Approximate medial axis as a Voronoi subcomplex

Dey, Tamal K.; Zhao, Wulue

doi:10.1016/s0010-4485(03)00061-7

Cited by 108 publications

(73 citation statements)

References 15 publications

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“…• The object angle α o [21], also referred to as the bisector angle [22], solid angle [23], medial angle [24] or separation angle ( [25], [26]), which describes the maximum angle included by two vectors from the sphere's center to two different nearest surface points p si and p sj touched by this sphere (see Fig. 1b, 1c).…”

Section: B the Grid Of Medial Spheresmentioning

confidence: 99%

Planning grasps for robotic hands using a novel object representation based on the medial axis transform

Przybylski

Asfour

Dillmann

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Many supporting activities that future service robots might perform in people's homes depend on the capability to grasp and manipulate arbitrary objects. Easily accomplished by humans, but very difficult to achieve for robots, grasping involves dealing with a high-dimensional space of parameters which include hand kinematics, object geometry, material properties and forces. We believe that the way a robot grasps an object should be motivated by the object's geometry and that the search space for stable grasps can be dramatically reduced if the underlying object representation reflects symmetry properties of the object that contain valuable information for grasp planning. In this paper, we introduce the grid of medial spheres, a volumetric object representation based on the medial axis transform. The grid of medial spheres represents arbitrarily shaped objects with arbitrary levels of detail and contains symmetry information that can be easily exploited by a grasp planning algorithm. We present the data structure as well as a grasp planning algorithm that exploits it and provide experimental results on various object models using two robot hands in simulation.

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Section: B the Grid Of Medial Spheresmentioning

confidence: 99%

Planning grasps for robotic hands using a novel object representation based on the medial axis transform

Przybylski

Asfour

Dillmann

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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“…During the first step, medial axis is computed from a sampled ventricle surface. The computation is performed using algorithm proposed by Dey [7] which approximates MA as a sub-complex of Voronoi diagram.…”

Section: Algorithmmentioning

confidence: 99%

“…It is approximated from surface samples and is computed according to the algorithm described in [7]. It is shown in [6] that if surface sampling density approaches infinity, then the medial axis approximation approaches true medial axis.…”

Section: Computation Of Medial Axismentioning

confidence: 99%

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An Algorithm for Partitioning of Right Heart Ventricle Medial Axis

Paulinas

Meilūnas

2010

Mathematical Modelling and Analysis

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Abstract. A right heart ventricle has a complex and irregular shape, this obscures analysis of ventricle surface movements. We are trying to quantitative evaluate morphological changes of right ventricle surface, these changes appear during heart beat cycle, between different age groups, due to heart diseases, and other factors. A method for such evaluation would open new possibilities for insights into heart function, disease course extrapolation and other. We see this as a multistage task, where the first step is partitioning whole surface into smaller, more manageable regions, and the second step is to analyse each region separately. In this paper we present a new algorithm for partitioning the medial axis of right heart ventricle surface. Such partitioning leads to division of surface into smaller regions with clear shape. The proposed algorithm first computes medial axis from sampled ventricle surface. Later, the medial axis is filtered and smoothed, and third, we compute curvature map and use it as weights in Dijkstra's algorithm for curvature guided partitioning. Algorithm provides a way for fully automatic partitioning of medial manifold into separate medial scaffolds and a semi automatic way for additional curvature based division of medial scaffolds.

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“…A brief review on these methods can be found in [9]. Most widely discussed are the Voronoi diagram [6,16,3,7] and distance field methods [1,24,27]. By nature, the Voronoi diagram is geometry-based and the distance field is often related to general differential equations.…”

Section: Introductionmentioning

confidence: 99%

Distance Solutions for Medial Axis Transform

Xia

Tucker

2009

Proceedings of the 18th International Meshing Roundtable

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Abstract.A method towards robust and efficient medial axis transform (MAT) of arbitrary domains using distance solutions is presented. The distance field, d, is calculated by solving the hyperbolic-natured Eikonal (or Level Set) equation. The solution is obtained on Cartesian grids. Both the fast-marching method and fast-sweeping method are used to calculate d. Medial axis point clouds are then extracted based on the distance solution via a simple criteria: the Laplacian or the Hessian determinant of d. These point clouds in 2D-pixel and 3D-voxel space are further thinned to curves and surfaces through binary image thinning algorithms. This results in an overall hybrid approach. As an alternative to other methods, the current d−MAT procedure bypasses difficulties that are usually encountered by pure geometric methods (e.g. the Voronoi approach), especially in 3D, and provides better accuracy than pure thinning methods. It is also shown that the d−MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Various examples are given to demonstrate the current approach.

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Approximate medial axis as a Voronoi subcomplex

Cited by 108 publications

References 15 publications

Planning grasps for robotic hands using a novel object representation based on the medial axis transform

Planning grasps for robotic hands using a novel object representation based on the medial axis transform

An Algorithm for Partitioning of Right Heart Ventricle Medial Axis

Distance Solutions for Medial Axis Transform

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