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Polyhedral Surface Approximation of Non-convex Voxel Sets through the Modification of Convex Hulls [chapter]

Henrik Schulz
Lecture Notes in Computer Science  
The algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background  ...  In this paper we want to introduce an algorithm for the creation of polyhedral approximations for objects represented as strongly connected sets of voxels in three-dimensional binary images.  ...  Acknowledgement The author is pleased to thank Vladimir Kovalevsky for many useful discussions on earlier versions of the manuscript.  ... 
doi:10.1007/978-3-540-78275-9_4 dblp:conf/iwcia/Schulz08 fatcat:kcyib5aosnaofdt6gdddtpdwgq

Polyhedral approximation and practical convex hull algorithm for certain classes of voxel sets

Henrik Schulz
2009 Discrete Applied Mathematics  
The proposed algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the  ...  cell complex Abstract polyhedron Surface approximation a b s t r a c t In this paper we introduce an algorithm for the creation of polyhedral approximations for certain kinds of digital objects in a three-dimensional  ...  In [8] we have already shown that for a convex voxel set the convex hull is such a polyhedral surface.  ... 
doi:10.1016/j.dam.2009.04.008 fatcat:ugr5bydufrfrtaalka5wz6mg7u

Accurate Minkowski sum approximation of polyhedral models

Gokul Varadhan, Dinesh Manocha
2006 Graphical Models  
Abstract We present an algorithm to approximate the 3D Minkowski sum of polyhedral objects.  ...  Our algorithm decomposes the polyhedral objects into convex pieces, generates pairwise convex Minkowski sums and computes their union.  ...  We thank Danny Halperin for many fruitful discussions on the complexity and practical implementations of Minkowski sum.  ... 
doi:10.1016/j.gmod.2005.11.003 fatcat:cyyrkoevgba33hzinq5woaeevy

Integration of Multiview Stereo and Silhouettes Via Convex Functionals on Convex Domains [chapter]

Kalin Kolev, Daniel Cremers
2008 Lecture Notes in Computer Science  
The key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional where the exact silhouette consistency is imposed as a convex constraint that restricts the  ...  As a consequence, we can retain the original stereo-weighted surface area as a cost functional without heuristic modifications by balloon terms or other strategies, yet still obtain meaningful (nonempty  ...  Acknowledgments This research was supported by the German Research Foundation, grant # CR250/1-2. We thank Carlos Hernandez and Yasutaka Furukawa for providing the data sets in Figures 5 and 6 .  ... 
doi:10.1007/978-3-540-88682-2_57 fatcat:7ndnjne7wbaxtdmvkxdmofheeq

Analysis of the spatial distribution of AgNOR proteins in cell nuclei using simultaneous confocal scanning laser fluorescence and transmitted light microscopy

F. PARAZZA, E. BERTIN, Z. WOZNIAK, Y. USSON
1995 Journal of Microscopy  
in the elaboration of the 2-D convex hull, Dr Catherine Humbert for her advice on the biological part of the manuscript, and Dr Pierre Charnpelovier for providing the leukaemic cell lines and for his  ...  Acknowledgments The authors wish to thank Dr Mark Overmars for providing the graphical interface builder, Dr Victoria von Hagen for her advice in editing the manuscript, Dr Raphael Marcelpoil for his help  ...  If this property was used in the convex hull extraction process, we would have obtained the set of the nucleus surface seeds belonging to the convex hull instead of having the surface representation of  ... 
doi:10.1111/j.1365-2818.1995.tb03602.x fatcat:cjfljtw7bneutpjzwayf5752uq

A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots

Gokul Varadhan, Shankar Krishnan, T. V.N. Sriram, Dinesh Manocha
2006 The international journal of robotics research  
The complexity of our algorithm varies as a function of the size of narrow passages in the configuration space.  ...  Instead of exactly computing an explicit representation of the free space, we compute a roadmap that captures its connectivity.  ...  We thank Danny Halperin for many fruitful discussions on the complexity and practical implementations of Minkowski sums in 3D.  ... 
doi:10.1177/0278364906071199 fatcat:rqvcomytqzcrtereyuryntdxki

A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots

Gokul Varadhan, Shankar Krishnan, T. V.N. Sriram, Dinesh Manocha
2005 The international journal of robotics research  
The complexity of our algorithm varies as a function of the size of narrow passages in the configuration space.  ...  Instead of exactly computing an explicit representation of the free space, we compute a roadmap that captures its connectivity.  ...  We thank Danny Halperin for many fruitful discussions on the complexity and practical implementations of Minkowski sums in 3D.  ... 
doi:10.1177/0278364905059061 fatcat:cny2ggd2brhphmmmlfthiwotgu

A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots [chapter]

Gokul Varadhan, Shankar Krishnan, T.V.N. Sriram, Dinesh Manocha
2005 Springer Tracts in Advanced Robotics  
The complexity of our algorithm varies as a function of the size of narrow passages in the configuration space.  ...  Instead of exactly computing an explicit representation of the free space, we compute a roadmap that captures its connectivity.  ...  We thank Danny Halperin for many fruitful discussions on the complexity and practical implementations of Minkowski sums in 3D.  ... 
doi:10.1007/10991541_30 fatcat:amlsbj4j4jb3hbfsro3r2ezgni

How many plans are needed in an IMRT multi-objective plan database?

