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Comprehensible Rendering of 3D Shapes
, 1990
"... We propose a new rendering technique that produces 3D images with enhanced visual comprehensibility. Shape features can be readily understood if certain geometric properties are enhanced. To achieve this, we develop drawing algorithms for discontinuities, edges, contour lines, and curved hatchin ..."
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Cited by 293 (0 self)
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We propose a new rendering technique that produces 3D images with enhanced visual comprehensibility. Shape features can be readily understood if certain geometric properties are enhanced. To achieve this, we develop drawing algorithms for discontinuities, edges, contour lines, and curved
Features of similarity.
 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 ..."
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Cited by 1455 (2 self)
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, errors of substitution, and correlation between occurrences. Analyses of these data attempt to explain the observed similarity relations and to capture the underlying structure of the objects under study. The theoretical analysis of similarity relations has been dominated by geometric models
Submodular functions, matroids and certain polyhedra
, 2003
"... The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all ..."
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Cited by 355 (0 self)
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The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts
Gradient flows and geometric active contour models
 in Proc. of the 5th International Conference on Computer Vision
, 1995
"... In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature of interes ..."
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Cited by 239 (19 self)
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In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature
On Beamforming with Finite Rate Feedback in Multiple Antenna Systems
, 2003
"... In this paper, we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any f ..."
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Cited by 272 (14 self)
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is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product
Graph embedding and extension: A general framework for dimensionality reduction
 IEEE TRANS. PATTERN ANAL. MACH. INTELL
, 2007
"... Over the past few decades, a large family of algorithms—supervised or unsupervised; stemming from statistics or geometry theory—has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper ..."
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Cited by 271 (29 self)
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in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric
Representations of Rigid Solids: Theory, Methods, and Systems
 ACM Computing Surveys
, 1980
"... Computerbased ystems for modehng the geometry ofrigid solid objects are becoming increasingly important inmechanical nd civil engineering, architecture, computer graphics, computer vision, and other fields that deal with spatial phenomena. At the heart of such systems are symbol structures (represe ..."
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Cited by 256 (2 self)
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representation of solids. The paper is divided into three parts. The first introduces a simple mathematical framework for characterizing certain important aspects of representations, for example, their semantic (geometric) ntegrity. The second part uses the framework to describe and compare all of the major
Ricci curvature for metricmeasure spaces via optimal transport
 ANN. OF MATH
, 2005
"... We define a notion of a measured length space X having nonnegative NRicci curvature, for N ∈ [1, ∞), or having ∞Ricci curvature bounded below by K, for K ∈ R. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P2(X) of proba ..."
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Cited by 231 (10 self)
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) of probability measures. We show that these properties are preserved under measured GromovHausdorff limits. We give geometric and analytic consequences.
A large N duality via a geometric transition
 Nucl. Phys. B
, 2001
"... We propose a large N dual of 4d, N = 1 supersymmetric, SU(N) YangMills with adjoint field Φ and arbitrary superpotential W(Φ). The field theory is geometrically engineered via Dbranes partially wrapped over certain cycles of a nontrivial CalabiYau geometry. The large N, or lowenergy, dual arise ..."
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Cited by 187 (27 self)
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We propose a large N dual of 4d, N = 1 supersymmetric, SU(N) YangMills with adjoint field Φ and arbitrary superpotential W(Φ). The field theory is geometrically engineered via Dbranes partially wrapped over certain cycles of a nontrivial CalabiYau geometry. The large N, or lowenergy, dual
Results 1  10
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4,950