The quality of underwater imagery is critical to the success of marine exploration, ecological monitoring, and autonomous underwater operations, where visual data often serve as the primary sensory modality. However, underwater image acquisition is fundamentally constrained by the physics of light propagation in water leading to color distortions, turbidity, scattering-induced haze, and loss of structural detail. Despite significant advancements in underwater image enhancement (UIE), the field of underwater image quality assessment (UIQA) remains underexplored, particularly in no-reference (NR) settings where pristine images are unavailable. Existing NR UIQA methods are either overly reliant on handcrafted features or exhibit limited generalizability across diverse underwater domains. In this paper, we introduce PUIQA, a physically grounded, multi-domain multi-scale descriptor framework for robust no-reference underwater image quality prediction. Our approach systematically fuses features derived from physical imaging priors (e.g., non-uniform illumination, veiling light gradients), perceptual features (e.g., local entropy, edge energy, contrast), and frequency-domain signatures (e.g., DCT-based structural degradation). To further model scale-variant degradations, we extend these descriptors across Gaussian and resolution-based multiscale domains. The extracted features are combined into a high-dimensional representation and regressed via a support vector regression (SVR) pipeline optimized for perceptual fidelity. To validate the generalizability and robustness of PUIQA, we conduct extensive experiments on two diverse and publicly available underwater image datasets: UID2021, and UIEB. PUIQA achieves SROCC of 0.726/0.768 and PLCC of 0.754/0.773 on UWIQA and UID2021, outperforming existing NR-IQA metrics, demonstrating strong cross-dataset transferability and effectiveness in handling both real and synthetic underwater distortions. This work presents a substantial step toward establishing a principled, generalizable foundation for blind UIQA in practical underwater imaging systems. The full implementation of PUIQA is publicly available at: https://github.com/Rehman1995/PUIQA.
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