Interpolating Polynomials

Abstract

This appendix shows how to predict the value of a pixel from those of 16 of its near neighbors by means of a two-dimensional interpolating polynomial. The results are used in Table 4.31. The main idea is to consider the 16 neighbor pixels as 4x4 equally spaced points on a surface (where the value of a pixel is interpreted as the height of the surface) and to use polynomials to find the mathematical expression of a surface P(u, w) that goes through all 16 points. The value of the pixel at the center of the 4x4 group can then be predicted by calculating the height of the center point P(.5, .5) of the surface. Mathematically, this surface is the two-dimensional polynomial interpolation of the 16 points.