SSIMULACRA 2 - Structural SIMilarity Unveiling Local And Compression Related Artifacts

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

Usage

ssimulacra2 original.png distorted.png

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

• negative scores: extremely low quality, very strong distortion.
• 10 = very low quality. MOS score close to 1 ('bad') in a BT.500 ACR test. Very obvious and annoying artifacts. This corresponds to the typical output of cjxl -d 14 / -q 12 or libjpeg-turbo 4:2:0 quality 14.
• 30 = low quality. MOS score around 2 ('poor') in a BT.500 ACR test. Obvious and annoying artifacts. This corresponds to the typical output of cjxl -d 9 / -q 20 or libjpeg-turbo 4:2:0 quality 20.
• 50 = medium quality. MOS score around 3 ('fair') in a BT.500 ACR test. Slightly annoying artifacts. This corresponds to the typical output of cjxl -d 5 / -q 45 or libjpeg-turbo 4:2:0 quality 35.
• 70 = high quality. MOS score around 4 ('good') in a BT.500 ACR test. Artifacts are perceptible, but not annoying. Distortion barely noticeable by an average observer in a side-by-side comparison at 1:1 from a normal viewing distance. Without reference to the original image, an average observer does not notice artifacts. This corresponds to the typical output of cjxl -d 2.5 / -q 73 or libjpeg-turbo 4:2:0 quality 70.
• 80 = very high quality. Distortion not noticeable by an average observer in a side-by-side comparison at 1:1 from a normal viewing distance. This corresponds to the typical output of cjxl -d 1.5 / -q 85 or libjpeg-turbo 4:2:2 quality 85.
• 85 = excellent quality. Distortion not noticeable by an average observer in the condition of in-place comparison at 1:1 from a normal viewing distance. This corresponds to the typical output of cjxl -d 1 / -q 90 or libjpeg-turbo 4:4:4 quality 90.
• 90 = visually lossless. Distortion not noticeable by an average observer in a flicker test at 1:1 from a normal viewing distance. This corresponds to the typical output of cjxl -d 0.5 / -q 95 or libjpeg-turbo 4:4:4 quality 95.
• 100 = mathematically lossless.

How it works

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:

Dataset | KRCC | SRCC | PCC | -- | -- | -- | -- CID22| 0.6903 | 0.8805 | 0.8583 TID2013| 0.6590 | 0.8445 | 0.8471 KADID-10k| 0.6175 | 0.8133 | 0.8030 KonFiG(F)| 0.7668 | 0.9194 | 0.9136

SSIMULACRA 2.0:

Dataset | KRCC | SRCC | PCC | -- | -- | -- | -- CID22| 0.6934 | 0.8820 | 0.8601 TID2013| 0.6322 | 0.8194 | 0.8103 KADID-10k| 0.5870 | 0.7851 | 0.7018 KonFiG(F)| 0.7813 | 0.9280 | 0.8710

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)

Metric performance

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:

Metric | KRCC | SRCC | PCC | -- | -- | -- | -- PSNR-Y | 0.4699 | 0.6394 | 0.428 PSNR-HVS | 0.5464 | 0.698 | 0.6846 SSIM | 0.5707 | 0.7552 | 0.764 MS-SSIM | 0.6068 | 0.7868 | 0.7802 VMAF | 0.5608 | 0.7439 | 0.7728 SSIMULACRA 2 | 0.6322 | 0.8194 | 0.8103 SSIMULACRA 2.1 | 0.659 | 0.8445 | 0.8471 DSSIM | -0.6984 | -0.871 | -0.8021 Butteraugli (3-norm) | -0.4935 | -0.6639 | -0.4878 PSNR (ImageMagick) | 0.4958 | 0.6869 | 0.6601

KADID-10k:

Metric | KRCC | SRCC | PCC | -- | -- | -- | -- PSNR-Y | 0.4555 | 0.6319 | 0.5932 PSNR-HVS | 0.4229 | 0.5927 | 0.5949 SSIM | 0.5889 | 0.7806 | 0.6576 MS-SSIM | 0.6466 | 0.8359 | 0.6836 VMAF | 0.5343 | 0.7253 | 0.7185 SSIMULACRA 2 | 0.587 | 0.7851 | 0.7018 SSIMULACRA 2.1 | 0.6175 | 0.8133 | 0.803 DSSIM | -0.6679 | -0.8561 | -0.6544 Butteraugli (3-norm) | -0.3846 | -0.543 | -0.4424 PSNR (ImageMagick) | 0.4876 | 0.6757 | 0.6214

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

Metric | KRCC | SRCC | PCC | -- | -- | -- | -- PSNR-Y | 0.5871 | 0.7598 | 0.6968 | PSNR-HVS | 0.7798 | 0.9277 | 0.8453 | SSIM | 0.6156 | 0.7795 | 0.7052 | MS-SSIM | 0.6635 | 0.8299 | 0.6834 | VMAF | 0.3866 | 0.4906 | 0.463 | SSIMULACRA 2 | 0.7813 | 0.928 | 0.871 | SSIMULACRA 2.1 | 0.7668 | 0.9194 | 0.9136 | DSSIM | -0.7595 | -0.9147 | -0.673 | Butteraugli (3-norm) | -0.771 | -0.9238 | -0.7587 | PSNR (ImageMagick) | 0.6531 | 0.8248 | 0.7218 |

CID22 full set: (22k subjective scores)

Metric | KRCC | SRCC | PCC | -- | -- | -- | -- PSNR-Y | 0.4452 | 0.6246 | 0.5901 PSNR-HVS | 0.6076 | 0.81 | 0.7559 SSIM | 0.5628 | 0.7577 | 0.7005 MS-SSIM | 0.5596 | 0.7551 | 0.7035 VMAF | 0.6176 | 0.8163 | 0.7799 SSIMULACRA 2 | 0.6934 | 0.882 | 0.8601 SSIMULACRA 2.1 | 0.6903 | 0.8805 | 0.8583 DSSIM | -0.6428 | -0.8399 | -0.7813 Butteraugli 3-norm | -0.6547 | -0.8387 | -0.7903 PSNR (ImageMagick) | 0.3472 | 0.5002 | 0.4817

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

Metric | KRCC | SRCC | PCC | -- | -- | -- | -- PSNR-Y | 0.4734 | 0.6577 | 0.6354 PSNR-HVS | 0.6199 | 0.8224 | 0.7848 SSIM | 0.6028 | 0.7871 | 0.7647 MS-SSIM | 0.5915 | 0.7781 | 0.7601 VMAF | 0.588 | 0.7884 | 0.7502 SSIMULACRA 2 | 0.7033 | 0.8854 | 0.8745 SSIMULACRA 2.1 | 0.7077 | 0.8904 | 0.8787 DSSIM | -0.6807 | -0.8722 | -0.822 Butteraugli 3-norm | -0.6102 | -0.7938 | -0.745 PSNR (ImageMagick) | 0.3491 | 0.4995 | 0.5013

Building

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.