Results 1 - 10 of 991

Features of similarity.

by Amos Tversky - Psychological Review , 1977
"... Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimu ..."
Abstract - Cited by 1455 (2 self) - Add to MetaCart
. These models represent objects as points in some coordinate space such that the observed dissimilarities between objects correspond to the metric distances between the respective points. Practically all analyses of proximity data have been metric in nature, although some (e.g., hierarchical clustering) yield

Holomorphic triangles and invariants for smooth four-manifolds

by Peter Ozsváth, Zoltán Szabó
"... Abstract. The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in [8] and [12]. This four-dimensional theory also endows the corresponding three-dimensional theories with additional structure: an absolute gradi ..."
Abstract - Cited by 124 (24 self) - Add to MetaCart
Abstract. The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in [8] and [12]. This four-dimensional theory also endows the corresponding three-dimensional theories with additional structure: an absolute

Non-Rigid Spectral Correspondence of Triangle Meshes

by Varun Jain, Hao Zhang, Oliver van Kaick , 2006
"... We present an algorithm for finding a meaningful vertex-to-vertex correspondence between two triangle meshes, which is designed to handle general non-rigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform s ..."
Abstract - Cited by 37 (7 self) - Add to MetaCart
We present an algorithm for finding a meaningful vertex-to-vertex correspondence between two triangle meshes, which is designed to handle general non-rigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform

Triangle Graphs

by Messaoud Benantar, Ugur Dogrusöz, Joseph E. Flaherty, Mukkai S. Krishnamoorthy , 1995
"... We introduce a new class of planar graphs called triangle graphs. First, we present a formal way of constructing and characterizing triangle graphs, and then show that they characterize the adjacencies of arbitrary triangulations and they are three-colorable for a certain subclass of triangulations. ..."
Abstract - Cited by 4 (3 self) - Add to MetaCart
. Subsequently, we discuss an application of triangle graphs to the parallel finite element solution of elliptic partial differential equations on triangulated domains. 1. Introduction The recent growth and availability of parallel computers has spurred a corresponding interest in the development of parallel

Triangle Rasterization

by Keegan Mcallister , 2007
"... We will have α, β, γ ∈ [0, 1] if and only if x is in the triangle. Intuitively, a triangle consists of all weighted averages of its vertices. We call (α, β, γ) the barycentric coordinates of x. This is a non-orthogonal coordinate system for the plane. (Of course, none of this works if the triangle i ..."
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algorithm for triangle rasterization. We assume that the pi are normalized device coordinates (NDC); that is, the canvas corresponds to the region [−1, 1] × [−1, 1]. This is what you get after applying all transformation matrices. First, identify a rectangular region on the canvas that contains all

Lifting Integer Variables in Minimal Inequalities Corresponding To Lattice-Free Triangles

by Santanu S. Dey, Laurence A. Wolsey
"... Recently, Andersen et al. [1] and Borozan and Cornuéjols [3] characterized the minimal inequalities of a system of two rows with two free integer variables and nonnegative continuous variables. These inequalities are either split cuts or intersection cuts derived using maximal lattice-free convex se ..."
Abstract - Cited by 31 (9 self) - Add to MetaCart
of the integer variables in the corresponding inequalities. In this paper, we analyze the lifting of minimal inequalities derived from lattice-free triangles. Maximal lattice-free triangles in R 2 can be classified into three categories: those with multiple integral points in the relative interior of one of its

Exchangeable Gibbs partitions and Stirling triangles

by Alexander Gnedin, Jim Pitman , 2008
"... For two collections of nonnegative and suitably normalised weights W = (Wj) and V = (Vn,k), a probability distribution on the set of partitions of the set {1,...,n} is defined by assigning to a generic partition {Aj, j ≤ k} the probability Vn,k W |A1 | · · ·W |Ak|, where |Aj | is the number of ele ..."
Abstract - Cited by 52 (8 self) - Add to MetaCart
single parameter α ∈ [−∞, 1]. The case α = 1 is trivial, and for each value of α ̸ = 1 the set of possible V-weights is an infinite-dimensional simplex. We identify the extreme points of the simplex by solving the boundary problem for a generalised Stirling triangle. In particular, we show

A Survey on Shape Correspondence

by Oliver van Kaick, Hao Zhang, Ghassan Hamarneh, Daniel Cohen-or , 2010
"... We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in ..."
Abstract - Cited by 75 (8 self) - Add to MetaCart
We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments

Triangles in Euclidean Arrangements

by Stefan Felsner, Klaus Kriegel - Discrete Comput. Geom , 1998
"... The number of triangles in arrangements of lines and pseudolines has been object of some research. Most results, however, concern arrangements in the projective plane. In this article we add results for the number of triangles in Euclidean arrangements of pseudolines. Though the change in the embedd ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
the corresponding result for the Euclidean plane, namely, that a simple arrangement of n pseudolines contains at least n \Gamma 2 triangles, we had to find a completely different proof. On the other hand a non-simple arrangements of n pseudolines in the Euclidean plane can have as few as 2n=3 triangles

Heron Triangles And Elliptic Curves

by Ralph H. Buchholz, Randall L. Rathbun, All L. Rathbun - Bull. Aust. Math. Soc , 1998
"... In this paper we present a proof that there exist innitely many rational sided triangles with two rational medians and rational area. These triangles correspond to rational points on an elliptic curve of rank one. We also display three triangles (one previously unpublished) which do not belong to an ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
In this paper we present a proof that there exist innitely many rational sided triangles with two rational medians and rational area. These triangles correspond to rational points on an elliptic curve of rank one. We also display three triangles (one previously unpublished) which do not belong
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