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 Computer Vision, Graphics, and Image Processing
, 1983
"... A method is proposed for determining the motion of a body relative to a fixed environment using the changing image seen by a camera attached to the body. The optical flow in the image plane is the input, while the instantaneous rotation and translation of the body are the output. If optical flow cou ..."
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Cited by 206 (8 self)
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A method is proposed for determining the motion of a body relative to a fixed environment using the changing image seen by a camera attached to the body. The optical flow in the image plane is the input, while the instantaneous rotation and translation of the body are the output. If optical flow could be determined precisely, it would only have to be known at a few places to compute the parameters of the motion. In practice, however, the measured optical flow will be somewhat inaccurate. It is therefore advantageous to consider methods which use as much of the available information as possible. We employ a leastsquares approach which minimizes some measure of the discrepancy between the measured flow and that predicted from the computed motion parameters. Several different error norms are investigated. In general, our algorithm leads to a system of nonlinear equations from which the motion parameters may be computed numerically. However, in the special cases where the motion of the camera is purely translational or purely rotational, use of the appropriate norm leads to a system of equations from which these parameters can be determined in closed form. 1.
Using the refinement equation for the construction of prewavelets II
, 1991
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Wavelet Radiosity
, 1993
"... Radiosity methods have been shown to be an effective means to solve the global illumination problem in Lambertian diffuse environments. These methods approximate the radiosity integral equation by projecting the unknown radiosity function into a set of basis functions with limited support resulting ..."
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Cited by 168 (10 self)
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Radiosity methods have been shown to be an effective means to solve the global illumination problem in Lambertian diffuse environments. These methods approximate the radiosity integral equation by projecting the unknown radiosity function into a set of basis functions with limited support resulting in a set of n linear equations where n is the number of discrete elements in the scene. Classical radiosity methods required the evaluation of n 2 interaction coefficients. Efforts to reduce the number of required coefficients without compromising error bounds have focused on raising the order of the basis functions, meshing, accounting for discontinuities, and on developing hierarchical approaches, which have been shown to reduce the required interactions to O(n). In this paper we show that the hierarchical radiosity formulation is an instance of a more general set of methods based on wavelet theory. This general framework offers a unified view of both higher order element approaches to...
Choosing the Forcing Terms in an Inexact Newton Method
 SIAM J. SCI. COMPUT
, 1994
"... An inexact Newton method is a generalization of Newton's method for solving F(x) = 0, F:/ /, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ]lF(x) + F'(x)s]l _< /]lF(xk)]l for a "forcing term" / [0,1). I ..."
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Cited by 156 (6 self)
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An inexact Newton method is a generalization of Newton's method for solving F(x) = 0, F:/ /, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ]lF(x) + F'(x)s]l _< /]lF(xk)]l for a "forcing term" / [0,1). In typical applications, the choice of the forcing terms is critical to the efficiency of the method and can affect robustness as well. Promising choices of the forcing terms arc given, their local convergence properties are analyzed, and their practical performance is shown on a representative set of test problems.
Building Your Own Wavelets at Home
"... Wavelets have been making an appearance in many pure and applied areas of science and engineering. Computer graphics with its many and varied computational problems has been no exception to this rule. In these notes we will attempt to motivate and explain the basic ideas behind wavelets and what mak ..."
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Cited by 151 (13 self)
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Wavelets have been making an appearance in many pure and applied areas of science and engineering. Computer graphics with its many and varied computational problems has been no exception to this rule. In these notes we will attempt to motivate and explain the basic ideas behind wavelets and what makes them so successful in application areas. The main
Is Gauss Quadrature Better Than Clenshaw–Curtis?
, 2008
"... We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to exp ..."
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Cited by 104 (4 self)
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We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O’Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of log((z +1)/(z − 1)) in the complex plane. Gauss quadrature corresponds to Padé approximation at z = ∞. Clenshaw–Curtis quadrature corresponds to an approximation whose order of accuracy at z = ∞ is only half as high, but which is nevertheless equally accurate near [−1, 1].
private communication
, 2003
"... Hyaluronandecorated polymer nanoparticles targeting the CD44 receptor for the combined photo/chemotherapy of cancer We propose a novel type of doublecoated biodegradable nanoparticle based on electrostatic interactions and coencapsulating a taxane chemotherapeutic and a porphyrine photosensitize ..."
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Cited by 100 (5 self)
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Hyaluronandecorated polymer nanoparticles targeting the CD44 receptor for the combined photo/chemotherapy of cancer We propose a novel type of doublecoated biodegradable nanoparticle based on electrostatic interactions and coencapsulating a taxane chemotherapeutic and a porphyrine photosensitizer, which demonstrate a tremendous improvement in free drug activity and specifi city. These fi ndings provide a solid rational basis for future extension of the system to other drug combinations also in an in vivo setting.
An immersed interface method for incompressible navierstokes equations
 SIAM J. Sci. Comput
, 2003
"... Abstract. The method developed in this paper is motivated by Peskin’s immersed boundary (IB) method, and allows one to model the motion of flexible membranes or other structures immersed in viscous incompressible fluid using a fluid solver on a fixed Cartesian grid. The IB method uses a set of discr ..."
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Cited by 98 (3 self)
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Abstract. The method developed in this paper is motivated by Peskin’s immersed boundary (IB) method, and allows one to model the motion of flexible membranes or other structures immersed in viscous incompressible fluid using a fluid solver on a fixed Cartesian grid. The IB method uses a set of discrete delta functions to spread the entire singular force exerted by the immersed boundary to the nearby fluid grid points. Our method instead incorporates part of this force into jump conditions for the pressure, avoiding discrete dipole terms that adversely affect the accuracy near the immersed boundary. This has been implemented for the twodimensional incompressible Navier–Stokes equations using a highresolution finitevolume method for the advective terms and a projection method to enforce incompressibility. In the projection step, the correct jump in pressure is imposed in the course of solving the Poisson problem. This gives sharp resolution of the pressure across the interface and also gives better volume conservation than the traditional IB method. Comparisons between this method and the IB method are presented for several test problems. Numerical studies of the convergence and order of accuracy are included.
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
 IN STACS
, 2005
"... We define Recursive Markov Chains (RMCs), a class of finitely presented denumerable Markov chains, and we study algorithms for their analysis. Informally, an RMC consists of a collection of finitestate Markov chains with the ability to invoke each other in a potentially recursive manner. RMCs offer ..."
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Cited by 92 (13 self)
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We define Recursive Markov Chains (RMCs), a class of finitely presented denumerable Markov chains, and we study algorithms for their analysis. Informally, an RMC consists of a collection of finitestate Markov chains with the ability to invoke each other in a potentially recursive manner. RMCs offer a natural abstract model for probabilistic programs with procedures. They generalize, in a precise sense, a number of well studied stochastic models, including Stochastic ContextFree Grammars (SCFG) and MultiType Branching Processes (MTBP). We focus on algorithms for reachability and termination analysis for RMCs: what is the probability that an RMC started from a given state reaches another target state, or that it terminates? These probabilities are in general irrational, and they arise as (least) fixed point solutions to certain (monotone) systems of nonlinear equations associated with RMCs. We address both the qualitative problem of determining whether the probabilities are 0, 1 or inbetween, and