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107,238
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 ..."
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Cited by 971 (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
Centroids and . . .
, 2005
"... For −1 < p < 1 we introduce the concept of a polar pcentroid body Γ ∗ pK of a star body K. We consider the question of whether Γ ∗ pK ⊂ Γ ∗ pL implies vol(L) ≤ vol(K). Our results extend the studies by Lutwak in the case p = 1 and Grinberg, Zhang in the case p> 1. ..."
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For −1 < p < 1 we introduce the concept of a polar pcentroid body Γ ∗ pK of a star body K. We consider the question of whether Γ ∗ pK ⊂ Γ ∗ pL implies vol(L) ≤ vol(K). Our results extend the studies by Lutwak in the case p = 1 and Grinberg, Zhang in the case p> 1.
Scripts Centroid
"... Circle through 3 pts Altitude feet Buried treasure solution Day 3 assignment Scrambled proofs in envelopes Flowchart proof templates TEAXTEAM Geometry Institute 2.2THE BURIED TREASURE Among his greatgrandfather’s papers, José found a parchment describing the location of a hidden treasure. The treas ..."
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Circle through 3 pts Altitude feet Buried treasure solution Day 3 assignment Scrambled proofs in envelopes Flowchart proof templates TEAXTEAM Geometry Institute 2.2THE BURIED TREASURE Among his greatgrandfather’s papers, José found a parchment describing the location of a hidden treasure. The treasure was buried by a band of pirates on a deserted island which contained an oak tree, a pine tree, and a gallows where the pirates hanged traitors. The map looked like the accompanying figure and gave the following directions. “Count the steps from the gallows to the oak tree. At the oak, turn 90 ° to the right. Take the same number of steps and then put a spike in the ground. Next, return to the gallows and walk to the pine tree, counting the number of steps. At the pine tree, turn 90° to the left, take the same number of steps, and then put another spike in the ground. The treasure is buried halfway between the spikes.” José found the island and the trees but could not find the gallows or the spikes, which had long since rotted. José dug all over the island, but because the island was large, he gave up. Devise a plan to help José find the treasure.
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 72 (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
Bregman sided and symmetrized centroids
 in ICPR. 2008, IEEE CS
"... We generalize the notions of centroids and barycenters to the broad class of informationtheoretic distortion measures called Bregman divergences. Because Bregman divergences are typically asymmetric, we consider both the leftsided and rightsided centroids and the symmetrized centroids, and prove ..."
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Cited by 3 (3 self)
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We generalize the notions of centroids and barycenters to the broad class of informationtheoretic distortion measures called Bregman divergences. Because Bregman divergences are typically asymmetric, we consider both the leftsided and rightsided centroids and the symmetrized centroids, and prove
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
On the Centroids of Polygons and Polyhedra
"... Abstract. In this paper we introduce the centroid of any finite set of points of the space and we find some general properties of centroids. These properties are then applied to different types of polygons and polyhedra. 1. ..."
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Abstract. In this paper we introduce the centroid of any finite set of points of the space and we find some general properties of centroids. These properties are then applied to different types of polygons and polyhedra. 1.
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