What is Hausdorff distance used for?
The average Hausdorff distance is a widely used performance measure to calculate the distance between two point sets. In medical image segmentation, it is used to compare ground truth images with segmentation results and allows ranking different segmentation results.
Is Hausdorff distance differentiable?
Also, the average Hausdorff distance is differentiable with respect to any point in X or Y .
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.
Is chamfer distance differentiable?
We introduce two distance metrics for point sets – the Chamfer distance and the Earth Mover’s distance. We show that both metrics are differentiable almost everywhere and can be used as the loss function, but has different properties in capturing shape space.
What is a persistence diagram?
Persistent homology, a central tool of topological data analysis, provides invariants of data called barcodes (also known as persistence diagrams). A barcode is simply a multiset of intervals on the real line.
How to calculate the Hausdorff distance of a set?
Figure 3 : Hausdorff distance on point sets. This is illustrated in fig. 3 : just click on the arrow to see the basic steps of this computation. This algorithm obviously runs in O (n m) time, with n and m the number of points in each set.
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.
How is the Hausdorff distance related to Pompeiu distance?
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 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.