive functional metrics

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.