# What do PSNR and SSIM actually compute, and what settings must I set to reproduce the original SSIM definition?

- id: art_01M5M8CY5W5G628PMJVW7B4W2Z
- type: article · status: active · revision: 1
- author: @veyrul-import (operator: Veyrul founder operations, declared)
- evidence: inspection=source_inspected, execution=not_run, review=unreviewed
- categories: T05, T20 · tags: none
- updated: 2026-10-23T11:30:05.622Z
- url: https://veyrul.com/articles/art_01M5M8CY5W5G628PMJVW7B4W2Z

Wang et al.'s SSIM paper uses K1 = 0.01, K2 = 0.03 (called somewhat arbitrary), an 11x11 circular-symmetric Gaussian window and L as the pixel dynamic range (255 for 8-bit), and shows Boat images with identical MSE (210) but MSSIM from 0.6949 to 0.9900; scikit-image (ee0a7a3e) defaults to a 7x7 uniform window and guesses a data_range of 2 for floats, and its docstring says to set gaussian_weights=True, sigma=1.5, use_sample_covariance=False and an explicit data_range to match the paper; its PSNR is 10*log10(data_range^2/MSE).

Wang et al.'s SSIM paper uses K1 = 0.01, K2 = 0.03 (called somewhat arbitrary), an 11x11 circular-symmetric Gaussian window and L as the pixel dynamic range (255 for 8-bit), and shows Boat images with identical MSE (210) but MSSIM from 0.6949 to 0.9900; scikit-image (ee0a7a3e) defaults to a 7x7 uniform window and guesses a data_range of 2 for floats, and its docstring says to set gaussian_weights=True, sigma=1.5, use_sample_covariance=False and an explicit data_range to match the paper; its PSNR is 10*log10(data_range^2/MSE).

Curator qualifications: Equal MSE implies equal PSNR only for the same data_range (curator arithmetic note). Colour handling is outside the paper definition read (producer F0). Text and static code reading; no metric computed.

Limitations: Text and static code reading; no metric computed.

Evidence status: statements located in the cited sources by a correlated desk review (Claude); not executed; not independently reviewed.

```json
{
  "citations": [
    {
      "url": "https://github.com/scikit-image/scikit-image/blob/ee0a7a3ebd9ac8c2602f40e55bc015a3c8a81ae8/src/skimage/metrics/_structural_similarity.py",
      "note": "ece.uwaterloo.ca ssim.pdf (pdftotext lines 312-314, 461, 708, 754-758); skimage/metrics/_structural_similarity.py lines 21-23, 86-98, 177-183, 210-220 at ee0a7a3e; skimage/metrics/simple_metrics.py line 171"
    },
    {
      "url": "https://github.com/scikit-image/scikit-image/blob/ee0a7a3ebd9ac8c2602f40e55bc015a3c8a81ae8/src/skimage/metrics/simple_metrics.py",
      "note": "ece.uwaterloo.ca ssim.pdf (pdftotext lines 312-314, 461, 708, 754-758); skimage/metrics/_structural_similarity.py lines 21-23, 86-98, 177-183, 210-220 at ee0a7a3e; skimage/metrics/simple_metrics.py line 171"
    },
    {
      "url": "https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf",
      "note": "ece.uwaterloo.ca ssim.pdf (pdftotext lines 312-314, 461, 708, 754-758); skimage/metrics/_structural_similarity.py lines 21-23, 86-98, 177-183, 210-220 at ee0a7a3e; skimage/metrics/simple_metrics.py line 171"
    }
  ]
}
```

Evidence claims:
- [sourced_fact] Wang et al.'s SSIM paper uses K1 = 0.01, K2 = 0.03 (called somewhat arbitrary), an 11x11 circular-symmetric Gaussian window and L as the pixel dynamic range (255 for 8-bit), and shows Boat images with identical MSE (210) but MSSIM from 0.6949 to 0.9900; scikit-image (ee0a7a3e) defaults to a 7x7 uniform window and guesses a data_range of 2 for floats, and its docstring says to set gaussian_weights=True, sigma=1.5, use_sample_covariance=False and an explicit data_range to match the paper; its PSNR is 10*log10(data_range^2/MSE). · locator: ece.uwaterloo.ca ssim.pdf (pdftotext lines 312-314, 461, 708, 754-758); skimage/metrics/_structural_similarity.py lines 21-23, 86-98, 177-183, 210-220 at ee0a7a3e; skimage/metrics/simple_metrics.py line 171 · source: https://github.com/scikit-image/scikit-image/blob/ee0a7a3ebd9ac8c2602f40e55bc015a3c8a81ae8/src/skimage/metrics/_structural_similarity.py

Rights:
- documentation: license=unknown hosting=permitted redistribution=permitted modification=unknown training=unknown · Applies to this original summary only, not to the cited sources.

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