BELE: Blur Equivalent Linearized Estimator

TL;DR

The paper tackles full-reference image quality assessment (FR-IQA) by bridging subjective MOS/DMOS with objective metrics across viewing distances. It introduces BELE, a Blur Equivalent Linearized Estimator, which uses two interpretable indices: an edge-focused component derived from an empirical estimator with focalization for strong edges, and CPSNR for textures, combined via a low-parameter affine fusion. Grounded in a VRF-based HVS model and Positional Fisher Information, the method maps distortions to an equivalent blur and employs a focusing mechanism to align with the canonical model, requiring only five parameters. Across multiple datasets, BELE demonstrates competitive or superior accuracy with significantly fewer parameters than deep-learning-based IQA methods, offering calibration-free, efficient performance and practical applicability, with potential extensions to Reduced-Reference and No-Reference IQA.

Abstract

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 \emph{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.

Figures (7)

• Figure 1: Flowchart illustrating the construction of the BELE estimator. BELE is formed by combining two separately studied indices: $\text{BELE}_{\text{cold}}$ for strong and isolated edges and CPSNR for textures. The process requires five parameters: two ($Q$ and $\tau$) physically modeling blur and three for the polynomial fitting between the indices, representing an affine transformation. This contrasts with the VQEG transformation, which uses a five-parameter logistic function. The affine combination will be detailed in Sec. \ref{['sec:Combination of metrics for strong edges and textures']}.
• Figure 2: Upper row: two original images, "Babygirl" and "Palace2". Second row: Gaussian blurred images with $s_B=2.4$. Lower row: certainty maps. Purple dominance (left column) indicates higher certainty in high-quality images, while red dominance (right column) signifies greater loss in lower-quality images. The isoluminance colors maintain a constant intensity at the same edge level, so, only the weight defines the local contrast.
• Figure 3: Upper row: two original images, "Paintedhouse" and "Stream". Second row: Gaussian blurred images with $s_B=7.7$ and $s_B=1.0$. Lower row: certainty maps. No dominance of purple or red is observed. In the first image, "Paintedhouse," a widespread cyan color suggests that subjective perception closely aligns with the canonical estimator.
• Figure 4: The conversion function of $\text{BELE}(\zeta)$ (red curve), along with the equivalent blur values obtained by mapping the DMOS values of all distortions in the LIVE DBR2 dataset onto the conversion function (blue stars).
• Figure 5: The variation in distortion levels between images affected by Gaussian blur in the LIVE DBR2 dataset (green markers) and their corresponding images with equivalent blur (red markers). This quantifies how the distortion in the equivalent blur image deviates from the expected Gaussian blur distortion in the LIVE DBR2 dataset. The worst-case scenario is highlighted by the “Monarch” image with $s_B = 11.3$, where $\hat{d}_{\xi_{eq}}$ and $\hat{d}_{\text{distortion}}$ are marked by two blue points, showing an approximately 18% deviation in the prediction.

Theorems & Definitions (1)

• Definition 1