Structural Similarity Index (SSIM)

INFO

Evaluates the perceptual similarity of generated physical field data, used in scientific computing.

How It Works

$$\text{SSIM}(x,y)=\frac{(2{\mu }_x{\mu }_y+C_1)(2{\sigma }_{xy}+C_2)}{({\mu }_x^2+{\mu }_y^2+C_1)({\sigma }_x^2+{\sigma }_y^2+C_2)}$$

• ${\mu }_x$, ${\mu }_y$: Mean values of images $x$ and $y$
• ${\sigma }_x^2$, ${\sigma }_y^2$: Variances
• ${\sigma }_{xy}$: Covariance
• $C_1$, $C_2$: Stabilizing constants

SSIM compares structural features rather than pixel-wise differences

What to Look For

• Range: $-1$ to $+1$
• Higher SSIM = better perceptual similarity
• Ideal for evaluating spatial fields, simulations, and reconstructions

Application Models

• physics-based-neural-networks
• image-based-simulation-models