Similarity measures for convex polyhedra based on Minkowski addition
نویسندگان
چکیده
منابع مشابه
Similarity measures for convex polyhedra based on Minkowski addition
In this paper we introduce and investigate similarity measures for convex polyhedra based on Minkowski addition and inequalities for the mixed volume, volume and surface area related to the Brunn-Minkowski theory. All measures considered are invariant under translations; furthermore, they may also be invariant under subgroups of the aane transformation group. For the case of rotation and scale ...
متن کاملSimilarity and Symmetry Measures for Convex Shapes Using Minkowski Addition
This paper is devoted to similarity and symmetry measures for convex shapes whose deenition is based on Minkowski addition and the Brunn-Minkowski inequality. This means in particular that these measures are region-based, in contrast to most of the literature, where one considers contour-based measures. All measures considered in this paper are invariant under translations; furthermore, they ca...
متن کاملMinkowski addition of convex polytopes
This note summarizes recent results from computational geometry which determine complexity of computing Minkowski sum of k convex polytopes in R, which are represented either in terms of facets or in terms of vertices. In particular, it is pointed out for which cases there exists an algorithm which runs in polynomial time. The note is based on papers of Gritzmann and Sturmfels [6] and Komei Fuk...
متن کاملContributing vertices-based Minkowski sum computation of convex polyhedra
Minkowski sum is an important operation. It is used in many domains such as: computer-aided design, robotics, spatial planning, mathematical morphology, and image processing. We propose a novel algorithm, named the Contributing Verticesbased Minkowski Sum (CVMS) algorithm for the computation of the Minkowski sum of convex polyhedra. The CVMS algorithm allows to easily obtain all the facets of t...
متن کاملSimilarity Measure Computation of Convex Polyhedra Revisited
We study the computation of rotation-invariant similarity measures of convex polyhedra, based on Minkowski’s theory of mixed volumes. To compute the similarity measure, a (mixed) volume functional has to be minimized over a number of critical orientations of these polyhedra. These critical orientations are those relative configurations where faces and edges of the two polyhedra are as much as p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pattern Recognition
سال: 2000
ISSN: 0031-3203
DOI: 10.1016/s0031-3203(99)00159-4