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EXTREMAL PROBLEMS FOR EXTREMAL DISTANCE AND HARMONIC MEASURE
"... Abstract: We formulate and solve some geometric extremal problems involving extremal distance and harmonic measure. The extremal configurations are symmetric. We answer a question raised in our earlier work [Bet]. 1. ..."
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Abstract: We formulate and solve some geometric extremal problems involving extremal distance and harmonic measure. The extremal configurations are symmetric. We answer a question raised in our earlier work [Bet]. 1.
Extreme Distances in Multicolored Point Sets
, 2003
"... Given a set of n coloredpointsinsomeddimensional Euclidean space, a bichromatic closest (resp. farthest) pair is a closest (resp. farthest) pair of points of different colors. We present efficient algorithms to maintain both a bichromatic closest pair and a bichromatic farthest pair when the the po ..."
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Cited by 1 (0 self)
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on the maximum multiplicity of extreme bichromatic distances in the plane.
Extreme Distances in Multicolored Point Sets
"... Given a set of n colored points in some ddimensional Euclidean space, a bichromatic closest (resp. farthest) pair is a closest (resp. farthest) pair of points of dierent colors. We present ecient algorithms to maintain both a bichromatic closest pair and a bichromatic farthest pair when the the ..."
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Given a set of n colored points in some ddimensional Euclidean space, a bichromatic closest (resp. farthest) pair is a closest (resp. farthest) pair of points of dierent colors. We present ecient algorithms to maintain both a bichromatic closest pair and a bichromatic farthest pair when the the points are xed but they dynamically change color. We do this by solving the more general problem of maintaining a bichromatic edge of minimum (resp. maximum) weight in an undirected weighted graph with colored vertices, when vertices dynamically change color.
Extremal Distance Maintenance for Parametric Curves and Surfaces
 In IEEE International Conference on Robotics and Automation
, 2002
"... A new extremal distance tracking algorithm is presented for parametric curves and surfaces undergoing rigid body motion. The essentially geometric extremization problem is transformed into a dynamical control problem by differentiating with respect to time. Extremization is then solved with the desi ..."
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Cited by 10 (2 self)
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A new extremal distance tracking algorithm is presented for parametric curves and surfaces undergoing rigid body motion. The essentially geometric extremization problem is transformed into a dynamical control problem by differentiating with respect to time. Extremization is then solved
Robust wide baseline stereo from maximally stable extremal regions
 In Proc. BMVC
, 2002
"... The widebaseline stereo problem, i.e. the problem of establishing correspondences between a pair of images taken from different viewpoints is studied. A new set of image elements that are put into correspondence, the so called extremal regions, is introduced. Extremal regions possess highly desir ..."
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Cited by 1016 (35 self)
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The widebaseline stereo problem, i.e. the problem of establishing correspondences between a pair of images taken from different viewpoints is studied. A new set of image elements that are put into correspondence, the so called extremal regions, is introduced. Extremal regions possess highly de
EXTREMAL DISTANCES BETWEEN SECTIONS OF CONVEX BODIES
"... Abstract. Let K, D be convex centrally symmetric bodies in R n. Let k < n and let dk(K, D) be the smallest Banach–Mazur distance between kdimensional sections of K and D. Define ∆(k, n) = sup dk(K, D), where the supremum is taken over all n−dimensional convex symmetric bodies K, D. We prove tha ..."
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Cited by 1 (0 self)
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Abstract. Let K, D be convex centrally symmetric bodies in R n. Let k < n and let dk(K, D) be the smallest Banach–Mazur distance between kdimensional sections of K and D. Define ∆(k, n) = sup dk(K, D), where the supremum is taken over all n−dimensional convex symmetric bodies K, D. We prove
Dual Polar Spaces as Extremal DistanceRegular Graphs
"... A new inequality for the parameters of distanceregular graphs is proved. It implies that if there are in nitely many distanceregular graphs with fixed ; ; a i and c i containing an induced quadrangle then necessarily c i+1 1 + ( 1)c i . As the dual polar graphs show, this inequality is best possib ..."
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A new inequality for the parameters of distanceregular graphs is proved. It implies that if there are in nitely many distanceregular graphs with fixed ; ; a i and c i containing an induced quadrangle then necessarily c i+1 1 + ( 1)c i . As the dual polar graphs show, this inequality is best
STRUCTURE OF NORMED SPACES WITH EXTREMAL DISTANCE TO THE EUCLIDEAN SPACE
"... Abstract. It is shown that a finite dimensional Banach space has the Euclidean distance of maximal order if and only if it contains a proportional dimensional subspace (and a quotient of a subspace) of a very special form. 1. ..."
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Abstract. It is shown that a finite dimensional Banach space has the Euclidean distance of maximal order if and only if it contains a proportional dimensional subspace (and a quotient of a subspace) of a very special form. 1.
GPSLess Low Cost Outdoor Localization for Very Small Devices.
 IEEE Personal Communications Magazine,
, 2000
"... AbstractInstrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where ..."
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Cited by 1000 (27 self)
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a given node is physically located in a network is a challenging one, and yet extremely crucial for many of these applications. Practical considerations such as the small size, form factor, cost and power constraints of nodes preclude the reliance on GPS (Global Positioning System) on all nodes
From Few to many: Illumination cone models for face recognition under variable lighting and pose
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a generative appearancebased method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a smal ..."
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Cited by 754 (12 self)
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illumination cone (based on Euclidean distance within the image space). We test our face recognition method on 4050 images from the Yale Face Database B; these images contain 405 viewing conditions (9 poses ¢ 45 illumination conditions) for 10 individuals. The method performs almost without error, except
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