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14
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.
Numerical Shape from Shading and Occluding Boundaries
 Artifical Intelligence
, 1981
"... An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereogra ..."
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Cited by 191 (14 self)
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An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereographic plane makes it possible to incorporate occluding boundary information, but forces us to employ a smoothness constraint different from the one previously proposed. The new constraint follows directly from a particular definition of surface smoothness. We solve the set of equations arising from the smoothness constraints and the imageirradiance equation iteratively, using occluding boundary information to supply boundary conditions. Good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution. Numerical experiments show that the method is effective and robust. Finally, we analyze scanning electron microscope (SEM) pictures using this method. Other applications are also proposed. 1.
HighOrder Stiff ODE Solvers via Automatic Differentiation and Rational Prediction
 In Lecture Notes in Comput. Sci
, 1996
"... For solving potentially stiff initial value problems in ordinary differential equations numerically, we examine a class of high order methods that was last considered by Wanner in the sixties. These high order schemes may be viewed as implicit Taylor series methods based on Hermite quadratures. On l ..."
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Cited by 10 (5 self)
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For solving potentially stiff initial value problems in ordinary differential equations numerically, we examine a class of high order methods that was last considered by Wanner in the sixties. These high order schemes may be viewed as implicit Taylor series methods based on Hermite quadratures. On linear problems the methods are equivalent to implicit Runge Kutta methods of the Legendre, Radau and Lobatto type and have therefore the same A or L stability properties. In contrast to earlier implementations we use improved automatic differentiation techniques for the calculation of Taylor coefficients and their Jacobian. To realize large steps on stiff problems we develop a new rational predictor that usually requires only a single correction by Newton's method to achieve solution accuracy at the discretization error level. Matrix sparsity is automatically detected and partly utilized, but other structural properties remain to be exploited. 1 Introduction The design and implementation ...
RealNumber Optimisation: A Speculative, ProfileGuided Approach
, 2007
"... From supercomputers for computational science to embedded processors in mobile phones, most important computing applications manipulate the set of real numbers, R. How these numbers are represented varies, with embedded applications picking fixedpoint formats compatible with integer operations and ..."
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From supercomputers for computational science to embedded processors in mobile phones, most important computing applications manipulate the set of real numbers, R. How these numbers are represented varies, with embedded applications picking fixedpoint formats compatible with integer operations and larger machines using IEEE754 floating point or a close variant. A large body of work describes methods for optimising floating point representations using static analysis techniques, however these must always take a conservative approach if they intend to ensure correctness. Taking our inspiration from work on speculative execution and profileguided compiler optimisations, we lay out a series of tools and techniques to produce optimised realnumber representations. Our speculative approach aims for greater reductions in hardware area and execution time than with more conservative approaches, while providing fallback options to ensure correctness in case of incorrect speculation. We describe a profiling tool for x86 binaries which reveals bucketised value ranges for floatingpoint operations within applications. A selection of profiling results for realworld scientific
Speculative Reduction of Floating Point
"... Abstract. This paper presents a methodology for generating floatingpoint arithmetic hardware designs which are, for suitable applications, dramatically reduced in size, while still retaining performance. We use a profiling tool for floatingpoint value ranges to identify arithmetic operations where ..."
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Abstract. This paper presents a methodology for generating floatingpoint arithmetic hardware designs which are, for suitable applications, dramatically reduced in size, while still retaining performance. We use a profiling tool for floatingpoint value ranges to identify arithmetic operations where the shifting required for operand alignment is almost always small. We synthesise hardware with reducedsize barrelshifters, but always detect when operands lie outside the range this optimised hardware can handle. These rare outofrange operations are handled by a separate full floatingpoint implementation, either onchip or by returning calculations to the host. Thus the system suffers no compromise in IEEE754 compliance. This paper presents results for two benchmark applications which profiling suggested would be profitable. We demonstrate the potential for this technique to yield an increase in parallel computing power of up to 43%, with a (correctable) error rate of less than 5%. We profile a number of other applications and comment on their suitability for our technique. 1
unknown title
, 811
"... Matrix approach to discrete fractional calculus II: partial fractional differential equations ..."
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Matrix approach to discrete fractional calculus II: partial fractional differential equations
unknown title
, 811
"... Matrix approach to discrete fractional calculus II: partial fractional differential equations ..."
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Matrix approach to discrete fractional calculus II: partial fractional differential equations
unknown title
, 811
"... Matrix approach to discrete fractional calculus II: partial fractional differential equations ..."
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Matrix approach to discrete fractional calculus II: partial fractional differential equations
unknown title
, 811
"... Matrix approach to discrete fractional calculus II: partial fractional differential equations ..."
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Matrix approach to discrete fractional calculus II: partial fractional differential equations
Implicit Two Step Continuous Hybrid Block Methods with Four OffSteps Points for Solving Stiff Ordinary Differential Equation
"... Abstract — In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Offstep points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single ..."
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Abstract — In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Offstep points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.