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10
Decision Trees For Geometric Models
, 1993
"... A fundamental problem in modelbased computer vision is that of identifying which of a given set of geometric models is present in an image. Considering a "probe" to be an oracle that tells us whether or not a model is present at a given point, we study the problem of computing efficient strategi ..."
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Cited by 31 (4 self)
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A fundamental problem in modelbased computer vision is that of identifying which of a given set of geometric models is present in an image. Considering a "probe" to be an oracle that tells us whether or not a model is present at a given point, we study the problem of computing efficient strategies ("decision trees") for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine which single model is present. We show that a dlg ke height binary decision tree always exists for k polygonal models (in fixed position), provided (1) they are nondegenerate (do not share boundaries) and (2) they share a common point of intersection. Further, we give an efficient algorithm for constructing such decision tress when the models are given as a set of polygons in the plane. We show that constructing a minimum height tree is NPcomplete if either of the two assumptions is omitted. We provide an efficient greedy heuristic strategy and show ...
Problems in Geometric Probing
, 1989
"... Manysensing problems in robotics can be formulated as problems in geometric probing; that is, givengeometric models of a sensor and an object, what information can be determined about the object and howefficiently can it be found. We r eviewresults in geometric probing and give a collection of ope ..."
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Cited by 22 (1 self)
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Manysensing problems in robotics can be formulated as problems in geometric probing; that is, givengeometric models of a sensor and an object, what information can be determined about the object and howefficiently can it be found. We r eviewresults in geometric probing and give a collection of open problems for a variety of probing models and objects.
Interactive reconstruction via geometric probing
 Proceedings of the IEEE
, 1992
"... Geometric probing considers problems of determining a geometric structure or some aspect of that structure from the results of a mathematical or physical measuring device, a probe. A variety of problems from robotics, medical instrumentation, mathematical optimization, integral and computational geo ..."
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Cited by 11 (0 self)
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Geometric probing considers problems of determining a geometric structure or some aspect of that structure from the results of a mathematical or physical measuring device, a probe. A variety of problems from robotics, medical instrumentation, mathematical optimization, integral and computational geometry, graph theory and other areas fit into this paradigm. This paper surveys the field of geometric probing, with results ordered by probing model. The emphasis is on interactive reconstruction, where the results of all previous measurements are used to determine the orientation of the next probe so it provides the maximum amount of information about the structure. Through interactive reconstruction, finite determination strategies exist for such diverse models as finger, xray, and halfplane probes. 1
Fast Construction of Near Optimal Probing Strategies
 Algorithms for Robotics Motion and Manipulation
, 1999
"... Probing is a common operation employed to reduce the position uncertainty of objects. This thesis demonstrates a technique for constructing provably near optimal probing strategies for precisely localizing polygonal parts. This problem is shown to be dual to the well studied grasping problem of comp ..."
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Cited by 11 (0 self)
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Probing is a common operation employed to reduce the position uncertainty of objects. This thesis demonstrates a technique for constructing provably near optimal probing strategies for precisely localizing polygonal parts. This problem is shown to be dual to the well studied grasping problem of computing optimal nger placements as dened by Mishra et al. [18] and others [11, 17]. A useful quality metric of any given probing strategy can easily be computed from simple geometric constructions in the displacement space of the polygon. The approach will always nd a minimal set of probes that is guaranteed to be near optimal for constraining the position of the polygon. The size of the resulting set of probes is within O(1) of the optimal number of probes and can be computed in O(n log 2 n) time whereas the exact optimal solution is in NPhard [8]. The result of this work is a probing strategy useful in practice for rening part poses. Acknowledgments I would like to express my most s...
Probing ConvexPolygons with Halfplanes
 J. Algorithms
, 1991
"... A halfplane probe through a polygon measures the area of intersection between a halfplane and the polygon. We develop techniques based on xray probing to determine convex ngons in 7n + 7halfplane probes. We also show n + 1halfplane probes are sufficient to verify a specified convex polygon ..."
