On the Feasibility of Cross-Validation in Image Analysis

Abstract

The performance of cross-validation as a device for selecting the optimal amount of regularisation in image analysis is examined. It is shown that cross-validation results in asymptotically optimal performance, provided the amount of blur does not exceed a certain ceiling. If blur exceeds that level, then cross-validation does not yield asymptotic optimality. The ceiling is surprisingly low. For example, if a fixed scene is subject to blur and is digitised on an increasingly fine grid, then cross-validation will only yield optimal image enhancement if the amount of blur decreases as the grid becomes finer. Two types of cross-validation are studied, one taken directly from methodology for nonparametric regression, and the other involving a modification that adjusts for image blur.