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25
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...
The Complexity of Sensing by Point Sampling
"... this paper we consider the problem of finding the minimum number of sensing points required to distinguish between a finite set of polygonal shapes. For instance, we might imagine embedding a series of point light detectors in a feeder tray. Then we would be interested in the question "What is the m ..."
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Cited by 7 (1 self)
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this paper we consider the problem of finding the minimum number of sensing points required to distinguish between a finite set of polygonal shapes. For instance, we might imagine embedding a series of point light detectors in a feeder tray. Then we would be interested in the question "What is the minimum number of light detectors that can fully distinguish between all the possible shapes?" Or we might imagine a set of mechanical probes that touches the feeder at a finite number of predetermined points. Then we would ask "What are the minimum number of probing points and where should the probes be located in order to distinguish all the possible shapes?" We address these questions in this paper. Intuitively, each sensing point can be regarded as a binary bit that has two values `contained' and `not contained '. So the robot senses a shape by reading out the binary representation of the shape, that is, by checking which points are contained in the shape and which are not. The formalized sensing problem: Given n polygons with a total of m edges in the plane, locate the fewest points such that each polygon contains a distinct subset of points in its interior. We show that this problem is equivalent to an NPcomplete settheoretic problem introduced as Discriminating Set. By a reduction to Hitting Set (and hence to Set Covering), an O(n
Shape Recognition and Twenty Questions
 IN PROC. RECONNAISSANCE DES FORMES ET INTELLIGENCE ARTIFICIELLE (RFIA
, 1993
"... We formulate shape recognition as a coding problem. There is a finite list of possible "hypotheses"  shape classes and/or spatial positionings  and we wish to determine which one is true based on the results of various "tests," which are local image features. We use a decision tree: each interior ..."
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Cited by 6 (2 self)
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We formulate shape recognition as a coding problem. There is a finite list of possible "hypotheses"  shape classes and/or spatial positionings  and we wish to determine which one is true based on the results of various "tests," which are local image features. We use a decision tree: each interior node is assigned one of the tests and each terminal node is assigned one of the hypotheses. The assignment of tests, or "strategy," is recursive: along each branch choose the next test to remove as much uncertainty as possible (as measured by entropy) about the true hypothesis. In contrast to the standard approach of "hypothesize and test," there is no repeated elicitation of hypotheses; instead, the "indexing" is dynamic and stochastic. We gradually formulate specific conjectures as the evolving distribution on hypotheses becomes increasingly peaked. We apply this "twenty questions" approach to the recognition of two types of linear, deformable structures: handwritten numerals and roads i...
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.
How Multirobot Systems Research Will Accelerate Our Understanding of Social Animal Behavior
, 2006
"... Researchers are tracking movements of ants and monkeys using robotics algorithms; they hope to automatically recognize animal behavior and to simulate it using robots. ..."
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Cited by 4 (1 self)
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Researchers are tracking movements of ants and monkeys using robotics algorithms; they hope to automatically recognize animal behavior and to simulate it using robots.
Randomized Inquiries About Shape; an Application to Handwritten Digit Recognition
, 1994
"... We describe an approach to shape recognition based on asking relational questions about the arrangement of landmarks, basically localized and oriented boundary segments. The questions are grouped into highly structured inquiries in the form of a tree. There are, in fact, many trees, each constructed ..."
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Cited by 4 (1 self)
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We describe an approach to shape recognition based on asking relational questions about the arrangement of landmarks, basically localized and oriented boundary segments. The questions are grouped into highly structured inquiries in the form of a tree. There are, in fact, many trees, each constructed from training data based on entropy reduction. The outcome of each tree is not a classification but rather a distribution over shape classes. The final classification is based on an aggregate distribution. The framework is nonEuclidean and there is no feature vector in the standard sense. Instead, the representation of the image data is graphical and each question is associated with a labeled subgraph. The ordering of the questions is highly constrained in order to maintain computational feasibility, and dependence among the trees is reduced by randomly subsampling from the available pool of questions. Experiments are reported on the recognition of handwritten digits. Although the amount ...
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) ...
Efficient and Reliable Template Set matching . . .
"... Object recognition in range image data is formulated as template set matching. The object model is represented as a set of voxel templates, one for each possible pose. The set of all templates is composed into a binary decision tree. Each leaf node references a small number of templates. Each intern ..."
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Object recognition in range image data is formulated as template set matching. The object model is represented as a set of voxel templates, one for each possible pose. The set of all templates is composed into a binary decision tree. Each leaf node references a small number of templates. Each internal node references a single voxel, and has two branches, T and F. The subtree branching from the T branch contains the subset of templates which contain the node voxel. Conversely, the subtree branching from F branch contains the subset of templates which do not contain the node voxel. Traversing the tree at any image location executes a point probe strategy. It efficiently determines agood match with the template set by interrogating only those elements which discriminate between the remaining possible interpretations. The method has been implemented for a number of different heuristic tree design and traversal methods. Results are presented of extensive tests for two objects under isolated, cluttered, and occluded scene conditions. It is shown that there exist traversal/design combinations which are both efficient and reliable, and that the method is robust.
Algorithmica DOI 10.1007/s0045301297156 Improved Approximation Algorithms for the AverageCase Tree Searching Problem
, 2012
"... a vertex has been marked and we want to identify it. In order to locate the marked vertex, we can use edge queries. An edge query e asks in which of the two connected components of T \ e the marked vertex lies. The worstcase scenario where one is interested in minimizing the maximum number of queri ..."
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a vertex has been marked and we want to identify it. In order to locate the marked vertex, we can use edge queries. An edge query e asks in which of the two connected components of T \ e the marked vertex lies. The worstcase scenario where one is interested in minimizing the maximum number of queries is well understood, and linear time algorithms are known for finding an optimal search strategy. Here we study the more involved averagecase analysis: A function w: V → R + is given which measures the likelihood for a vertex to be the one marked, and we seek to determine the strategy (decision tree) that minimizes the weighted average number of queries. In a companion paper we prove that the above tree search problem is NPcomplete even for the class of trees of bounded diameter or bounded degree. Here, we match this complexity result with a tight algorithmic analysis of the bounded degree instances. We show that any optimal strategy (i.e., one that minimizes the weighted average number of queries) performs at most O(�(T)(log V +log(w(T)/wmin))) queries in the worst case, where w(T) is the sum of the likelihoods of the vertices