Results 1  10
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47
ThreeDimensional Modeling of Human Organs and Its Application to Diagnosis and Surgical Planning
, 1993
"... We describe a method to obtain a 3D representation of objects given by a series of parallel crosssections. We define a contourtocontour connection based on geometric closeness and show a practical way to calculate an approximation using the Delaunay triangulation. The performance of our method is ..."
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Cited by 90 (3 self)
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We describe a method to obtain a 3D representation of objects given by a series of parallel crosssections. We define a contourtocontour connection based on geometric closeness and show a practical way to calculate an approximation using the Delaunay triangulation. The performance of our method is shown on several medical examples. We further evaluate the precision of 3D models reconstructed from synthetic data and compare it to the marching cube reconstruction. In the third part, we use the 3D model of a pelvis and a fetal head for simulating a delivery. We calculate the forces applying on the head and define a measure of adequateness. This measure may be interesting for the decision of making a cesarean section. Keywords: 3D reconstruction, Delaunay triangulation, Voronoi diagram, Hausdorff distance, robotics, obstetrics. Acknowledgement I am deeply indebted to my supervisor JeanDaniel Boissonnat. He gave me the opportunity to work at INRIA in a stimulating environment and on ...
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
 In Proc. 8th Workshop Alg. Eng. Exper. (Alenex’06
, 2006
"... We present an exact implementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R 3. Our implementation is complete in the sense that it does not assume general position. Namely, it can handle degenerate input, and it produces exact results. We also present applicati ..."
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Cited by 40 (10 self)
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We present an exact implementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R 3. Our implementation is complete in the sense that it does not assume general position. Namely, it can handle degenerate input, and it produces exact results. We also present applications of the Minkowskisum computation to answer collision and proximity queries about the relative placement of two convex polyhedra in R 3. The algorithms use a dual representation of convex polyhedra, and their implementation is mainly based on the Arrangement package of Cgal, the Computational Geometry Algorithm Library. We compare our Minkowskisum construction with the only three other methods that produce exact results we are aware of. One is a simple approach that computes the convex hull of the pairwise sums of vertices of two convex polyhedra. The second is based on Nef polyhedra embedded on the sphere, and the third is an outputsensitive approach based on linear programming. Our method is significantly faster. The results of experimentation with a broad family of convex polyhedra are reported. The relevant programs, source code, data sets, and documentation are available at
Online manipulation planning for two robot arms in a dynamic environment
 International Journal of Robotics Research
, 1997
"... In a constantly changing and partially unpredictable environment, robotmotion planning must be online. The planner receives a continuous flow of information about occurring events and generates new plans while previously planned motions are being executed. This article describes an online plann ..."
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Cited by 35 (4 self)
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In a constantly changing and partially unpredictable environment, robotmotion planning must be online. The planner receives a continuous flow of information about occurring events and generates new plans while previously planned motions are being executed. This article describes an online planner for two cooperating arms whose task is to grab parts of various types on a conveyor belt and transfer them to their respective goals, while avoiding collisions with obstacles. Parts arrive on the belt in random order, at any time. Both goals and obstacles may be dynamically changed. This scenario is typical of manufacturing cells serving machine tools, assembling products, or packaging objects. The proposed approach breaks the overall planning problem into subproblems, each involving a lowdimensional configuration or configuration x time space, and orchestrates very fast primitives solving these subproblems. The resulting planner has been implemented and extensively tested in a simulated environment, as well as with a real dualarm system. Its competitiveness has been evaluated against an oracle making (almost) the best decision at any one time; the results show that the planner compares extremely well. 1.
Almost tight upper bounds for the single cell and zone problems in three dimensions
 Geom
, 1995
"... We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of n lowdegree algebraic surface patches in 3space. We show that this complexity is O(n ..."
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Cited by 31 (17 self)
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We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of n lowdegree algebraic surface patches in 3space. We show that this complexity is O(n
Almost tight upper bounds for vertical decompositions in four dimensions
 In Proc. 42nd IEEE Symposium on Foundations of Computer Science
, 2001
"... We show that the complexity of the vertical decomposition of an arrangement of n fixeddegree algebraic surfaces or surface patches in four dimensions is O(n 4+ε), for any ε> 0. This improves the best previously known upper bound for this problem by a nearlinear factor, and settles a major proble ..."
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Cited by 30 (4 self)
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We show that the complexity of the vertical decomposition of an arrangement of n fixeddegree algebraic surfaces or surface patches in four dimensions is O(n 4+ε), for any ε> 0. This improves the best previously known upper bound for this problem by a nearlinear factor, and settles a major problem in the theory of arrangements of surfaces, open since 1989. The new bound can be extended to higher dimensions, yielding the bound O(n 2d−4+ε), for any ε> 0, on the complexity of vertical decompositions in dimensions d ≥ 4. We also describe the immediate algorithmic applications of these results, which include improved algorithms for point location, range searching, ray shooting, robot motion planning, and some geometric optimization problems. 1
The geometry of uncertainty in moving objects databases
 In Proc. of the 8th Intl. Conf. on Extending Database Technology (EDBT
, 2002
"... Abstract. This work addresses the problem of querying moving objects databases. which capture the inherent uncertainty associated with the location of moving point objects. We address the issue of modeling, constructing, and querying a trajectories database. We propose to model a trajectory as a 3D ..."
