  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.
