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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.
1. GINZBURGLANDAU MODEL
, 2001
"... We propose a finitedifference algorithm for solving the timedependent GinzburgLandau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semiimplicit scheme which, for intermediate values of the GinzburgLandau parameter κ, allow ..."
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We propose a finitedifference algorithm for solving the timedependent GinzburgLandau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semiimplicit scheme which, for intermediate values of the GinzburgLandau parameter κ, allows timesteps two orders of magnitude larger than commonly used in explicit schemes. We demonstrate the use of the method by solving a fully threedimensional problem of a currentcarrying wire with longitudinal and transverse magnetic fields. c ○??? Academic Press