Between shapes, using the Hausdorff distance

MESH: measuring errors between surfaces using the Hausdorff distance

This paper proposes an efficient method to estimate the distance between discrete 3D surfaces represented by triangular 3D meshes. The metric used is based on an approximation of the Hausdorff distance, which has been appropriately implemented in order to reduce unnecessary computations and memory usage. Results show that when compared to similar tools, a significant gain in both memory and spe...

Calculating the Hausdorff Distance Between Curves

Computing the Hausdorff Distance between Curved Objects

The Hausdorff distance between two sets of curves is a measure for the similarity of these objects and therefore an interesting feature in shape recognition. If the curves are algebraic computing the Hausdorff distance involves computing the intersection points of the Voronoi edges of the one set with the curves in the other. Since computing the Voronoi diagram of curves is quite difficult we c...

On the Hausdorff Distance Between Compact Subsets

In [1] the pseudo-metric dist min on compact subsets A and B of a topological space generated from arbitrary metric space is defined. Using this notion we define the Hausdorff distance (see e.g. [5]) of A and B as a maximum of the two pseudo-distances: from A to B and from B to A. We justify its distance properties. At the end we define some special notions which enable to apply the Hausdorff d...

On the Hausdorff Distance Between Compact Subsets1

In [2] the pseudo-metric distmax min on compact subsets A and B of a topological space generated from arbitrary metric space is defined. Using this notion we define the Hausdorff distance (see e.g. [6]) of A and B as a maximum of the two pseudo-distances: from A to B and from B to A. We justify its distance properties. At the end we define some special notions which enable to apply the Hausdorf...