Results 31  40
of
147
Fast oriented bounding box optimization on the rotation group SO(3, R)
 ACM TRANSACTIONS ON GRAPHICS
, 2011
"... An exact algorithm to compute an optimal 3D oriented bounding box was published in 1985 by Joseph O’Rourke, but it is slow and extremely hard to implement. In this article we propose a new approach, where the computation of the minimalvolume OBB is formulated as an unconstrained optimization proble ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
An exact algorithm to compute an optimal 3D oriented bounding box was published in 1985 by Joseph O’Rourke, but it is slow and extremely hard to implement. In this article we propose a new approach, where the computation of the minimalvolume OBB is formulated as an unconstrained optimization problem on the rotation group SO(3,R). It is solved using a hybrid method combining the genetic and NelderMead algorithms. This method is analyzed and then compared to the current stateoftheart techniques. It is shown to be either faster or more reliable for any accuracy.
A Fully Dynamic Algorithm for Planar Width
 in Proc. 17th ACM Sympos. Comput. Geom
, 2002
"... We show how to maintain the width of a set of n planar points subject to insertions and deletions of points in O( n) amortized time per update. Previously, no fully dynamic algorithm with a guaranteed sublinear time bound was known. ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
We show how to maintain the width of a set of n planar points subject to insertions and deletions of points in O( n) amortized time per update. Previously, no fully dynamic algorithm with a guaranteed sublinear time bound was known.
Fitting superellipses
 IEEE Trans. Pattern Anal. Mach. Intell
, 2000
"... In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the nonlinear nature of the problem. This paper describes and tests several fitting techniques which provide different tradeoffs between efficiency and accuracy. In addition, we describe variou ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
(Show Context)
In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the nonlinear nature of the problem. This paper describes and tests several fitting techniques which provide different tradeoffs between efficiency and accuracy. In addition, we describe various alternative error of fits (EOF) that can be applied by most superellipse fitting methods.
Capturing a Convex Object with Three Discs
 IEEE TRANSACTIONS ON ROBOTICS
"... This paper addresses the problem of capturing an arbitrary convex object P in the plane with three congruent discshaped robots. Given two stationary robots in contact with P, we characterize the set of positions of a third robot, the socalled capture region, that prevent P from escaping to infinit ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
This paper addresses the problem of capturing an arbitrary convex object P in the plane with three congruent discshaped robots. Given two stationary robots in contact with P, we characterize the set of positions of a third robot, the socalled capture region, that prevent P from escaping to infinity via continuous rigid motion. We show that the computation of the capture region reduces to a visibility problem. We present two algorithms for solving this problem and computing the capture region when P is a polygon and the robots are points (zeroradius discs). The first algorithm is exact and has polynomial time complexity. The second one uses simple hiddensurface removal techniques from computer graphics to output an arbitrarily accurate approximation of the capture region; it has been implemented and examples are presented.
Optimized Bounding Boxes for ThreeDimensional Treatment Planning in Brachytherapy
, 2000
"... It is sometimes necessary to determine the optimal value for a direction dependent quantity. Using a search technique based on Powell's quadratic convergent method such an optimal direction can be approximated. The necessary geometric transformations in ndimensional space are introduced. As an ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
It is sometimes necessary to determine the optimal value for a direction dependent quantity. Using a search technique based on Powell's quadratic convergent method such an optimal direction can be approximated. The necessary geometric transformations in ndimensional space are introduced. As an example we consider the approximation of the minimum bounding box of a set of threedimensional points. Minimum bounding boxes can significantly improve accuracy and efficiency of the calculations in modern brachytherapy treatment planning of the volumes of objects or the dose distribution inside an object. A covariance matrix based approximation method for the minimum bounding box is compared with the results of the search method. The benefits of the use of optimal oriented bounding boxes in brachytherapy treatment planning systems are demonstrated and discussed.
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
 Comput. Geom. Theory Appl
"... Abstract Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S that contains C. More precisely, for any ε > 0, we find an axially symmetric convex polygon Q ⊂ C ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
(Show Context)
Abstract Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S that contains C. More precisely, for any ε > 0, we find an axially symmetric convex polygon Q ⊂ C with area Q > (1 − ε)S and we find an axially symmetric convex polygon Q containing C with area Q  < (1 + ε)S . We assume that C is given in a data structure that allows to answer the following two types of query in time T C : given a direction u, find an extreme point of C in direction u, and given a line , find C ∩ . For instance, if C is a convex ngon and its vertices are given in a sorted array, then T C = O(log n). Then we can find Q and Q in time O(ε −1/2 T C + ε −3/2 ). Using these techniques, we can also find approximations to the perimeter, area, diameter, width, smallest enclosing rectangle and smallest enclosing circle of C in time O(ε −1/2 T C ). 2005 Elsevier B.V. All rights reserved.
Shape orientability
 In ACCV(2
, 2006
"... Abstract. In this paper we consider some questions related to the orientation of shapes. We introduce as a new shape feature shape orientability, i.e. the degree to which a shape has distinct (but not necessarily unique) orientation. A new method is described for measuring shape orientability, and h ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we consider some questions related to the orientation of shapes. We introduce as a new shape feature shape orientability, i.e. the degree to which a shape has distinct (but not necessarily unique) orientation. A new method is described for measuring shape orientability, and has several desirable properties. In particular, unlike the standard moment based measure of elongation, it is able to differentiate between the varying levels of orientability of nfold rotationally symmetric shapes. 1
Hierarchical Radiosity with Multiresolution Meshes
, 2000
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation or the United States government. Keywords: global illumination, hierarchical radiosity, f ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation or the United States government. Keywords: global illumination, hierarchical radiosity, face cluster hierarchies, multiresolution The hierarchical radiosity algorithm solves for the global transfer of diffuse illumination in a scene. While its potential algorithmic complexity is superior to both previous radiosity methods and distributed ray tracing, for scenes containing detailed polygonal models, or highly tessellated curved surfaces, its time performance and memory consumption are less than ideal. My thesis is that by using hierarchies similar to those of multiresolution models, the performance of the hierarchical radiosity algorithm can be made sublinear in the number of input polygons, and thus make radiosity on scenes containing detailed models tractable. The underlying goal of my thesis work has been to make highspeed radiosity solutions possible with such scenes. To achieve this goal, a new face clustering technique for automatically partitioning polygonal models has been developed. The face clusters produced
Computational Geometry and Computer Vision
 Contemporary Mathematics
, 1991
"... Computer vision is concerned with the development of machines that can process visual information. Computational geometry is concerned with the design of algorithms for solving geometric problems. Most problems in computer vision can be couched in geometric terms. In this paper we outline how comput ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Computer vision is concerned with the development of machines that can process visual information. Computational geometry is concerned with the design of algorithms for solving geometric problems. Most problems in computer vision can be couched in geometric terms. In this paper we outline how computational geometry may significantly contribute to almost every aspect of computer vision and we provide pointers to a selection of the computational geometry literature where some of the most relevant results can be found. 1. Introduction Computer vision has flourished now for some forty years as a subdiscipline of artificial intelligence and hundreds of books are readily available on the subject and will not be mentioned here. The best early book on computer vision, and still up to date from the point of view of discriminant function analysis, is the text by Duda & Hart [DH73]. Popular more recent books include Ballard & Brown [BB82] and Horn [Ho86]. Finally we mention the first two books ...