Topic
Nearest-neighbor interpolation
About: Nearest-neighbor interpolation is a research topic. Over the lifetime, 4955 publications have been published within this topic receiving 122203 citations. The topic is also known as: proximal interpolation & point sampling.
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TL;DR: It is demonstrated that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N), which is comparable to that of a simple truncation method of 10 A or less.
Abstract: The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less
17,897 citations
Book•
01 Mar 1964
3,431 citations
TL;DR: It can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines.
Abstract: Cubic convolution interpolation is a new technique for resampling discrete data. It has a number of desirable features which make it useful for image processing. The technique can be performed efficiently on a digital computer. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero. With the appropriate boundary conditions and constraints on the interpolation kernel, it can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines. A one-dimensional interpolation function is derived in this paper. A separable extension of this algorithm to two dimensions is applied to image data.
3,280 citations
Book•
01 Jan 1972
TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.
Abstract: This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.
2,477 citations
TL;DR: Simulation results demonstrate that the new interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional linear interpolation.
Abstract: This paper proposes an edge-directed interpolation algorithm for natural images. The basic idea is to first estimate local covariance coefficients from a low-resolution image and then use these covariance estimates to adapt the interpolation at a higher resolution based on the geometric duality between the low-resolution covariance and the high-resolution covariance. The edge-directed property of covariance-based adaptation attributes to its capability of tuning the interpolation coefficients to match an arbitrarily oriented step edge. A hybrid approach of switching between bilinear interpolation and covariance-based adaptive interpolation is proposed to reduce the overall computational complexity. Two important applications of the new interpolation algorithm are studied: resolution enhancement of grayscale images and reconstruction of color images from CCD samples. Simulation results demonstrate that our new interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional linear interpolation.
1,933 citations