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On the numerical approximation of first-order Hamilton-Jacobi equations

Abgrall R., Perrier V.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 3

403-412

Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.

Computing optical flow with a triangular finite element mesh

Condel J., Scotney B., Morrow P.

Image Processing & Communications

2001

Vol. 7, no 3-4

3-14

This paper presents algorithms to implement the estimation of motion, focusing on the finite element method as a framework for the development of techniques. The finite element approach has the advantages of a rigorous mathematical formulation, speed of reconstruction, conceptual simplicity and ease of implementation via well-established finite element procedures in comparison to finite volume or finite difference techniques. The finite elemcnt techniques are implemented using a triangular discretisation, and preliminary results are presented. An important advantage is the capacity to tackle problems in which non-uniform sampling of the image sequence is appropriate.