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Multidimensional vector product
, 2002
"... It is shown that multidimensional generalization of the vector product is only possible in seven dimensional space. The threedimensional vector product proved to be useful in various physical problems. A natural question is whether multidimensional generalization of the vector product is possible ..."
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Cited by 1 (0 self)
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It is shown that multidimensional generalization of the vector product is only possible in seven dimensional space. The threedimensional vector product proved to be useful in various physical problems. A natural question is whether multidimensional generalization of the vector product
Snakes, Shapes, and Gradient Vector Flow
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1998
"... Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new extern ..."
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Cited by 743 (16 self)
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external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a graylevel or binary edge map derived from the image. It differs fundamentally from traditional snake external forces
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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vector machine' (RVM), a model of identical functional form to the popular and stateoftheart `support vector machine' (SVM). We demonstrate that by exploiting a probabilistic Bayesian learning framework, we can derive accurate prediction models which typically utilise dramatically fewer
LIBSVM: a Library for Support Vector Machines
, 2001
"... LIBSVM is a library for support vector machines (SVM). Its goal is to help users can easily use SVM as a tool. In this document, we present all its implementation details. 1 ..."
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Cited by 6287 (82 self)
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LIBSVM is a library for support vector machines (SVM). Its goal is to help users can easily use SVM as a tool. In this document, we present all its implementation details. 1
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our
A practical guide to support vector classification
, 2010
"... The support vector machine (SVM) is a popular classification technique. However, beginners who are not familiar with SVM often get unsatisfactory results since they miss some easy but significant steps. In this guide, we propose a simple procedure which usually gives reasonable results. ..."
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Cited by 787 (7 self)
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The support vector machine (SVM) is a popular classification technique. However, beginners who are not familiar with SVM often get unsatisfactory results since they miss some easy but significant steps. In this guide, we propose a simple procedure which usually gives reasonable results.
Training Support Vector Machines: an Application to Face Detection
, 1997
"... We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision sur ..."
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Cited by 728 (1 self)
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We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision
Sonification of ThreeDimensional Vector Fields
 in Proceedings of the SCS High Perfor mance Computing Symposium
, 2004
"... We describe and analyze a new technique for sonification of threedimensional vector fields. This technique allows the user to use commodity hardware and widely available 3D sound interfaces to map vectors in a listener’s local neighborhood into smooth windlike sound (aerodynamic sound). The four ..."
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Cited by 6 (0 self)
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We describe and analyze a new technique for sonification of threedimensional vector fields. This technique allows the user to use commodity hardware and widely available 3D sound interfaces to map vectors in a listener’s local neighborhood into smooth windlike sound (aerodynamic sound). The four
Inverse Operation of Fourdimensional Vector Matrix
"... Abstract—This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes fourdimensional vector matrix determinant, fourdimensional vector matrix inverse and related properties. There are innovative concepts of multidimensional vector matrix mathematic ..."
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Abstract—This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes fourdimensional vector matrix determinant, fourdimensional vector matrix inverse and related properties. There are innovative concepts of multidimensional vector matrix
Results 1  10
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