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statistics.md

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Statistics

The statistics tab can show very basic statistics for an image equation. By default it will display the average, min and max Luminance.

Luminance is the radiant power weighted by a spectral sensitivity function that is characteristic of vision. The magnitude is proportional to physical power, but the spectral composition is related to the brightness sensitivity of human vision. Luminance is computed in linear color space with: dot(RGB*A, (0.2125, 0.7154, 0.0721)).

The following components can be selected instead of luminance:

  • Average - equally weights each channel (good for general error comparison)
  • Luma - video luma (sRGB)
  • Lightness - gamma corrected luminance
  • Alpha - image alpha channel (for coverage)
  • SSIM - compares two images with the SSIM index

MAE/MSE and more

Most of the popular error metrics can be computed by using an appropriate image equation in combination with the statistics tab. In this case I0 is the original and I1 the biased image:

Error Metric Image Equation Statistic Full Name
MAE abs(I1 - I0) Average Mean Average Error
MSE (I1-I0)^2 Average Mean Squared Error
RMSE (I1-I0)^2 Root Average Root MSE
RMSRE (I1/I0-1)^2 Root Average Root Mean Squared Relative Error
RMSRE (alt.) (2*(I1 - I0)/(I1 + I0))^2 Root Average Alternative version of RMSRE

Rule of thumb:

  • Choose Luminance for RGB weighted linear error
  • Choose Average if RGB should be weighted equally
  • Choose SSIM for perceived error

PSNR

Peak signal-to-noise ratio (PSNR) is the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. PSNR is defined as: PSNR = 20*log10(MAX_I0) - 10*log10(MSE)

Three steps are required to determine the PSNR:

  1. set I0 as equation and copy the Max value
  2. set (I1-I0)^2 as equation and copy the Average value
  3. use first value as MAX_I0 and second value as MSE

SSIM

The Structural Similarity (SSIM) index is another method for predicting the perceived difference between two images. SSIM is based on visible structure differences instead of per-pixel absolute differences (like RMSE or MAE). It is computed with the luma grayscale (sRGB space).

SSIM Interpretation
1 Images are identical
0 Images have no relation
-1 Images are inversed