Results 1  10
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14,247
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 654 (15 self)
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In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing
Typesetting Concrete Mathematics
 TUGBOAT
, 1989
"... ... tried my best to make the book mathematically interesting, but I also knew that it would be typographically interestingbecause it would be the first major use of a new typeface by Hermann Zapf, commissioned by the American Mathematical Society. This typeface, called AMS Euler, had been carefull ..."
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Cited by 661 (1 self)
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closes together smoothly when the curve returns to its starting point. A handwritten rather than mechanical style is appropriate for mathematics because people generally create math with pen, pencil, or chalk. The Euler letters are upright, not italic, so that there is a general consistency
The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of onedimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” twodimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 513 (20 self)
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link between the developed filter bank and the associated continuousdomain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth
Casting Curved Shadows on Curved Surfaces
 In Computer Graphics (SIGGRAPH ’78 Proceedings
, 1978
"... Shadowing has historically been used to increase the intelligibility of scenes in electron microscopy and aerial survey. Various methods have been published for the determination of shadows in computer synthesized scenes. The display of shadows may make the shape and relative position of objects i ..."
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Cited by 401 (1 self)
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to display shadows cast by objects modelled of smooth surface patches. The method can be applied
Principal Curves
, 1989
"... Principal curves are smooth onedimensional curves that pass through the middle of a pdimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curve starts with some prior summary, suc ..."
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Cited by 394 (1 self)
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Principal curves are smooth onedimensional curves that pass through the middle of a pdimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curve starts with some prior summary
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 436 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
Curvelets: a surprisingly effective nonadaptive representation of objects with edges
 IN CURVE AND SURFACE FITTING: SAINTMALO
, 2000
"... It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense ‘tracks ’ the shape of the discontinuity set. This folkbelief — some would say folktheorem — is incorrect. At the very least ..."
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Cited by 395 (21 self)
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least, the possible quantitative advantage of such adaptation is vastly smaller than commonly believed. We have recently constructed a tight frame of curvelets which provides stable, efficient, and nearoptimal representation of otherwise smooth objects having discontinuities along smooth curves
CE: Basic principles of ROC analysis
 Seminars in Nuclear Medicine
, 1978
"... The l imitations of diagnostic "accuracy " as a measure of decision performance require introduction of the concepts of the "sensit iv ity " and "specif ic i ty " of a diagnostic test, These measures and the related indices, "true positive fraction " and &quo ..."
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Cited by 376 (0 self)
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simple yet complete empirical description of this decision threshold effect, indicating all possible combinations of the relative frequencies of the various kinds of correct and incorrect decisions. Practical experimental techniques for measuring ROC curves are described,
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation
, 1991
"... This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set o ..."
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Cited by 314 (2 self)
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of zeros of a smooth function of two variables XY, a surface is the set of zeros of a smooth function of three variables X~Z, and a space curve is the intersection of two surfaces, which are the set of zeros of two linearly independent smooth functions of three variables X!/Z. For example, the surface
Results 1  10
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14,247