This paper concerns digital image compression using adaptive thinning algorithms. Adaptive thinning is a recursive point removal scheme which works with decremental Delaunay triangulations. When applied to digital images, adaptive thinning returns a scattered set of most significant pixels. This requires efficient and customized methods for coding these pixels (but not their connectivities). To...

For the unit sphere embedded in a Euclidean space, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered points (sites). The number of scattered sites required is comparable to the dimension of the space for which the quadrature formula is required to be exact. As a part of the proof, we der...

Abstract: This paper is concerned with methods for mapping meshes in IR to meshes in IR in such a way that the local geometry of the mesh is as far as possible preserved. Two linear methods are analyzed and compared. The first, which is more general and more stable, is based on convex combinations while the second is based on minimizing weighted squared lengths of edges. These methods can be us...

Abstract. Rational data fitting has proved extremely useful in a number of scientific applications. We refer among others to the computation of cell loss probabilities in network traffic [5, 6, 14, 15], to the modelling of electro-magnetic components [20, 12] to model reduction of linear shift-invariant systems [2, 3, 7] and so on. When computing a rational interpolant in one variable, all exis...

In this paper, we modify the robust local image estimation method of R. van den Boomgaard and J. van de Weijer for the approximation of scattered data. The derivation of our knot and data dependent approximation method is based on the relation between the Gaussian facet model in image processing and the moving least square technique known from approximation theory. Numerical examples demonstrat...