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Cited by 8 (2 self)
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A halfplane probe through a polygon measures the area of intersection between a halfplane and the polygon. We develop techniques based on xray probing to determine convex ngons in 7n + 7halfplane probes. We also show n + 1halfplane probes are sufficient to verify a specified convex polygon and prove linear lower bounds for determination and verification.
Point Probe Decision Trees for Geometric Concept Classes
, 1993
"... A fundamental problem in modelbased computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a "probe" to be an oracle that tells whether or not the observed model is present at a given point in an image, we study t ..."
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Cited by 7 (5 self)
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A fundamental problem in modelbased computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a "probe" to be an oracle that tells whether or not the observed model is present at a given point in an image, we study the problem of computing efficient strategies ("decision trees") for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine in which class the observed model belongs. We prove a hardness result and give strategies that obtain decision trees whose height is within a log factor of optimal. These results grew out of discussions that began in a series of workshops on Geometric Probing in Computer Vision, sponsored by the Center for Night Vision and ElectroOptics, Fort Belvoir, Virginia, and monitored by the U.S. Army Research Office. The views, opinions, and/or findings contained in this report are those of the authors and should not be con...
Modelbased probing strategies for convex polygons
 Comput. Geom. Theory Appl
, 1992
"... We prove that n + 4finger probes are sufficient to determine the shape of a convex ngon from a finite collection of models, improving the previous result of 2n + 1. Further, weshow that n − 1are necessary, proving this is optimal to within an additive constant. For line probes, we show that 2n + 4p ..."
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Cited by 2 (2 self)
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We prove that n + 4finger probes are sufficient to determine the shape of a convex ngon from a finite collection of models, improving the previous result of 2n + 1. Further, weshow that n − 1are necessary, proving this is optimal to within an additive constant. For line probes, we show that 2n + 4probes are sufficient and 2n − 3necessary. The difference between these results is particularly interesting in light of the duality relationship between finger and line probes.
Optimal Probing Strategies
, 2001
"... Probing is a common operation employed to reduce the position uncertainty of objects. This paper demonstrates a technique for constructing provably near optimal probing strategies for precisely localizing polygonal parts. This problem is shown to be dual to the well studied grasping problem of compu ..."
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Cited by 1 (0 self)
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Probing is a common operation employed to reduce the position uncertainty of objects. This paper demonstrates a technique for constructing provably near optimal probing strategies for precisely localizing polygonal parts. This problem is shown to be dual to the well studied grasping problem of computing optimal finger placements as defined by Mishra et al. [Mishra et al., 1987] and others [Ferrari and Canny, 1992, Mirtich and Canny, 1994]. A useful quality metric of any given probing strategy can easily be computed from simple geometric constructions in the displacement space of the polygon. The approach will always find a minimal set of probes that is guaranteed to be near optimal for constraining the position of the polygon. The size of the resulting set of probes is within O#1# of the optimal number of probes and can be computed in O#n log n# time whereas the exact optimal solution is in NPhard [Das and Joseph, 1990].
Pattern Analysis and Applications manuscript No. (will be inserted by the editor) Recognizing Convex Polygons with Few Finger Probes
"... Abstract The problem considered is that of recognizing if a given convex polygon belongs to a known collection by applying socalled finger probes (i.e., probes by laserlike rays that each return the location of contact). Existing approaches use a number of probes that is linear in the number of si ..."
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Abstract The problem considered is that of recognizing if a given convex polygon belongs to a known collection by applying socalled finger probes (i.e., probes by laserlike rays that each return the location of contact). Existing approaches use a number of probes that is linear in the number of sides of the polygon. The current premise is that probing is expensive, while computing is not. Accordingly, a method is proposed that recognizes a polygon (arbitrarily oriented) from the given collection, with high probability, using only a constant number of finger probes, at the cost of fairly large computing resources, particularly, in setting up and applying a range tree data structure. Analysis, though partly heuristic, is validated with software and experimental results.