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Determining Optical Flow
 ARTIFICIAL INTELLIGENCE
, 1981
"... Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent veloc ..."
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Cited by 1727 (7 self)
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Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
ADAPTIVE POLYNOMIAL INTERPOLATION ON EVENLY SPACED MESHES
, 2006
"... The problem of oscillatory polynomial interpolants arising from equally spaced mesh points is considered. It is shown that by making use of adaptive approaches that the oscillations may be contained and that the resulting polynomials are data bounded and monotone on each interval. This is achieved a ..."
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Cited by 7 (1 self)
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The problem of oscillatory polynomial interpolants arising from equally spaced mesh points is considered. It is shown that by making use of adaptive approaches that the oscillations may be contained and that the resulting polynomials are data bounded and monotone on each interval. This is achieved at the cost of using a different polynomial on each subinterval. Computational results for a number of challenging functions including a number of problems similar to Runge’s function with as many as 511 points per interval are shown. keywords Adaptive polynomial interpolation, data bounded polynomials, Runge’s function
Propagation in Smooth Random Potentials
, 2002
"... The theoretical study of micronscale quantummechanical systems generally begins with two assumptions about the potential: that there is no background potential, and that any confining potential is hardwalled. In this thesis, we will look at a phenomenon that is seen when these assumptions are not ..."
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Cited by 1 (0 self)
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The theoretical study of micronscale quantummechanical systems generally begins with two assumptions about the potential: that there is no background potential, and that any confining potential is hardwalled. In this thesis, we will look at a phenomenon that is seen when these assumptions are not made, in the context of electron conductance through twodimensional electron gasses (2DEGs).
Estimation of Image Motion in Scenes Containing Multiple Moving Objects
, 1995
"... This thesis is concerned primarily with the development of algorithms for estimating and segmenting image motion fields that contain discontinuities. An errorweighted regularization algorithm for image motion field estimation is proposed as a computationally attractive alternative to stochastic opt ..."
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This thesis is concerned primarily with the development of algorithms for estimating and segmenting image motion fields that contain discontinuities. An errorweighted regularization algorithm for image motion field estimation is proposed as a computationally attractive alternative to stochastic optimization based schemes. Block matching errors in the local motion measurement process are used in the regularization functional in order to avoid oversmoothing across motion boundaries. A second algorithm, anisotropic regularization, improves on the local measurement process, by employing alternative matching criteria and matching window organization. A selective confidence measure derived from anisotropic local measurements is used to further improve the errorweighted regularization.
UDC 661.511.32:551.658.2:661.501.76:619.24 Use of Approximating Polynomials to Estimate Profiles of Wind, Divergence, and Vertical Motion
"... ABSTRACl“Leastsquares ” approximating polynomials are used to suppress bias and random errors in estimating vertical profiles of winds, divergence, and vertical motion. A quadratic polynomial is used to filter each wind profile. Profiles of divergence and vertical motion computed from a linear, a ..."
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ABSTRACl“Leastsquares ” approximating polynomials are used to suppress bias and random errors in estimating vertical profiles of winds, divergence, and vertical motion. A quadratic polynomial is used to filter each wind profile. Profiles of divergence and vertical motion computed from a linear, a crossproduct, and a quadratic twodimensional (horizontal) approximating polynomial model and from the Bellamy technique are compared. The randomerror variance component of the wind observations is estimated from the filtering polynomial prediction errors. In turn, the randomerror variance component of the filtered wind, divergence, and vertical motion is determined from the wind observational error variance for the various models. ’In the presence of nonlinear variation in the horizontal wind field, the Bellamy modeling assumption of linear wind variation introduces biased divergence errors. The bias divergence errors will persist through a considerable portion of the troposphere as a result of the thermal wind relation and, in the vertical integration, will cause large ‘kpurious ” vertical motion estimates of w at the top of the profile. Divergencc estimates from both the crossproduct and the quadratic approximating polynomial models of the horizontal wind field tend to be less biased in this situation and normally produce superior vertical motion profiles. 1.
Heine transformations for a new kind of basic hypergeometric series in U(n)
, 1994
"... Heine transformations are proved for a new kind of multivariate basic hypergeometric series which had been previously introduced by Krattenthaler in connection with generating functions for nonintersecting lattice paths. As a consequence, a qGauss and qChuVandermonde sum are proved and also a gen ..."
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Heine transformations are proved for a new kind of multivariate basic hypergeometric series which had been previously introduced by Krattenthaler in connection with generating functions for nonintersecting lattice paths. As a consequence, a qGauss and qChuVandermonde sum are proved and also a generalization of Ramanujan's 1~01 sum.
Theory of Cluj Napoca in Approximation Theory of the functions.
"... To Professor Dan Pascali, at his 70’s anniversary We consider from a historical point of view the principal contributions of the Romanian School of Numerical Analysis and Approximation ..."
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To Professor Dan Pascali, at his 70’s anniversary We consider from a historical point of view the principal contributions of the Romanian School of Numerical Analysis and Approximation
Bernoulli, Ramanujan, Toeplitz and the triangular matrices
, 2013
"... By using one of the definitions of the Bernoulli numbers, we prove that they solve particular odd and even lower triangular Toeplitz (l.t.T.) systems of equations. In a paper Ramanujan writes down a sparse lower triangular system solved by Bernoulli numbers; we observe that such system is equivalent ..."
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By using one of the definitions of the Bernoulli numbers, we prove that they solve particular odd and even lower triangular Toeplitz (l.t.T.) systems of equations. In a paper Ramanujan writes down a sparse lower triangular system solved by Bernoulli numbers; we observe that such system is equivalent to a sparse l.t.T. system. The attempt to obtain the sparse l.t.T. Ramanujan system from the l.t.T. odd and even systems, has led us to study efficient methods for solving generic l.t.T. systems. Such methods are here explained in detail in case n, the number of equations, is a power of b, b = 2, 3 and b generic.