Noise Characteristics of Higher Order Predictive Interpolation for Sub-pixel Registration

Sub-pixel registration has application in many image processing tasks. Predictive interpolation, a novel registration technique, solves the problems of choosing a particular interpolation function and needing to search for the best offset. Predictive interpolation determines the optimum interpolation function for a given pair of images, and estimates the offset from the interpolation weights. The estimate of the offset between the images is biased, and this bias depends strongly on any noise present in the image. It is shown that the bias resulting from the noise is opposite from the bias from the image. This leads to the counter-intuitive result that the registration accuracy can improve significantly (by a factor of 10 for a second order filter) with the addition of moderate amounts of noise. A 5^th order filter is accurate to better than 0.5% of a pixel over a wide range of noise levels. These results are verified by measuring the accuracy of registration on sample images.