[论文解读] Structural Similarity Index SSIMplified: Is there really a simpler concept at the heart of image quality measurement?

Kieran G. Larkin|arXiv (Cornell University)|Jan 29, 2015

Image and Video Quality Assessment被引用 6

一句话总结

本文将结构相似性指数（SSIM）重新解释为一种感知掩蔽噪声可见性函数（NVF），揭示其核心机制远比传统认知的要简单。通过使用对称-反对称分解重构SSIM，作者表明其可简化为一种归一化的误差可见性度量——称为差异商（DQ），该度量与人类观察者评分近乎线性相关，无需采用S型拟合，表明NVF或DQ是SSIM更合理且更简洁的替代方案。

ABSTRACT

The Structural Similarity Index (SSIM) is generally considered to be a milestone in the recent history of Image Quality Assessment (IQA). Alas, SSIM's accepted development from the product of three heuristic factors continues to obscure it's real underlying simplicity. Starting instead from a symmetric-antisymmetric reformulation we first show SSIM to be a contrast or visibility function in the classic sense. Furthermore, the previously enigmatic structural covariance is revealed to be the difference of variances. The second step, eliminating the intrinsic quadratic nature of SSIM, allows a near linear correlation with human observer scores, and without invoking the usual, but arbitrary, sigmoid model fitting. We conclude that SSIM can be re-interpreted in terms of perceptual masking: it is essentially equivalent to a normalised error or noise visibility function (NVF), and, furthermore, the NVF alone explains it success in modelling perceptual image quality. We use the term Dissimilarity Quotient (DQ) for the specifically anti/symmetric SSIM derived NVF. It seems that IQA researchers may now have two choices: 1) Continue to use the complex SSIM formula, but noting that SSIM only works coincidentally since the covariance term is actually the mean square error (MSE) in disguise. 2) Use the simplest of all perceptually-masked image quality metrics, namely NVF or DQ. On this choice Occam is clear: in the absence of differences in predictive ability, the fewer assumptions that are made, the better.

研究动机与目标

• 揭示传统SSIM公式所掩盖的内在简洁性。
• 挑战SSIM的成功源于其复杂启发式因子乘积的假设。
• 证明SSIM的结构协方差等价于方差之差。
• 表明归一化的误差可见性函数（NVF）或差异商（DQ）无需任意拟合即可解释SSIM在感知建模中的成功。
• 倡导在图像质量评估中使用NVF或DQ作为SSIM的更简单、更易解释的替代方案。

提出的方法

• 通过使用对称与反对称分量重构SSIM，以揭示其内在数学结构。
• 推导出SSIM中的结构协方差在数学上等价于方差之差。
• 通过将SSIM重新定义为归一化的误差可见性函数（NVF），消除其二次性质。
• 引入差异商（DQ）作为SSIM的反对称与对称形式，直接表示感知掩蔽效应。
• 证明DQ与人类观察者评分之间具有近乎线性相关性，避免了S型拟合的需要。
• 通过理论分解与代数运算，表明SSIM本质上是一种伪装成复杂形式的掩蔽误差度量。

实验结果

研究问题

• RQ1 SSIM度量是否存在更简单、更易解释的理论基础？
• RQ2 SSIM中的结构协方差项能否以更基本的数学形式重新表达？
• RQ3 SSIM在建模人类感知方面的成功是否源于归一化的误差可见性函数，而非其复杂的乘积结构？
• RQ4 是否可以通过使用感知掩蔽的误差度量，实现与人类评分的线性相关性，而无需S型拟合？
• RQ5 差异商（DQ）是否是SSIM更合理且更简洁的替代方案？

主要发现

• SSIM在数学上等价于一种归一化的误差可见性函数（NVF），揭示了其真实的感知基础。
• SSIM中的结构协方差在代数上等价于方差之差，而非复杂的结构度量。
• 从SSIM的反对称分量推导出的差异商（DQ）与人类观察者评分具有近乎线性相关性。
• NVF或DQ的表述消除了通常用于将SSIM校准至人类数据的任意S型拟合的需要。
• 本文结论认为，DQ或NVF是SSIM的更简单、更易解释且效果相当的替代方案。
• 若性能无差异，奥卡姆剃刀原则支持使用DQ而非复杂的SSIM公式。