BELE: Blur Equivalent Linearized Estimator

In the Full-Reference Image Quality Assessment context, Mean Opinion Score values represent subjective evaluations based on retinal perception, while objective metrics assess the reproduced image on the display. Bridging these subjective and objective domains requires parametric mapping functions, which are sensitive to the observer's viewing distance. This paper introduces a novel parametric model that separates perceptual effects due to strong edge degradations from those caused by texture distortions. These effects are quantified using two distinct quality indices. The first is the Blur Equivalent Linearized Estimator, designed to measure blur on strong and isolated edges while accounting for variations in viewing distance. The second is a Complex Peak Signal-to-Noise Ratio, which evaluates distortions affecting texture regions. The first-order effects of the estimator are directly tied to the first index, for which we introduce the concept of focalization, interpreted as a linearization term. Starting from a Positional Fisher Information loss model applied to Gaussian blur distortion in natural images, we demonstrate how this model can generalize to linearize all types of distortions. Finally, we validate our theoretical findings by comparing them with several state-of-the-art classical and deep-learning-based full-reference image quality assessment methods on widely used benchmark datasets.