10 For a property measured at several locations, interpolation algorithms provide a 11 unique and smooth function yielding a locally realistic estimation at any point within 12 the sampled region. Previous studies searching for optimal interpolation strategies by 13 measuring cross-validation error have not found consistent rankings; this fact was 14 traditionally explained by differences in th...

In this paper a trade-off between the computation effort and the accuracy of the resulting disparity map, obtained using interpolation over spatial domain, is presented. The accuracy of the obtained disparity map is presented as the mean squared error calculated over the known disparity ground truth of test images, while efficiency increase is presented in terms of algorithm run-times. Even whe...

Terrain is an ordered surface where locations relate to each other through their elevations. Preservation of this topographic orderliness by an interpolation method so that “if point A is higher than point B in the terrain, the interpolated elevation of A remains higher” is important to assure the practical value of the resultant DEM. Based on the concepts in group theory, this paper points out...

The problem of phase estimation (or amplitude estimation) admits a quadratic quantum speedup. Wang, Higgott, and Brierley [Wang, Brierley, Phys. Rev. Lett. 122, 140504 (2019)] have shown that there is continuous tradeoff between speedup circuit depth [by defining family algorithms known as $\ensuremath{\alpha}$-quantum $(\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{QPE})$]. In this paper, we...

Given a multidimensional data set and a model of its density, we consider how to deene the optimal interpolation between two points. This is done by assigning a cost to each path through space, based on two competing goals|one to interpolate through regions of high density, the other to minimize arc length. From this path functional, we derive the Euler-Lagrange equations for extremal motion; g...

Consumer-level digital cameras observe a single value at each pixel. The remaining two channels of a three-channel image are reconstructed through a process called demosaicking. This paper describes a methodology for enhancing current demosaicking methods. Using an iterative relaxation approach from probabilistic AI literature, our empirical results show that we can improve the results of the s...

Fractal interpolation techniques provide good deterministic representations of complex phenomena. This paper approaches the Hermite interpolation using fractal procedures. This problem prescribes at each support abscissa not only the value of a function but also its first p derivatives. It is shown here that the proposed fractal interpolation function and its first p derivatives are good approx...

Given a multidimensional data set and a model of its density, we consider how to define the optimal interpolation between two points. This is done by assigning a cost to each path through space, based on two competing goals-one to interpolate through regions of high density, the other to minimize arc length. From this path functional, we derive the Euler-Lagrange equations for extremal motionj ...

We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value...