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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 ..."
Abstract

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.
What the Course Tries to Do
, 2003
"... It is always a good idea to start by saying what we are trying to do, and how you will recognise if you have succeeded! Modern education jargon sums up this by emphasising “aims ” and “learning objectives”. Here they are in the same form as in the “Catalogue of Courses”. It is hard to understand wha ..."
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It is always a good idea to start by saying what we are trying to do, and how you will recognise if you have succeeded! Modern education jargon sums up this by emphasising “aims ” and “learning objectives”. Here they are in the same form as in the “Catalogue of Courses”. It is hard to understand what the objectives mean before you have finished the course; but at that stage, you should come back here and check that they do make sense. If they don’t, you may have missed something important. Aims The overall aim of the course is to present modern computer programming techniques in the context of mathematical computation and numerical analysis and to foster the independence needed to use these techniques as appropriate in subsequent work. Learning Objectives By the end of the course the student should: • be aware of the background of computing within mathematics, and of possible choices of programming language; • be able to analyse appropriate mathematical problems in a form suitable for programming; • be able to construct programs in a modern objectoriented programming language, using the available facilities appropriately; • be able to describe, analyse, program and contrast a number of methods for investigating problems in symbolic computation and numerical analysis. These problems will include at least three topics from the following: – root finding; – numerical integration; – the solution of ordinary differential equations; – digital signatures; – Monte Carlo methods; iii iv • be able to write programs to assist investigations in subsequent mathematics courses; and • have improved analytic skills.
A Mixed Quadrature Rule by Blending ClenshawCurtis and GaussLegendre Quadrature Rules for Approximation of Real Definite Integrals in Adaptive Environment
"... Abstract A mixed quadrature rule blending ClenshawCurtis five point rule and GaussLegendre three point rule is formed. The mixed rule has been tested in adaptive environment and it is found to be more effective than that of ClenshawCurtis five point rule. Key Words ClenshawCurtis quadrature ru ..."
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Abstract A mixed quadrature rule blending ClenshawCurtis five point rule and GaussLegendre three point rule is formed. The mixed rule has been tested in adaptive environment and it is found to be more effective than that of ClenshawCurtis five point rule. Key Words ClenshawCurtis quadrature rule, GaussLegendre 3point rule, mixed quadrature rule. Adaptive quadrature method.