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An ndimensional generalization of the rhombus tiling
 Discrete Mathematics and Theoretical Computer Science, Proceedings of the 1st international conference Discrete Models: Combinatorics, Computation, and Geometry (DMCCG'01
, 2001
"... Several classic tilings, including rhombuses and dominoes, possess height functions which allow us to 1) prove ergodicity and polynomial mixing times for Markov chains based on local moves, 2) use coupling from the past to sample perfectly random tilings, 3) map the statistics of random tilings at l ..."
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Cited by 7 (0 self)
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at large scales to physical models of random surfaces, and and 4) are related to the “arctic circle ” phenomenon. However, few examples are known for which this approach works in three or more dimensions. Here we show that the rhombus tiling can be generalized to ndimensional tiles for any n ¡ 3. For each
Insertion and expansion operations for nDimensional Generalized Maps
, 2008
"... Hierarchical representations, such as irregular pyramids, are the bases of several applications in the field of discrete imagery. So, ndimensional ”bottomup” irregular pyramids can be defined as stacks of successively reduced ndimensional generalized maps (nGmaps) [11], each nGmap being defi ..."
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Hierarchical representations, such as irregular pyramids, are the bases of several applications in the field of discrete imagery. So, ndimensional ”bottomup” irregular pyramids can be defined as stacks of successively reduced ndimensional generalized maps (nGmaps) [11], each nGmap being
Class. Quantum Grav. 13 (1996) 3211–3219. Printed in the UK On the Gaussian curvature of maximal surfaces in ndimensional generalized Robertson–Walker spacetimes
, 1996
"... Abstract. We study compact maximal surfaces in the family of generalized Robertson–Walker spacetimes. We prove an integral inequality for their Gaussian curvature K, with equality characterizing the totally geodesic case. This gives an integral alternative to the irregular behaviour of K, which is d ..."
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Abstract. We study compact maximal surfaces in the family of generalized Robertson–Walker spacetimes. We prove an integral inequality for their Gaussian curvature K, with equality characterizing the totally geodesic case. This gives an integral alternative to the irregular behaviour of K, which
Data cube: A relational aggregation operator generalizing groupby, crosstab, and subtotals
, 1996
"... Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zerodimensional or onedimensional aggregates. Applications need the Ndimensional generalization of these op ..."
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Cited by 860 (11 self)
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Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zerodimensional or onedimensional aggregates. Applications need the Ndimensional generalization
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 534 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in ND Images
, 2001
"... In this paper we describe a new technique for general purpose interactive segmentation of Ndimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph ..."
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Cited by 1010 (20 self)
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In this paper we describe a new technique for general purpose interactive segmentation of Ndimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph
Laplacian eigenmaps and spectral techniques for embedding and clustering.
 Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
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Cited by 668 (7 self)
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of t he same object is the number of degrees of freedom of the camera in fact the space has the natural structure of a manifold embedded in rn: n2 . While there is a large body of work on dimensionality reduction in general, most existing approaches do not explicitly take into account the structure
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 984 (32 self)
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Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any
Recognitionbycomponents: A theory of human image understanding
 Psychological Review
, 1987
"... The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recog ..."
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Cited by 1272 (23 self)
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, recognitionbycomponents (RBC), is that a modest set of generalizedcone components, called geons (N ^ 36), can be derived from contrasts of five readily detectable properties of edges in a twodimensional image: curvature, collinearity, symmetry, parallelism, and cotermmation. The detection
Action recognition in the premotor cortex
 Brain
, 1996
"... We recorded electrical activity from 532 neurons in the rostral part of inferior area 6 (area F5) of two macaque monkeys. Previous data had shown that neurons of this area discharge during goaldirected hand and mouth movements. We describe here the properties of a newly discovered set of F5 neurons ..."
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Cited by 671 (47 self)
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neurons ('mirror neurons', n = 92) all of which became active both when the monkey performed a given action and when it observed a similar action performed by the experimenter. Mirror neurons, in order to be visually triggered, required an interaction between the agent of the action
Results 1  10
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