Principles of local polynomial interpolation

The sub-pixel analysis of large volumes of digital imagery requires precise methods of interpolation. To be computationally feasible, the methods must be massively parallelizable, and this constrains them to be local. This paper develops a set of principles for generating local interpolators, which apply to both one and higher-dimensional problems. The principles are demonstrated here for the four-point one-dimensional problem and produce both a generalization of cubic convolution that applies to non-uniform grids and a new quintic method. Based on three common metrics, the new method achieves equal or better performance than cubic convolution and the comparable non-local method. The new principles suggest that any higher-order polynomial method beyond quintic is unnatural and causes higher low-frequency error.