Contour lines from topographic maps are still the most common form of elevation data for the Earth’s surface and in the case of historical landscapes, they often are the only available source of information. In this paper we present a new contour interpolation method that solves this bivariate problem by considering univariate curve interpolation along the approximate gradient directions of the...

An improvement to the traditional Finite Volume Method (FVM) for the solution of boundary value problems is presented. The new method applies the local Hermitian interpolation with Radial Basis Functions (RBF) as an interpolation scheme to the FVM discretization. This approach, called the Control Volume-Radial Basis Function (CV-RBF) method, uses an interpolation scheme based on the meshless Sy...

Eight interpolation methods are implemented and tested over a 60 km × 60 km region in Korea, using the results from automatic stereo-matching of SPOT images. First, with the simulated elevation data from digitised contours of paper maps, Kriging and Multiquadric methods show higher performance: with the accuracy better than 3 m than other methods and the speed of ~400 s on a Sparc 20 machine. S...

where P(x — A) represents a power series in (a„ — A), (bn — A), (a;n+1 — A), quadratic terms and higher. As a numerical example consider the first root of x tan x — 1 = 0. Taking a = 0.8, b = 0.9 equation (4) yields the tabulated value 0.8603. Two or more applications of Newton's method will involve interpolation if one has only a two place table at hand. Estimates of the magnitude of error inv...

Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish ...

In this paper we present a novel method for interpolating images with repetitive structures. Unlike other conventional interpolation methods, the unknown pixel value is not estimated based on its local surrounding neighbourhood, but on the whole image. In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information a...

This paper presents an advance on image interpolation based on ant colony algorithm (AACA) for high resolution image scaling. The difference between the proposed algorithm and the previously proposed optimization of bilinear interpolation based on ant colony algorithm (OBACA) is that AACA uses global weighting, whereas OBACA uses local weighting scheme. The strength of the proposed global weigh...

We consider the model Dirichlet problem for Poisson’s equation on a plane polygonal convex domain W with data f in a space smoother than L2. The regularity and the critical case of the problem depend on the measure of the maximum angle of the domain. Interpolation theory and multilevel theory are used to obtain estimates for the critical case. As a consequence, sharp error estimates for the cor...

We present a mechanised formalisation, in Isabelle/HOL, of Brotherston and Goré’s proof of Craig interpolation for a large class display calculi for various propositional substructural logics. Along the way, we discuss the particular difficulties associated with the local interpolation property for various rules, and some important differences between our proofs and those of Brotherston and Gor...

Everyone that has ever tried to apply simple linear interpolation to find a value between pairs of data points will be only too aware that such attempts are extremely unlikely to provide reliable results if the data being used is anything other than broadly linear. In an attempt to deal with inherent non-linearity, the next step usually involves some sort of polynomial interpolation. This gener...