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Cited by 29 (3 self)
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Abstract. This work addresses the problem of querying moving objects databases. which capture the inherent uncertainty associated with the location of moving point objects. We address the issue of modeling, constructing, and querying a trajectories database. We propose to model a trajectory as a 3D cylindrical body. The model incorporates uncertainty in a manner that enables efficient querying. Thus our model strikes a balance between modeling power, and computational efficiency. To demonstrate efficiency, we report on experimental results that relate the length of a trajectory to its size in bytes. The experiments were conducted using a real map of the Chicago Metropolitan area. We introduce a set of novel but natural spatiotemporal operators which capture uncertainty, and are used to express spatiotemporal range queries. We also devise and analyze algorithms to process the operators. The operators have been implemented as a part of our DOMINO project. 1
Arrangements and their Applications in Robotics: Recent Developments
, 1995
"... this paper addresses and survey previous work on these problems. We state the basic new results in Section 3. We exemplify the usefulness of these results by applying them to problems involving robot motion planning (Section 4) and visibility and aspect graphs (Section 5). Section 6 deals with new r ..."
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Cited by 23 (9 self)
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this paper addresses and survey previous work on these problems. We state the basic new results in Section 3. We exemplify the usefulness of these results by applying them to problems involving robot motion planning (Section 4) and visibility and aspect graphs (Section 5). Section 6 deals with new results on Minkowski sums of convex polyhedra in three dimensions, which have applications in robot motion planning and in other related areas. The paper concludes in Section 7, with further applications of the new results and with some open problems.
Hybrid motion planning: Coordinating two discs moving among polygonal obstacles in the plane
 In Workshop on the Algorithmic Foundations of Robotics
, 2002
"... The basic motionplanning problem is to plan a collisionfree motion for objects moving among obstacles between free initial and goal positions, or to determine that no such motion exists. The basic problem as well as numerous variants of it have been intensively studied over the past two decades yi ..."
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Cited by 21 (6 self)
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The basic motionplanning problem is to plan a collisionfree motion for objects moving among obstacles between free initial and goal positions, or to determine that no such motion exists. The basic problem as well as numerous variants of it have been intensively studied over the past two decades yielding a wealth of results and techniques, both theoretical and practical. In this paper, we propose a novel approach to motion planning, hybrid motion planning, in which we integrate complete solutions along with Probabilistic Roadmap (PRM) techniques in order to combine their strengths and offset their weaknesses. We incorporate robust tools, that have not been available before, in order to implement the complete solutions. We exemplify our approach in the case of two discs moving among polygonal obstacles in the plane. The planner we present easily solves problems where a narrow passage in the workspace can be arbitrarily small. Our planner is also capable of providing correct nontrivial “no ” answers, namely it can, for some queries, detect the situation where no solution exists. We envision our planner not as a total solution but rather as a new tool that cooperates with existing planners. We demonstrate the advantages and shortcomings of our planner with experimental results. 1
Motion Planning for a Convex Polygon in a Polygonal Environment
 Geom
, 1997
"... We study the motionplanning problem for a convex mgon P in a planar polygonal environment Q bounded by n edges. We give the first algorithm that constructs the entire free configuration space (the 3dimensional space of all free placements of P in Q) in time that is nearquadratic in mn, which i ..."
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Cited by 17 (8 self)
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We study the motionplanning problem for a convex mgon P in a planar polygonal environment Q bounded by n edges. We give the first algorithm that constructs the entire free configuration space (the 3dimensional space of all free placements of P in Q) in time that is nearquadratic in mn, which is nearly optimal in the worst case. The algorithm is also conceptually relatively simple. Previous solutions were incomplete, more expensive, or produced only part of the free configuration space. Combining our solution with parametric searching, we obtain an algorithm that finds the largest placement of P in Q in time that is also nearquadratic in mn. In addition, we describe an algorithm that preprocesses the computed free configuration space so that `reachability' queries can be answered in polylogarithmic time. All three authors have been supported by a grant from the U.S.Israeli Binational Science Foundation. Pankaj Agarwal has also been supported by a National Science Foundation Gr...
Challenges and applications for selfassembled DNAnanostructures
 In: Proceedings of the Sixth DIMACS Workshop on DNA Based Computers (meeting at
, 2000
"... Abstract. DNA selfassembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA selfassemble into DNA crossover molecules (tiles). These DNA tiles have sticky ends that preferentially match the sticky ends of certain other ..."
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Cited by 14 (4 self)
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Abstract. DNA selfassembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA selfassemble into DNA crossover molecules (tiles). These DNA tiles have sticky ends that preferentially match the sticky ends of certain other DNA tiles, facilitating the further assembly into tiling lattices. We discuss key theoretical and practical challenges of DNA selfassembly, aswell as numerous potential applications. The selfassembly of large 2D lattices consisting of up to thousands of tiles have been recently demonstrated, and 3D DNA lattices maysoonbe feasible to construct. We describe various novel DNA tiles with properties that facilitate selfassembly and their visualization by imaging devices such as atomic force microscope. We discuss bounds on the speed and error rates of the various types of selfassembly reactions, as well as methods that may minimize errors in selfassembly. We brie y discuss the ongoing development of attachment chemistry from DNA lattices