About PSNR and SSIM of your reversible halftones

[LLLddddd]

When comparing halftone images in terms of PSNR and SSIM (for example, Ostromoukhov method, Structure-aware halftoning, and this paper method), you have mentioned that "Higher PSNR/SSIM indicate better quality".

I want to ask that for SSIM metric, does higher SSIM indicate better halftone quality, or lower SSIM indicate better halftone quality? Because the reversible halftone gets lower PSNR than Ostromoukhov method, but with higher SSIM, and "Structure-aware halftoning" has lower SSIM with only 0.0340.

So does higher SSIM indicate better quality, or lower indicate better?

[MenghanXia]

As mentioned in the paper, higher PSNR and SSIM indicate better halftone quality because it means the more accurate simulation to the input luminance. PSNR is more focus on average intensity while SSIM is more sensitive to structure or edge signal. The reversible halftone achieves the best structure similarity but slightly inferior to Ostromoukhov's method in intensity similarity.
Besides, the reason why "Structure-aware halftoning" has unexpectedly low SSIM is that this method requires hyper-parameter tuning for every example to get good result but that is impossible for the evaluation on a large-scale dataset (so we just take their default setting and get bad statistic results). For informative comparison, you are recommended to check those examples (attached with PSNR/SSIM) in Fig.7 of the paper and Fig.2~5 of the supplementary material.