Bias of higher order predictive interpolation for sub-pixel registration

Sub-pixel registration has application in many image processing tasks. Predictive interpolation solves the problem of choosing a particular interpolation function and needing to search for the best offset by determining the optimum interpolation function for a given pair of images, and estimating the offset from the interpolation weights. By analysing sinusoids and step edges, it is shown that even order predictive interpolation filters inherently have more bias than odd order filters. It is also demonstrated that increasing the filter order significantly improves registration bias. The form of the bias is verified by measuring the accuracy of registration on sample images.