This paper describes an algorithm for computation of the Hausdorff distance between sets of plane algebraic rational parametric curves. The Hausdorff distance is one of the frequently used similarityâ€¦ (More)

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 theâ€¦ (More)

In order to determine the similarity between two planar shapes, which is an important problem in computer vision and pattern recognition, it is necessary to first match the two shapes as good asâ€¦ (More)

We consider the problem of computing the depth of the arrangement of n axis-aligned rectangles in the plane, which is the maximum number of rectangles containing a common point. For this problem weâ€¦ (More)

Analysis and comparison of geometric shapes are of importance in various application areas within computer science, e.g., pattern recognition and computer vision. The general situation in a shapeâ€¦ (More)

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes A and B, the algorithm computes aâ€¦ (More)

We show that the Hausdorff distance for two sets of non-intersecting line segments can be computed in parallel in O(log n) time using O(n) processors in a CREW-PRAM computation model. We discuss howâ€¦ (More)

An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328`â€¦ (More)

Bose et al. [1] asked whether for every simple arrangement A of n lines in the plane there exists a simple n-gon P that induces A by extending every edge of P into a line. We prove that such aâ€¦ (More)