Depth-Aware Super-Resolution via Distance-Adaptive Variational Formulation

• URL: http://arxiv.org/abs/2509.05746v2
• Date: Wed, 29 Oct 2025 04:32:16 GMT
• Title: Depth-Aware Super-Resolution via Distance-Adaptive Variational Formulation
• Authors: Tianhao Guo, Bingjie Lu, Feng Wang, Zhengyang Lu,
• Abstract summary: Single image super-resolution traditionally assumes spatially-invariant degradation models.<n>Real-world imaging systems exhibit complex distance-dependent effects including atmospheric scattering, depth-of-field variations, and perspective distortions.<n>We propose a rigorous variational framework that characterizes super-resolution as a spatially-varying inverse problem.
• Score: 5.1767204510818985
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Single image super-resolution traditionally assumes spatially-invariant degradation models, yet real-world imaging systems exhibit complex distance-dependent effects including atmospheric scattering, depth-of-field variations, and perspective distortions. This fundamental limitation necessitates spatially-adaptive reconstruction strategies that explicitly incorporate geometric scene understanding for optimal performance. We propose a rigorous variational framework that characterizes super-resolution as a spatially-varying inverse problem, formulating the degradation operator as a pseudodifferential operator with distance-dependent spectral characteristics that enable theoretical analysis of reconstruction limits across depth ranges. Our neural architecture implements discrete gradient flow dynamics through cascaded residual blocks with depth-conditional convolution kernels, ensuring convergence to stationary points of the theoretical energy functional while incorporating learned distance-adaptive regularization terms that dynamically adjust smoothness constraints based on local geometric structure. Spectral constraints derived from atmospheric scattering theory prevent bandwidth violations and noise amplification in far-field regions, while adaptive kernel generation networks learn continuous mappings from depth to reconstruction filters. Comprehensive evaluation across five benchmark datasets demonstrates state-of-the-art performance, achieving 36.89/0.9516 and 30.54/0.8721 PSNR/SSIM at 2 and 4 scales on KITTI outdoor scenes, outperforming existing methods by 0.44dB and 0.36dB respectively. This work establishes the first theoretically-grounded distance-adaptive super-resolution framework and demonstrates significant improvements on depth-variant scenarios while maintaining competitive performance across traditional benchmarks.

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