Hausdorff Distance - Related Concepts

Related Concepts

A measure for the dissimilarity of two shapes is given by Hausdorff distance up to isometry, denoted D_H. Namely, let X and Y be two compact figures in a metric space M (usually a Euclidean space); then D_H(X,Y) is the infimum of d_H(I(X),Y) along all isometries I of the metric space M to itself. This distance measures how far the shapes X and Y are from being isometric.

The Gromov–Hausdorff convergence is a related idea: we measure the distance of two metric spaces M and N by taking the infimum of d_H(I(M),J(N)) along all isometric embeddings I:M→L and J:N→L into some common metric space L.