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559
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
Abstract

Cited by 989 (4 self)
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translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the rootmeansquare deviations of the coordinates in the two systems from their respective centroids
Constrained centroidal Voronoi tessellations for surfaces
 SIAM J. Sci. Comput
"... Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available; for exa ..."
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Cited by 74 (25 self)
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Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available
The BurbeaRao and Bhattacharyya centroids
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2011
"... We study the centroid with respect to the class of informationtheoretic BurbeaRao divergences that generalize the celebrated JensenShannon divergence by measuring the nonnegative Jensen difference induced by a strictly convex and differentiable function. Although those BurbeaRao divergences are ..."
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Cited by 26 (14 self)
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We study the centroid with respect to the class of informationtheoretic BurbeaRao divergences that generalize the celebrated JensenShannon divergence by measuring the nonnegative Jensen difference induced by a strictly convex and differentiable function. Although those BurbeaRao divergences
PERIODIC CENTROIDAL VORONOI TESSELLATIONS
 INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
, 2012
"... Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations whose generators coincide with the mass centroids of the respective Voronoi regions. CVTs have become useful tools in many application domains of arts, sciences and engineering. In this work, for the first time the concept of the pe ..."
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Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations whose generators coincide with the mass centroids of the respective Voronoi regions. CVTs have become useful tools in many application domains of arts, sciences and engineering. In this work, for the first time the concept
Centroidal bases in graphs
, 2014
"... We introduce the notion of a centroidal locating set of a graph G, that is, a set L of vertices such that all vertices in G are uniquely determined by their relative distances to the vertices of L. A centroidal locating set of G of minimum size is called a centroidal basis, and its size is the centr ..."
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is the centroidal dimension CD(G). This notion, which is related to previous concepts, gives a new way of identifying the vertices of a graph. The centroidal dimension of a graph G is lowerand upperbounded by the metric dimension and twice the locationdomination number of G, respectively. The latter two
Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations
 SIAM Journal on Numerical Analysis
"... Abstract. Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi tesse ..."
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Cited by 45 (4 self)
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Abstract. Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi
FITTING CENTROIDS BY A PROJECTIVE TRANSFORMATION
"... Abstract. Given two subsets of Rd, when does there exist a projective transformation that maps them to two sets with a common centroid? When is this transformation unique modulo affine transformations? We study these questions for 0 and ddimensional sets, obtaining several existence and uniqueness ..."
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Abstract. Given two subsets of Rd, when does there exist a projective transformation that maps them to two sets with a common centroid? When is this transformation unique modulo affine transformations? We study these questions for 0 and ddimensional sets, obtaining several existence
Kcentroids Hierarchical Classes Analysis
"... models for N–way N–mode data that do allow for linked and structured classifications of the N modes. More specifically, in the HICLAS models the equivalences classes of each mode–partition are structurally organized in terms of if–then type partial orders. However, up to now, the hierarchical classe ..."
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structure for that mode. Alternatively, in a confirmatory approach, a researcher may have a prior model of the partitioning schema of the selected mode in terms of the number of classes in the partition; in this second case, the main goal is to test the goodness of fit of the constrained model with respect
Charting a Manifold
 Advances in Neural Information Processing Systems 15
, 2003
"... this paper we use m i ( j ) N ( j ; i , s ), with the scale parameter s specifying the expected size of a neighborhood on the manifold in sample space. A reasonable choice is s = r/2, so that 2erf(2) > 99.5% of the density of m i ( j ) is contained in the area around y i where the manifold i ..."
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Cited by 206 (7 self)
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similar covariances and small angles between their respective subspaces. Even if a local subset of data points are dense in a direction perpendicular to the manifold, the prior encourages the local chart to orient parallel to the manifold as part of a globally optimal solution, protecting against a
Distributed Centroid Estimation from Noisy Relative Measurements
"... We propose an anchorless distributed technique for estimating the centroid of a network of agents from noisy relative measurements. The positions of the agents are then obtained relative to the estimated centroid. The usual approach to multiagent localization assumes instead that one anchor agent e ..."
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exists in the network, and the other agents positions are estimated with respect to the anchor. We show that our centroidbased algorithm converges to the optimal solution, and that such a centroidbased representation produces results that are more accurate than anchorbased ones, irrespective
Results 1  10
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559