Abstract

In this paper the comparative analysis for quality of some interpolation non-adaptive methods of doubling the image size is carried out. We used the value of a mean square error for estimation accuracy (quality) approximation. Artifacts (aliasing, Gibbs effect (ringing), blurring, etc.) introduced by interpolation methods were not considered. The description of the doubling interpolation upscale algorithms are presented, such as: the nearest neighbor method, linear and cubic interpolation, Lanczos convolution interpolation (with a = 1, 2, 3), and 17-point interpolation method. For each method of upscaling to twice optimal coefficients of kernel convolutions for different down-scale to twice algorithms were found. Various methods for reducing the image size by half were considered the mean value over 4 nearest points and the weighted value of 16 nearest points with optimal coefficients. The optimal weights were calculated for each method of doubling described in this paper. The optimal weights were chosen in such a way as to minimize the value of mean square error between the accurate value and the found approximation. A simple method performing correction for approximation of any algorithm of doubling size is offered. The proposed correction method shows good results for simple interpolation algorithms. However, these improvements are insignificant for complex algorithms (17-point interpolation, Lanczos a = 3). According to the results of numerical experiments, the most accurate among the reviewed algorithms is the 17-point interpolation method, slightly worse is Lanczos convolution interpolation with the parameter a = 3 (see Table 2).

中文翻译：

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图像算法大小加倍的比较

摘要

本文对几种内插非自适应图像尺寸加倍的方法进行了质量比较分析。我们使用均方误差的值进行估计精度（质量）近似。没有考虑由插值方法引入的伪像（锯齿，吉布斯效应（振铃），模糊等）。的倍增插值高档算法的描述中呈现，诸如：最近邻法，线性和立方内插，兰克泽斯卷积内插（与一个= 1、2、3）和17点插值方法。对于每种将内核卷积提升到两倍的最佳方法，对于不同的缩减到两次算法，都可以找到。各种将图像尺寸减小一半的方法被认为是4个最近点的平均值和16个具有最佳系数的最近点的加权值。针对本文中介绍的每种加倍方法计算了最佳权重。选择最佳权重，以使准确值和找到的近似值之间的均方误差值最小。提供了一种简单的方法，可以对任何加倍大小的算法进行近似校正。所提出的校正方法对于简单的插值算法显示出良好的效果。然而，a = 3）。根据数值实验的结果，在所审查的算法中，最准确的算法是17点插值方法，稍差的是参数为a = 3的Lanczos卷积插值（请参见表2）。