Image interpolation algorithms pervade many modern image processing and analysis applications. However, when their weighting schemes inefficiently generate very unrealistic estimates, they may negatively affect the performance of the end user applications. Therefore, in this work, the author introduced four weighting schemes based on some geometric shapes for digital image interpolation operations. And, the quantity used to express the extent of each shape weight was the normalized area, especially when the sums of areas exceeded a unit square size. The introduced four weighting schemes are based on the minimum side based diameter (MD) of a regular tetragon, hypotenuse based radius (HR), the virtual pixel length based height for the area of the triangle (AT), and the virtual pixel length for hypotenuse based radius for the area of the circle (AC). At the smaller scaling ratio, the image interpolation algorithm based on the HR scheme scored the highest at 66.6 % among non traditional image interpolation algorithms presented. But, at the higher scaling ratio, the AC scheme based image interpolation algorithm scored the highest at 66.6 % among non traditional algorithms presented and, here, its image interpolation quality was generally superior or comparable to the quality of images interpolated by both non traditional and traditional algorithms.

翻译：图像插值算法广泛应用于现代图像处理与分析应用。然而，当加权方案低效地生成极不真实的估计值时，可能会对最终用户应用的性能产生负面影响。为此，本文作者针对数字图像插值操作引入了四种基于几何形状的加权方案。各形状权重的量化指标采用归一化面积，特别当面积总和超过单位正方形尺寸时。所提出的四种加权方案分别基于：正四边形的最小边直径（MD）、基于斜边的半径（HR）、三角形面积（AT）的虚拟像素长度高度，以及圆形面积（AC）的基于斜边半径的虚拟像素长度。在较小缩放比下，基于HR方案的图像插值算法在非传统图像插值算法中得分最高，达到66.6%；而在较大缩放比下，基于AC方案的图像插值算法在非传统算法中同样以66.6%的得分位居首位，且其图像插值质量普遍优于或可比肩非传统与传统算法所插值的图像。