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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 32 (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 ...
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...
Recognizing Polygonal Parts from Width Measurements
, 1995
"... Automatic recognition of parts is an important problem in many industrial applications. One model of the problem is: Given a finite set of polygonal parts, use a set of "width" measurements taken by a paralleljaw gripper to determine which part is present. We study the problem of computing effic ..."
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Cited by 5 (0 self)
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Automatic recognition of parts is an important problem in many industrial applications. One model of the problem is: Given a finite set of polygonal parts, use a set of "width" measurements taken by a paralleljaw gripper to determine which part is present. We study the problem of computing efficient strategies ("grasp plans"), with the goal to minimize the number of measurements necessary in the worst case. We show that finding a minimum length grasp plan is Af7hard, and give a polynomial time approximation algorithm that is simple and produces a solution that is within a log factor from optimal.
Distributed Sensing and Probing With Multiple Search Agents: Toward SystemLevel Landmine Detection Solutions
, 1995
"... The problem of landmine detection has been studied for decades. Mine detection systems have typically been developed by first identifying a sensor technology, then testing on particular manmade testbeds, then deploying the sensor on a vehicle or manportable device. Despite much effort, current syst ..."
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Cited by 3 (2 self)
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The problem of landmine detection has been studied for decades. Mine detection systems have typically been developed by first identifying a sensor technology, then testing on particular manmade testbeds, then deploying the sensor on a vehicle or manportable device. Despite much effort, current systems still exhibit gaps between existing and desired capability, e.g., in terms of rate of advance, detection rate, and false alarm rate within demonstration testbeds. In this paper, we propose a new systemlevel approach to landmine detection. We argue that "the landmine detection problem" cannot be attacked in a piecewise fashion: systemlevel solutions must simultaneously consider functional requirements, sensor technologies, models of sensors, the method of sensor application, and the platforms from which sensors are applied. This perspective allows us to shift our focus from the previous emphasis on novel sensor technology, and to go somewhat beyond traditional doctrines governing stand...
Probe Trees for Touching Character Recognition
 In Proc. International Conference on Imaging Science, Systems and Technology, (CISST
, 1998
"... The problem of touching characters is very important for the recognition of low quality text. A solution is presented here for the problem of touching character recognition for fixed font, using a decision tree classifier paradigm. The method is based on the concept of probe trees, a fast recognitio ..."
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Cited by 2 (2 self)
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The problem of touching characters is very important for the recognition of low quality text. A solution is presented here for the problem of touching character recognition for fixed font, using a decision tree classifier paradigm. The method is based on the concept of probe trees, a fast recognition method that uses character probes to acquire knowledge about the input samples. Touching characters are recognized without segmentation, so errors common in segmentationbased methods are avoided. Speed is achieved by constructing a decision tree for a specific font offline, before any samples are seen. A deformation model is used to generate probes that withstand certain image distortions. Experimental results are presented in support of the method. Keywords: Touching Characters, Probe Trees, Optical Character Recognition, Document Image Understanding. sazaklis@cs.sunysb.edu. Supported in part by a grant from Syngen Corp. and by the Strategic Partnership for Industrial Resurgence, Coll...
Decision Tree Construction in Fixed Dimensions: Being Global is Hard but Local Greed is Good
, 1995
"... We study the problem of finding optimal linear decision trees for classifying a set of points in IR d partitioned into concept classes, where d is a fixed, but arbitrary, constant. We show that optimal decision tree construction is NPcomplete, even for 3dimensional point sets. Nevertheless, we c ..."
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Cited by 1 (1 self)
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We study the problem of finding optimal linear decision trees for classifying a set of points in IR d partitioned into concept classes, where d is a fixed, but arbitrary, constant. We show that optimal decision tree construction is NPcomplete, even for 3dimensional point sets. Nevertheless, we can prove a number of interesting approximation bounds on the use of random sampling for finding optimal splitting hyperplanes in greedy decision tree constructions. We give experimental evidence that, while providing asymptotic guarantees on split quality, this random sampling approach behaves as good in practice as uniform randomization strategies that do not provide such guarantees. Finally, we provide experimental justification for coupling this random sampling strategy with locallygreedy "hill climbing" methods. 1 Introduction A general framework for machine learning is that one is given a (hopefully representative) sample S of n points taken from some much larger (possibly infinite) ...