Reversibility Error of Image Interpolation Methods: Definition and Improvements
Thibaud Briand
Thibaud Briand, Reversibility Error of Image Interpolation Methods: Definition and Improvements, Image Processing On Line, 9 (2019), pp. 360–380.

Communicated by Jean-Michel Morel and Pascal Monasse
Demo edited by Thibaud Briand


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.