David Craft, Thomas Bortfeld
2008 Physics in Medicine and Biology  
PCA reveals that the feasible beamlet solutions of a Pareto database lie in a narrow, small dimensional subregion of the full beamlet space, which helps explain why the number of plans needed to characterize  ...  , where N is the number of objectives, was enough for <15% error.  ...  A feasible convex MOP has either one Pareto optimal solution, or infinitely many, so one typically seeks a discrete set of points on the Pareto surface (PS) which approximates the surface well.  ... 
doi:10.1088/0031-9155/53/11/002 pmid:18451463 fatcat:rkrtv2hkgjg4zokudcqcedljva

A New Fast and Robust Collision Detection and Force Computation Algorithm Applied to the Physics Engine Bullet: Method, Integration, and Evaluation [article]

Mikel Sagardia, Theodoros Stouraitis, Joao Lopes E Silva
2014 EuroVR International Conference  
We compared our algorithm with Bullet's native GJK, GJK with convex decomposition, and GImpact, varying the resolution and the scenarios.  ...  Utilizing sphere hierarchies, we are able to rapidly detect likely colliding areas, while the point trees can be used for processing colliding regions in a level-of-detail manner.  ...  non-convex triangle meshes.  ... 
doi:10.2312/eurovr.20141341 dblp:conf/eurovr/SagardiaSS14 fatcat:grbpdf5n7fg3db5wqlcagq4iqe

Reliable Distance and Intersection Computation Using Finite Precision Geometry [chapter]

Katja Bühler, Eva Dyllong, Wolfram Luther
2004 Lecture Notes in Computer Science  
Using smoother enclosures on the highest level, a link is provided to well-known algorithms for convex and non-convex objects.  ...  The particular structure of (I)LIEs allows the construction of effective hierarchies of bounding volumes and the development of effective intersection tests for the enclosed object with rays, boxes and  ...  By applying a convex hull algorithm on the set of extreme vertices we find simple convex enclosing sets. The convex hull of the extreme vertices is shown in Figure 5 .  ... 
doi:10.1007/978-3-540-24738-8_9 fatcat:y5in65einzcold45buufvilmey

On the polyhedral complexity of the integer points in a hyperball

Valentin E. Brimkov, Reneta P. Barneva
2008 Theoretical Computer Science  
Upper bounds for FC (B n Z ) follow from a well-known bound for the number of facets and vertices of the convex hull of B n Z [I. Bárány, D.G.  ...  Define polyhedral facet an enclosing polyhedron for B n Z and f 0 (P) is the number of the 0-facets (vertices) of P.  ...  Acknowledgements The authors thank the three anonymous referees for their useful remarks and suggestions, in particular for a hint by one of the referees how to simplify the proof of Theorem 8.  ... 
doi:10.1016/j.tcs.2008.07.014 fatcat:pv7gk3l4rzacnfz4eba7apue5i

Imaging and analysis techniques for electrical trees using X-ray computed tomography

Roger Schurch, Simon Rowland, Robert Bradley, Philip Withers
2014 IEEE transactions on dielectrics and electrical insulation  
Through the cross-section analysis, the progression of the number of tree channels and the area covered by them can be investigated.  ...  Moreover, taking virtual slices through the replica so created brings the possibility of internal exploration of the electrical tree, without the destruction of the specimen.  ...  Tobias Starborg in the EM facility at the Faculty of Life Sciences in the University of Manchester for his assistance, and the Wellcome Trust for equipment grant support to the EM facility.  ... 
doi:10.1109/tdei.2013.003911 fatcat:2bfktbqcwrgwffnsc43oe5tgiy

Imaging and analysis techniques for electrical trees using X-ray computed tomography

Roger Schurch, Simon Rowland, Robert Bradley, Philip Withers
2014 IEEE transactions on dielectrics and electrical insulation  
Through the cross-section analysis, the progression of the number of tree channels and the area covered by them can be investigated.  ...  Moreover, taking virtual slices through the replica so created brings the possibility of internal exploration of the electrical tree, without the destruction of the specimen.  ...  Tobias Starborg in the EM facility at the Faculty of Life Sciences in the University of Manchester for his assistance, and the Wellcome Trust for equipment grant support to the EM facility.  ... 
doi:10.1109/tdei.2014.6740725 fatcat:f7k5a6p6dffapikockus4nelji

ϵ-maps: Characterizing, detecting and thickening thin features in geometric models

Daniela Cabiddu, Marco Attene
2017 Computers & graphics  
We discuss the importance of this kind of analysis in the design of robust structures and in the creation of geometry to be fabricated with modern additive manufacturing technology.  ...  other parts of the shape unchanged.  ...  Having said that, y is the antipodean of x if one of the following conditions holds: • y is in the middle of a polyhedral triangle; (a) Convex hull and triangulation. (b) R(e) at the first iteration.  ... 
doi:10.1016/j.cag.2017.05.014 fatcat:veotfzesune2lfrqcsd4mybtv4
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