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In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil,… (More)

A line integral is defined as the integral of two-dimensional data along a (one-dimensional, straight) line of given length and orientation. Line integrals are used in various forms of edge and line detectors in images and in the computation of the Radon transform. We present a recursive algorithm which enables approximation of discretized line integrals at… (More)

The biharmonic equation can be rewritten as a system of two Pois-son equations 8, 6]. Multigrid solution of this system is expected to converge with the same amount of work as solving two Poisson equations. For periodic boundary conditions, this goal is attained by simple, straightforward application of multigrid. For Dirichlet boundary conditions ,… (More)

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