Is Hausdorff distance a metric?

Informally, the Hausdorff distance gives the largest length out of the set of all distances between each point of a set to the closest point of a second set. Given any metric space, we find that the Hausdorff distance defines a metric on the space of all nonempty compact subsets of the metric space.

What is the unit of Hausdorff distance?

In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right.

How to calculate the Hausdorff distance?

Definition of Hausdorff distance: (a) h(Oq, Eq + 1) measures the maximum distance of a model point to the nearest edge pixel, and (b) h(Eq + 1, Oq) measures the maximum distance of an edge pixel to the nearest model point.

How to use Hausdorff distance?

The Hausdorff distance [66] is the maximum deviation between two models, measuring how far two point sets are from each other [26]. Given two nonempty point sets A={x1,x2,…,xn} and B={y1,y2,…,ym}, the Hausdorff distance between A and B is defined as H(A,B).

What is the name of the Hausdorff metric?

Hausdorff distance. In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff.

Which is the best description of the Hausdorff distance?

In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right.

How is the Hausdorff distance related to Pompeiu distance?

In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie Pompeiu .

How is the Gromov-Hausdorff convergence distance calculated?

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.