Evaluation of Sharpness Measures and Proposal of a Stop Criterion for Reverse Diffusion in the Context of Image Deblurring

Abstract

The heat equation can be used to model the diffusion process shown in a defocused (blurry) region of a picture taken with conventional camera lens. The original focused image can be recovered by reverting the heat equation, that is, by reverse diffusion. However, the main difficulty with this technique is that it becomes unstable very quickly due to the finite precision of pixel values and the image values blow up. For that reason, detecting the exact time when the reverse diffusion process should stop is crucial. The goal of this work it to evaluate the behavior of different non-reference state-of-the-art sharpness measures (that is, when a perfectly focused image is not available) for the forward and inverse diffusion processes and to propose a robust stop criterion to reliably detect the moment before each region becomes unstable. To find out a good stop criterion, we carry out a set of experiments with test and real images. The results in this paper can be valuable not only to estimate monocular depth from blur cues, but also to any other image processing fields that require image deblurring.