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Motion estimation with object based regularisation
A dynamic programming based matching method for motion estimation, that optimises a Bayesian maximum likelihood function in a 3-D optimisation space, is presented. The Bayesian function consists of a matching cost and an object based 2-D regularisation cost. The method gives results more accurate than block-based matching since the motion boundaries are close to the actual object boundaries
Totally positive refinable functions with general dilation M
We construct a new class of approximating functions that are M-refinable and provide shape preserving approximations. The refinable functions in the class are smooth, compactly supported, centrally symmetric and totally positive. Moreover, their refinable masks are associated with convergent subdivision schemes. The presence of one or more shape parameters gives a great flexibility in the applications. Some examples for dilation M=4and M=5are also given
Area preservation in computational fluid dynamics
Incompressible two-dimensional flows such as the advection (Liouville)
equation and the Euler equations have a large family of conservation laws
related to conservation of area. We present two Eulerian numerical methods
which preserve a discrete analog of area. The first is a fully discrete model
based on a rearrangement of cells; the second is more conventional, but still
preserves the area within each contour of the vorticity field. Initial tests
indicate that both methods suppress the formation of spurious oscillations in
the field.Comment: 14 pages incl. 3 figure
Efficient implementation of finite volume methods in Numerical Relativity
Centered finite volume methods are considered in the context of Numerical
Relativity. A specific formulation is presented, in which third-order space
accuracy is reached by using a piecewise-linear reconstruction. This
formulation can be interpreted as an 'adaptive viscosity' modification of
centered finite difference algorithms. These points are fully confirmed by 1D
black-hole simulations. In the 3D case, evidence is found that the use of a
conformal decomposition is a key ingredient for the robustness of black hole
numerical codes.Comment: Revised version, 10 pages, 6 figures. To appear in Phys. Rev.
Continuous State Dynamic Programming via Nonexpansive Approximation
This paper studies fitted value iteration for continuous state dynamic programming using nonexpansive function approximators. A number of nonexpansive approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm.Dynamic Programming; Approximation
Continuous State Dynamic Programming Via Nonexpansive Approximation
This paper studies fitted value iteration for continuous state dynamic programming using nonexpansive function approximators. A number of nonexpansive approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm.
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