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25
An Active Testing Model for Tracking Roads in Satellite Images
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... We present a new approach for tracking roads from satellite images, and thereby illustrate a general computational strategy ("active testing") for tracking 1D structures and other recognition tasks in computer vision. Our approach is related to recent work in active vision on "where to look next" a ..."
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Cited by 162 (5 self)
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We present a new approach for tracking roads from satellite images, and thereby illustrate a general computational strategy ("active testing") for tracking 1D structures and other recognition tasks in computer vision. Our approach is related to recent work in active vision on "where to look next" and motivated by the "divideandconquer" strategy of parlor games such as "Twenty Questions." We choose "tests" (matched filters for short road segments) one at a time in order to remove as much uncertainty as possible about the "true hypothesis" (road position) given the results of the previous tests. The tests are chosen online based on a statistical model for the joint distribution of tests and hypotheses. The problem of minimizing uncertainty (measured by entropy) is formulated in simple and explicit analytical terms. To execute this entropy testing rule we then alternate between data collection and optimization: at each iteration new image data are examined and a new entropy minimizat...
Surface Approximation and Geometric Partitions
 IN PROC. 5TH ACMSIAM SYMPOS. DISCRETE ALGORITHMS
, 1994
"... Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x ..."
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Cited by 97 (15 self)
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Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x; y) of minimum complexity (that is, a xymonotone polyhedral surface, with a minimum number of vertices, edges, or faces) such that j\Sigma(x p ; y p ) \Gamma z p j "; for all (x p ; y p ; z p ) 2 S: We prove that the decision version of this problem is NPHard . The main result of our paper is a polynomialtime approximation algorithm that computes a piecewise linear surface of size O(K o log K o ), where K o is the complexity of an optimal surface satisfying the constraints of the problem. The technique
Localizing a Robot with Minimum Travel
, 1995
"... We consider the problem of localizing a robot in a known environment modeled by a simple polygon P . We assume that the robot has a map of P but is placed at an unknown location inside P . From its initial location, the robot sees a set of points called the visibility polygon V of its location. I ..."
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Cited by 44 (4 self)
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We consider the problem of localizing a robot in a known environment modeled by a simple polygon P . We assume that the robot has a map of P but is placed at an unknown location inside P . From its initial location, the robot sees a set of points called the visibility polygon V of its location. In general, sensing at a single point will not suffice to uniquely localize the robot, since the set H of points in P with visibility polygon V may have more than one element. Hence, the robot must move around and use range sensing and a compass to determine its position (i.e.
Generalized binary search
 In Proceedings of the 46th Allerton Conference on Communications, Control, and Computing
, 2008
"... This paper addresses the problem of noisy Generalized Binary Search (GBS). GBS is a wellknown greedy algorithm for determining a binaryvalued hypothesis through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideratio ..."
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Cited by 30 (0 self)
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This paper addresses the problem of noisy Generalized Binary Search (GBS). GBS is a wellknown greedy algorithm for determining a binaryvalued hypothesis through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets, a natural generalization of the idea underlying classic binary search. GBS is used in many applications, including fault testing, machine diagnostics, disease diagnosis, job scheduling, image processing, computer vision, and active learning. In most of these cases, the responses to queries can be noisy. Past work has provided a partial characterization of GBS, but existing noisetolerant versions of GBS are suboptimal in terms of query complexity. This paper presents an optimal algorithm for noisy GBS and demonstrates its application to learning multidimensional threshold functions. 1
Geometric sensing of known planar shapes
 In Proceedings of the 1996 IEEE International Conference on Robotics and Automation
, 1996
"... Industrial assembly involves sensing the pose (orientation and position) of a part. Efficient and reliable sensing strategies can be developed for an assembly task if the shape of the part is known in advance. In this article we investigate two problems of determining the pose of a polygonal part of ..."
