Reversibility Error of Image Interpolation Methods: Definition and Improvements

Abstract

There is no universal procedure in image processing for evaluating the quality and performance of an interpolation method. In this work, we introduce a new quantity: the reversibility error. For a given image, it measures the error after applying successively a homography close to the identity, a crop (removing boundary artifacts) and the inverse homography. An average over random homographies is made to remove the dependency on the homography. A more precise measurement discarding very high-frequency artifacts is obtained by clipping the spectrum of the difference. We also propose new fine-tuned interpolation methods that are based on the DFT zoom-in and pre-existing (or base) interpolation methods. The zoomed version of an interpolation method is obtained by applying it to the DFT zoom-in of the image. In the periodic plus smooth version of interpolation methods, the non-periodicity is handled by applying the zoomed version to the periodic component and a base interpolation method to the smooth component. In an experimental part, we show that the proposed fine-tuned methods have smaller reversibility errors than their base interpolation methods and that the error is mainly localized in a small high-frequency band. We recommend to use the periodic plus smooth versions of high order B-spline. It is more efficient and provides better results than trigonometric polynomial interpolation.