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An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge
 IEEE Transactions on Computers
, 1981
"... In many computer applications areas such as graphics, automated cartography, image processing, and robotics the notion of visibility among objects modeled as polygons is a recurring theme. This paper is concerned with the visibility of a simple polygon from one of its edges. Three natural definition ..."
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Cited by 43 (10 self)
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In many computer applications areas such as graphics, automated cartography, image processing, and robotics the notion of visibility among objects modeled as polygons is a recurring theme. This paper is concerned with the visibility of a simple polygon from one of its edges. Three natural definitions of the visibility of a polygon from an edge are presented. The following computational problem is considered. Given an n sided simple polygon, is the polygon visible from a specified edge? An O(n), and thus optimal, algorithm is exhibited for determining edge visibility under any of the three definitions. The paper closes with an interesting characterization of visibility and some open problems in this area. Index Terms  Algorithms, computational complexity, computational geometry, computer graphics, hidden line problems, image processing, robotics, simple polygon, visibility. 1. Introduction The notion of visibility in geometric objects is one that appears in many applications: the ...
Robotic Manipulation for Parts Transfer and Orienting: Mechanics, Planning, and Shape Uncertainty
, 1996
"... Robots can modify their environmentby manipulating objects. To fully exploit this ability, it is important to determine the manipulation capabilities of a given robot. Such characterization in terms of the physics and geometry of the task has important implications for manufacturing applications, wh ..."
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Cited by 18 (7 self)
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Robots can modify their environmentby manipulating objects. To fully exploit this ability, it is important to determine the manipulation capabilities of a given robot. Such characterization in terms of the physics and geometry of the task has important implications for manufacturing applications, where simpler hardware leads to cheaper and more reliable systems. This thesis develops techniques for robots to transfer parts from a known position and orientation to a goal position and orientation, and to orient parts by bringing them from an unknown initial orientation to a goal orientation. This parts feeding process is an important aspect of flexible assembly. Designing automatic planners that capture the task mechanics and geometry leads to flexible parts transfer and orienting systems. The implemented parts feeding systems use simple effectors that allow manipulation of a broad class of parts, and simple sensors that are robust and inexpensive. The main research issues are to identify a ...
Fundamentals of restrictedorientation convexity
 Information Sciences
, 1996
"... Abstract A restrictedorientation convex set, also called an Oconvex set, is a set of points whose intersection with lines from some fixed set is empty or connected. The notion of Oconvexity generalizes standard convexity and orthogonal convexity. We explore some of the basic properties of Oconve ..."
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Cited by 13 (9 self)
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Abstract A restrictedorientation convex set, also called an Oconvex set, is a set of points whose intersection with lines from some fixed set is empty or connected. The notion of Oconvexity generalizes standard convexity and orthogonal convexity. We explore some of the basic properties of Oconvex sets in two and higher dimensions. We also study Oconnected sets, which are a subclass of Oconvex sets, with several special properties. We introduce and investigate restrictedorientation analogs of lines, flats, and hyperplanes, and characterize Oconvex and Oconnected sets in terms of their intersections with hyperplanes. We then explore properties of Oconnected curves; in particular, we show when replacing a segment of an Oconnected curve with a new curvilinear segment yields an Oconnected curve and when the catenation of several curvilinear segments forms an Oconnected segment. We use these results to characterize an Oconnected set in terms of Oconnected segments, joining pairs of its points, that are wholly contained in the set. We also identify some of the major properties of standard convex sets that hold for Oconvexity. In particular, we demonstrate that the intersection of a collection ofOconvex sets is an Oconvex set, every Oconnected curvilinear segment is a segment of some Oconnected curve, and, for every two points of an Oconvex set, there is anOconvex segment joining them that is wholly contained in the set.
Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization
, 1997
"... The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility pr ..."
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Cited by 13 (3 self)
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The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualification from convex analysis implies bounded linear regularity, which in turn yields the strong conical hull intersection property. Jameson's duality for two cones, which relates bounded linear regularity to property (G), is rederived and refined. For polyhedral cones, a statement dual to Hoffman's error bound result is obtained. A sharpening of a result on error bounds for convex inequalities by Auslender and Crouzeix is presented. Finally, for two subspaces, property (G) is quantified by the angle between the subspaces. 1991 M.R. Subject Classification. Primary 90C25; Secondary 15A39, 41A29, 46A40...
The dangers of extreme counterfactuals
 Political Analysis
, 2006
"... We address the problem that occurs when inferences about counterfactuals—predictions, ‘‘whatif’ ’ questions, and causal effects—are attempted far from the available data. The danger of these extreme counterfactuals is that substantive conclusions drawn from statistical models that fit the data well ..."