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Cited by 19 (10 self)
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Industrial assembly involves sensing the pose (orientation and position) of a part. Efficient and reliable sensing strategies can be developed for an assembly task if the shape of the part is known in advance. In this article we investigate two problems of determining the pose of a polygonal part of known shape for the cases of a continuum and a finite number of possible poses respectively. The first problem, named sensing by inscription, involves determining the pose of a convex ngon from a set of m supporting cones. An algorithm with running time O(nm) that almost always reduces to O(n+m log n) is presented to solve for all possible poses of the polygon. We prove that the number of possible poses cannot exceed 6n, given m â‰¥ 2 supporting cones with distinct vertices. Simulation experiments demonstrate that two supporting cones are sufficient to determine the real pose of the ngon in most cases. Our results imply that sensing in practice can be carried out by obtaining viewing angles of a planar part at multiple exterior sites in the plane. On many occasions a parts feeder will have reduced the number of possible poses of a part to a small finite set. Our second problem, named sensing by point sampling,
Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization
"... Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions t ..."
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Cited by 17 (2 self)
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Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor placement, viral marketing and poolbased active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases and leads to natural generalizations. 1
On the Area of Overlap of Translated Polygons
, 1994
"... Given two simple polygons P and Q in the plane and a translation vector t 2 R 2 , the areaofoverlap function of P and Q is the function Ar(t) = Area(P " (t +Q)), where t +Q denotes Q translated by t. This function has a number of applications in areas such as motion planning and object recognit ..."
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Cited by 14 (0 self)
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Given two simple polygons P and Q in the plane and a translation vector t 2 R 2 , the areaofoverlap function of P and Q is the function Ar(t) = Area(P " (t +Q)), where t +Q denotes Q translated by t. This function has a number of applications in areas such as motion planning and object recognition. We present a number of mathematical results regarding this function. We also provide efficient algorithms for computing a representation of this function, and for tracing contour curves of constant area of overlap. The support of the National Science Foundation under grant CCR 9310705 is gratefully acknowledged, as is the help of Sandy German in preparing this paper. A preliminary version of this paper appeared in Vision Geometry II , R.A. Melter and A.Y. Wu, Editors, Proc. SPIE 2060, 1993, 254264. 1 Introduction An important geometric problem involving planar shapes is whether two simple polygons intersect one another. If the polygons do intersect it is often useful to acquire mo...
A Theoretical Analysis of Query Selection for Collaborative Filtering
 Machine Learning
, 2003
"... We consider the problem of determining which of a set of experts has tastes most similar to a given user by asking the user questions about his likes and dislikes. We describe a simple and fast algorithm for a theoretical model of this problem with a provable approximation guarantee, and prove that ..."
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Cited by 11 (1 self)
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We consider the problem of determining which of a set of experts has tastes most similar to a given user by asking the user questions about his likes and dislikes. We describe a simple and fast algorithm for a theoretical model of this problem with a provable approximation guarantee, and prove that solving the problem exactly is NPHard.
Approximating Optimal Binary Decision Trees
"... Abstract. We give a (ln n + 1)approximation for the decision tree (DT) problem. We also show that DT does not have a PTAS unless P=NP. An instance of DT is a set of m binary tests T = (T1,..., Tm) and a set of n items X = (X1,..., Xn). The goal is to output a binary tree where each internal node is ..."
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Cited by 10 (0 self)
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Abstract. We give a (ln n + 1)approximation for the decision tree (DT) problem. We also show that DT does not have a PTAS unless P=NP. An instance of DT is a set of m binary tests T = (T1,..., Tm) and a set of n items X = (X1,..., Xn). The goal is to output a binary tree where each internal node is a test, each leaf is an item and the total external path length of the tree is minimized. DT has a rich history in computer science with applications ranging from medical diagnosis to experiment design. Our work, while providing the first nontrivial upper and lower bounds on approximating DT, also demonstrates that DT and a subtly different problem which also bears the name decision tree (but which we call ConDT) have fundamentally different approximation complexity. We conclude with a stronger lower bound for a third decision tree problem called MinDT. 1