GEOMETRIC METHODS FOR RASTER IMAGE INTERPOLATION IN POINT CALCULUS

The aim of the work is to analyze several methods of interpolation of raster images at their scaling. The idea is to model a composite interpolation response surface by pixels of a raster image and its representation in vector form with subsequent calculation of intermediate color values between interpolation node points. To verify and compare several geometric interpolation algorithms, a method of numerical evaluation of the degree of similarity of geometric objects in the form of two points sets based on the use of the coefficient of determination is used. Parabolic curves of second and third orders, as well as a third-order interpolation curve derived from the Dezarg configuration, were used as shape elements for constructing response surfaces. Parameterization of the curves and response surfaces was performed by means of the mathematical apparatus “Point Calculus”. A software package capable of interpolating raster images by various methods was written for computational experiments. This complex allows comparing numerically the results of interpolation of raster images with the reference image and among themselves using the coefficient of determination. As a result of computational experiments, biparabolic interpolation based on second-order curves showed the best result.