Perceptual metric developed by Jon Sneyers (Cloudinary) in July-October 2022, updated in April 2023.

ssimulacra2 original.png distorted.png

Returns a score in range -inf..100, which correlates to subjective visual quality scores as follows:

• 30 = low quality. This corresponds to the p10 worst output of mozjpeg -quality 30.
• 50 = medium quality. This corresponds to the average output of cjxl -q 40 or mozjpeg -quality 40, or the p10 output of cjxl -q 50 or mozjpeg -quality 60.
• 70 = high quality. This corresponds to the average output of cjxl -q 65 or mozjpeg -quality 70, p10 output of cjxl -q 75 or mozjpeg -quality 80.
• 90 = very high quality. Likely impossible to distinguish from the original when viewed at 1:1 from a normal viewing distance. This corresponds to the average output of mozjpeg -quality 95 or the p10 output of cjxl -q 95.

SSIMULACRA 2 is based on the concept of the multi-scale structural similarity index measure (MS-SSIM), computed in a perceptually relevant color space, adding two other (asymmetric) error maps, and aggregating using two different norms.

• XYB color space (rescaled to a 0..1 range and with B-Y)
• Three error maps:
  • SSIM map (with a corrected SSIM formula that avoids applying gamma correction twice)
  • 'blockiness/ringing' map (error means distorted has edges where original is smooth)
  • 'smoothing/blur' map (error means distorted is smooth where original has edges)
• Each of these error maps is computed at 6 scales (1:1 to 1:32) for each component (X,Y,B)
• Downscaling is done in linear color (i.e. the perceptually correct way)
• For each of these 6*3*3=54 maps, two norms are computed: 1-norm (mean) and 4-norm
• A weighted sum of these 54*2=108 norms leads to the final score
• Weights were tuned based on a large set of subjective scores (CID22, TID2013, Kadid10k, KonFiG-IQA), including images compressed with JPEG, JPEG 2000, JPEG XL, WebP, AVIF, HEIC, and various artificial distortions.

Final results after tuning:

SSIMULACRA 2.1:

SSIMULACRA 2.0:

The weight tuning was done by running Nelder-Mead simplex search, optimizing to minimize MSE and to maximize Kendall and Pearson correlation for training data consisting of the CID22 training data, TID2013, KADID-10k and KonFiG (F boosting).

Changes compared to SSIMULACRA 2.0:

• weights retuned to correlate better with other datasets
• changed the range of the 3 components to ensure they are in 0..1 so the SSIM formula makes sense
• added a polynomial remapping of the error score to allow a better fit to datasets with higher distortions

Changes compared to the original version (SSIMULACRA 1):

• works in XYB color space instead of CIE Lab
• linear downscaling
• fixed SSIM formula
• uses 1-norm and 4-norm (instead of 1-norm and max-norm-after-downscaling)
• penalizes both smoothing and ringing artifacts (instead of only penalizing ringing but not smoothing)
• removed specific grid-like blockiness detection
• tuned using a much larger set of subjective opinions (and using absolute quality scores, not just relative comparison results)

These tables show the correlation of various metrics in terms of Kendall Rank Correlation Coefficient (KRCC), Spearman Rank Correlation Coefficient (SRCC), and Pearson Correlation Coefficient (PCC), for various IQA datasets.

TID2013:

KADID-10k:

KonFiG-IQA: (Experiment I, F boosting, clamping negative JND (better than reference) to zero)

CID22 full set: (22k subjective scores)

CID22 validation set: (4292 subjective scores, not used for tuning)

Building instructions for Debian:

sudo apt install build-essential git libhwy-dev liblcms2-dev libjpeg62-turbo-dev libpng-dev cmake ninja-build
mkdir build
cd build
cmake ../src -G Ninja
ninja ssimulacra2

or simply execute build_ssimulacra2. Other distributions should be similar; you may need to use libjpeg-turbo8-dev instead of libjpeg62-turbo-dev. Version 2.13 of lcms2 is needed.

The source code of SSIMULACRA 2 is also part of the tools of libjxl.

The bash script build_ssimulacra2_from_libjxl_repo can be used to fetch the code and compile only what is needed for SSIMULACRA 2.