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Cited by 13 (7 self)
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We address the problem that occurs when inferences about counterfactuals—predictions, ‘‘whatif’ ’ questions, and causal effects—are attempted far from the available data. The danger of these extreme counterfactuals is that substantive conclusions drawn from statistical models that fit the data well turn out to be based largely on speculation hidden in convenient modeling assumptions that few would be willing to defend. Yet existing statistical strategies provide few reliable means of identifying extreme counterfactuals. We offer a proof that inferences farther from the data allow more model dependence and then develop easytoapply methods to evaluate how model dependent our answers would be to specified counterfactuals. These methods require neither sensitivity testing over specified classes of models nor evaluating any specific modeling assumptions. If an analysis fails the simple tests we offer, then we know that substantive results are sensitive to at least some modeling choices that are not based on empirical evidence. Free software that accompanies this article implements all the methods developed. 1
Geodesic Star Convexity for Interactive Image Segmentation
"... In this paper we introduce a new shape constraint for interactive image segmentation. It is an extension of Veksler’s [25] starconvexity prior, in two ways: from a single star to multiple stars and from Euclidean rays to Geodesic paths. Global minima of the energy function are obtained subject to t ..."
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Cited by 10 (0 self)
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In this paper we introduce a new shape constraint for interactive image segmentation. It is an extension of Veksler’s [25] starconvexity prior, in two ways: from a single star to multiple stars and from Euclidean rays to Geodesic paths. Global minima of the energy function are obtained subject to these new constraints. We also introduce Geodesic Forests, which exploit the structure of shortest paths in implementing the extended constraints. The starconvexity prior is used here in an interactive setting and this is demonstrated in a practical system. The system is evaluated by means of a “robot user ” to measure the amount of interaction required in a precise way. We also introduce a new and harder dataset which augments the existing Grabcut dataset [1] with images and ground truth taken from the PASCAL VOC segmentation challenge [7]. 1.
Composite Multiclass Losses
"... We consider loss functions for multiclass prediction problems. We show when a multiclass loss can be expressed as a “proper composite loss”, which is the composition of a proper loss and a link function. We extend existing results for binary losses to multiclass losses. We determine the stationarity ..."
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Cited by 9 (5 self)
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We consider loss functions for multiclass prediction problems. We show when a multiclass loss can be expressed as a “proper composite loss”, which is the composition of a proper loss and a link function. We extend existing results for binary losses to multiclass losses. We determine the stationarity condition, Bregman representation, ordersensitivity, existence and uniqueness of the composite representation for multiclass losses. We subsume existing results on “classification calibration ” by relating it to properness and show that the simple integral representation for binary proper losses can not be extended to multiclass losses. 1
Generalized halfspaces in restrictedorientation convexity
 JOURNAL OF GEOMETRY
, 1995
"... Restrictedorientation convexity, also called Oconvexity, is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. The notion ofOconvexity generalizes standard convexity and several types of nontraditional convexity. We introduce Ohalfspaces, whic ..."
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Cited by 8 (7 self)
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Restrictedorientation convexity, also called Oconvexity, is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. The notion ofOconvexity generalizes standard convexity and several types of nontraditional convexity. We introduce Ohalfspaces, which are an analog of halfspaces in the theory of Oconvexity. We show that this notion generalizes standard halfspaces, explore properties of these generalized halfspaces, and demonstrate their relationship to Oconvex sets. We also describe directed Ohalfspaces, which are a subclass of Ohalfspaces that has some special properties. We first present some basic properties of Ohalfspaces and compare them with the properties of standard halfspaces. We show that Ohalfspaces may be disconnected, characterize an Ohalfspace in terms of its connected components, and derive the upper bound on the number of components. We then study properties of the boundaries of Ohalfspaces. Finally, we describe the complements of Ohalfspaces and give a necessary and sufficient condition under which the complement of an Ohalfspace is an Ohalfspace.
Asymptotics For The Tukey Depth
"... We describe the asymptotic behavior of the normalized empirical Tukey depth process. It is seen that in general the latter does not converge weakly, even though its marginals are always do. Closed subsets of the index set where weak convergence does occur are identified and a necessary and sufficien ..."
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Cited by 6 (1 self)
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We describe the asymptotic behavior of the normalized empirical Tukey depth process. It is seen that in general the latter does not converge weakly, even though its marginals are always do. Closed subsets of the index set where weak convergence does occur are identified and a necessary and sufficient condition for the asymptotic normality of the marginals is given. Finally, for smooth symmetric distributions asymptotic normality of a multivariate trimmed mean based on the Tukey depth is obtained.
A new convexity measure based on a probabilistic interpretation of images
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... In this article we present a novel convexity measure for object shape analysis. The proposed method is based on the idea of generating pairs of points from a set, and measuring the probability that a point dividing the corresponding line segments belongs to the same set. The measure is directly appl ..."
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Cited by 5 (0 self)
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In this article we present a novel convexity measure for object shape analysis. The proposed method is based on the idea of generating pairs of points from a set, and measuring the probability that a point dividing the corresponding line segments belongs to the same set. The measure is directly applicable to image functions representing shapes, and also to grayscale images which approximate image binarizations. The approach introduced gives rise to a variety of convexity measures, which makes it possible to obtain more information about the object shape. The proposed measure turns out to be easy to implement using the Fast Fourier Transform and we will consider this in detail. Finally, we illustrate the behavior of our measure in different situations and compare it to other similar ones.