Algorithmica

In the context of discrete curve evolution the following problem is of relevance: decompose the boundary of a plane digital object into convex and concave parts. Such a decomposition is very useful for describing the form of an object, e.g. for shape ...

This paper deals with the polyhedrization of discrete volumes. The aim is to do a reversible transformation from a discrete volume to a Euclidean polyhedron, i.e. such that the discretization of the Euclidean volume is exactly the initial discrete ...

The Hausdorff distance is a very natural and straightforward distance measure for comparing geometric shapes like curves or other compact sets. Unfortunately, it is not an appropriate distance measure in some cases. For this reason, the Fréchet distance ...

Point pattern matching is an important problem in computational geometry, with applications in areas like computer vision, object recognition, molecular modeling, and image registration. Traditionally, it has been studied in an exact formulation, where ...

In this article we discuss the 2D–3D pose estimation problem of 3D free-form contours. We observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means estimating the relative position and orientation of the 3D object to the ...

We define and prove properties of the consensus shape for a protein family, a protein-like structure that provides a compact summary of the significant structural information for a protein family. If all members of the protein family exhibit a geometric ...

In this paper we give bounds on the complexity of some algorithms for approximating 2-D and 3-D polygonal paths with the infinite beam measure of error. While the time/space complexities of the algorithms known for other error measures are well ...

We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of such covers and present an efficient randomized approximation ...

We consider the problem of testing the roundness of manufactured disks and balls using the finger probing model of Cole and Yap. The running time of our procedures depends on the quality of the object being considered. Quality is a parameter that is ...

The medial axis of a surface in 3D is the closure of all points that have two or more closest points on the surface. It is an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial ...

Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new ...

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression and simplification of three-dimensional shapes. Different features, such as flats, limbs, tips, pits and ...

This paper introduces two efficient algorithms that compute the Contour Tree of a three-dimensional scalar field F and its augmented version with the Betti numbers of each isosurface. The Contour Tree is a fundamental data structure in scientific ...