SSIM Limit Theory: Statistical Breakdown Fingerprints (Δμ, Δσ)

This study introduces the SSIM Limit Theory, establishing a mathematical framework for analyzing the degradation of structural similarity. To capture the underlying distributional shifts that drive SSIM collapse, we propose Statistical Breakdown Fingerprints (Δμ, Δσ), a concise representation of these changes. The dataset accompanying this work includes the full theoretical manuscript, database schema, reproducible SQL resources, and integrity-verified data blocks that support transparent scientific validation. These results are built upon an exhaustive analysis of over 82 million records and are presented alongside a demonstration video verifying the system's operation. Dataset and Mandatory Citation:- Source: NIH ChestX-ray8 (Hospital-scale chest x-ray database)- Citation: Wang, X., Peng, Y., Lu, L., Lu, Z., Bagheri, M., & Summers, R. M. (2017). "ChestX-ray8: Hospital-scale chest x-ray database and benchmarks on weakly-supervised classification and localization of common thoracic diseases." Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 3462–3471. - Download: https://nihcc.app.box.com/v/ChestXray-NIHCC Software and Models Used The image processing and upscaling in this study were conducted using the following open-source software and AI models: Upscayl: Used as the primary GUI/Engine for image upscaling. (https://github.com/upscayl/upscayl) Real-ESRGAN / SwinIR: The underlying AI models used for image restoration and enhancement. License: Upscayl is open-source under the GNU AGPLv3. SwinIR is licensed under the Apache License 2.0. Credits & Citations Upscayl: Developed by Nayam Amarshe and TGS963. SwinIR: Liang, J., et al. "SwinIR: Image Restoration Using Swin Transformer." arXiv:2108.10257 (2021). (https://github.com/JingyunLiang/SwinIR) Real-ESRGAN: Wang, X., et al. "Real-ESRGAN: Training Real-World Blind Iterative Image Restoration." Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2021. (https://github.com/xinntao/Real-ESRGAN) Contact : [e-mail]