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702
OBBTree: A hierarchical structure for rapid interference detection
 PROC. ACM SIGGRAPH, 171–180
, 1996
"... We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bo ..."
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Cited by 843 (50 self)
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We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bounding box trees. At runtime, the algorithm traverses the tree and tests for overlaps between oriented bounding boxes based on a new separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates, almost one order of magnitude faster than earlier methods.
ROC Graphs: Notes and Practical Considerations for Researchers
, 2004
"... Receiver Operating Characteristics (ROC) graphs are a useful technique for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly adopted in the machine learning and data mining research communitie ..."
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Cited by 378 (1 self)
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Receiver Operating Characteristics (ROC) graphs are a useful technique for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly adopted in the machine learning and data mining research communities. Although ROC graphs are apparently simple, there are some common misconceptions and pitfalls when using them in practice. This article serves both as a tutorial introduction to ROC graphs and as a practical guide for using them in research.
Robust Classification for Imprecise Environments
, 1989
"... In realworld environments it is usually difficult to specify target operating conditions precisely. This uncertainty makes building robust classification systems problematic. We present a method for the comparison of classifier performance that is robust to imprecise class distributions and misclas ..."
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Cited by 332 (15 self)
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In realworld environments it is usually difficult to specify target operating conditions precisely. This uncertainty makes building robust classification systems problematic. We present a method for the comparison of classifier performance that is robust to imprecise class distributions and misclassification costs. The ROC convex hull method combines techniques from ROC analysis, decision analysis and computational geometry, and adapts them to the particulars of analyzing learned classifiers. The method is efficient and incremental, minimizes the management of classifier performance data, and allows for clear visual comparisons and sensitivity analyses. We then show that it is possible to build a hybrid classifier that will perform at least as well as the best available classifier for any target conditions. This robust performance extends across a wide variety of comparison frameworks, including the optimization of metrics such as accuracy, expected cost, lift, precision, recall, and ...
ROC graphs: Notes and practical considerations for data mining researchers
, 2003
"... Receiver Operating Characteristics (ROC) graphs are a useful technique for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly adopted in the machine learning and data mining research communitie ..."
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Cited by 205 (0 self)
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Receiver Operating Characteristics (ROC) graphs are a useful technique for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly adopted in the machine learning and data mining research communities. Although ROC graphs are apparently simple, there are some common misconceptions and pitfalls when using them in practice. This article serves both as a tutorial introduction to ROC graphs and as a practical guide for using them in research. Keywords: 1
GraspIt!  A Versatile Simulator for Robotic Grasping
, 2004
"... Research in robotic grasping has flourished in the last 25 years. A recent survey by Bicchi [1] covered over 140 papers, and many more than that have been published. Stemming from our desire to implement some of the work in grasp analysis for particular hand designs, we created an interactive graspi ..."
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Cited by 174 (20 self)
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Research in robotic grasping has flourished in the last 25 years. A recent survey by Bicchi [1] covered over 140 papers, and many more than that have been published. Stemming from our desire to implement some of the work in grasp analysis for particular hand designs, we created an interactive grasping simulator that can import a wide variety of hand and object models and can evaluate the grasps formed by these hands. This system, dubbed “GraspIt!,” has since expanded in scope to the point where we feel it could serve as a useful tool for other researchers in the field. To that end, we are making the system publicly available (GraspIt! is available for download for a variety of platforms from
How good are convex hull algorithms?
, 1996
"... A convex polytope P can be speci ed in two ways: as the convex hull of the vertex set V of P, or as the intersection of the set H of its facetinducing halfspaces. The vertex enumeration problem is to compute V from H. The facet enumeration problem it to compute H from V. These two problems are esse ..."
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Cited by 109 (9 self)
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A convex polytope P can be speci ed in two ways: as the convex hull of the vertex set V of P, or as the intersection of the set H of its facetinducing halfspaces. The vertex enumeration problem is to compute V from H. The facet enumeration problem it to compute H from V. These two problems are essentially equivalent under point/hyperplane duality. They are among the central computational problems in the theory of polytopes. It is open whether they can be solved in time polynomial in jHj + jVj. In this paper we consider the main known classes of algorithms for solving these problems. We argue that they all have at least one of two weaknesses: inability todealwell with "degeneracies," or, inability tocontrol the sizes of intermediate results. We then introduce families of polytopes that exercise those weaknesses. Roughly speaking, fatlattice or intricate polytopes cause algorithms with bad degeneracy handling to perform badly; dwarfed polytopes cause algorithms with bad intermediate size control to perform badly. We also present computational experience with trying to solve these problem on these hard polytopes, using various implementations of the main algorithms.
Double Description Method Revisited
, 1996
"... . The double description method is a simple and useful algorithm for enumerating all extreme rays of a general polyhedral cone in IR d , despite the fact that we can hardly state any interesting theorems on its time and space complexities. In this paper, we reinvestigate this method, introduce som ..."
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Cited by 106 (2 self)
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. The double description method is a simple and useful algorithm for enumerating all extreme rays of a general polyhedral cone in IR d , despite the fact that we can hardly state any interesting theorems on its time and space complexities. In this paper, we reinvestigate this method, introduce some new ideas for efficient implementations, and show some empirical results indicating its practicality in solving highly degenerate problems. 1 Introduction A pair (A; R) of real matrices A and R is said to be a double description pair or simply a DD pair if the relationship Ax 0 if and only if x = R for some 0 holds. Clearly, for a pair (A; R) to be a DD pair, it is necessary that the column size of A is equal to the row size of R, say d. The term "double description" was introduced by Motzkin et al. [MRTT53], and it is quite natural in the sense that such a pair contains two different descriptions of the same object. Namely, the set P (A) represented by A as P (A) = fx 2 IR d : Ax...
Feature Extraction from Point Clouds
 In Proceedings of the 10 th International Meshing Roundtable
, 2001
"... This paper describes a new method to extract feature lines directly from a surface point cloud. No surface reconstruction is needed in advance, only the inexpensive computation of a neighbor graph connecting nearby points. ..."
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Cited by 70 (0 self)
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This paper describes a new method to extract feature lines directly from a surface point cloud. No surface reconstruction is needed in advance, only the inexpensive computation of a neighbor graph connecting nearby points.
The Natural Element Method In Solid Mechanics
, 1998
"... The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal descripti ..."
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Cited by 61 (14 self)
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The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal description of the boundary @ In the Natural Element Method, the trial and test functions are constructed using natural neighbor interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N . The interpolants are smooth (C NEM is identical to linear finite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and nonconvex bodies (cracks) using NEM is also described.
Incremental search methods for reachability analysis of continuous and hybrid systems
 In Hybrid Systems: Computation and Control
, 2004
"... Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and conseq ..."
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Cited by 59 (6 self)
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Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and consequently on the generation of safety certificates; however, inability to prove safety with these tools does not necessarily result in a proof of unsafety. In this paper, we propose an alternative approach, which aims at the fast falsification of safety properties; this approach provides the designer with a complementary set of tools to the ones based on conservative analysis, providing additional insight into the characteristics of the system under analysis. Our algorithms are based on algorithms originally proposed for robotic motion planning; the key idea is to incrementally grow a set of feasible trajectories by exploring the state space in an efficient way. The ability of the proposed algorithms to analyze the reachability and safety properties of general continuous and hybrid systems is demonstrated on examples from the literature. 1