Image Quality: MSE and PSNR

Intuition

How close is a compressed or denoised image to the original? The mean squared error averages the squared pixel differences. PSNR (peak signal-to-noise ratio) puts that error on a logarithmic scale relative to the largest possible pixel value, in decibels: higher is better.

Precise explanation

MSE=1N∑(I−K)2,PSNR=10log⁡102552MSE dB\text{MSE} = \frac{1}{N}\sum (I - K)^2,\qquad \text{PSNR} = 10\log_{10}\frac{255^2}{\text{MSE}}\ \text{dB} 
cv2.PSNR(reference, distorted)        # uint8 images, peak 255
  • Compute differences in floating point: reference - distorted on uint8 arrays wraps around (3 − 5 = 254).
  • Identical images have MSE 0 and infinite PSNR; cv2.PSNR instead returns a large finite value (about 361 dB), so handle MSE = 0 yourself.
  • Rough guide for 8-bit images: above 40 dB differences are hard to see; 30–40 dB is good compression; below 20 dB the distortion is obvious. PSNR does not model human perception well — SSIM is a common complement.

Worked example

If every pixel differs by exactly 1, MSE = 1 and PSNR = 10·log₁₀(65025) = 48.13 dB. Uniform noise of ±10 gives about 28 dB.

What the library does inside

The formula you implement by hand in CV-17 (the optional deep dive after this step), computed in double precision over all channels.

Common mistakes

  • Subtracting uint8 arrays directly.
  • Comparing images of different sizes or channel orders.
  • Reporting cv2.PSNR's 361 dB for identical images as a meaningful number.

Why this matters

PSNR is the standard sanity metric for compression, super-resolution and denoising models, and a quick way to check that an image pipeline did not change pixels it should not have.

References