Calculate Mean Squared Pixel Error
Two processed images look close, but their pixels differ.
Read the full lesson and open its transcript below. A narrated video will be added after production.
What you will learn
Two processed images look close, but their pixels differ.
A practical question
Two restored versions of a photograph look nearly alike. How different are their pixel measurements from a chosen reference? Mean squared error gives one straightforward answer. For corresponding pixels, subtract one value from the other, square the difference, and average those squares.
The useful idea
Try just two pixel errors: two and four. Their squares are four and sixteen; their average is ten. Squaring makes a larger error contribute more strongly. But the number is only meaningful when the images have the same shape, alignment, channel interpretation, and numeric range.
Work through the example
Shift an otherwise identical image by one pixel and see how the error changes around its edges. The score can become large even though the scene content is nearly unchanged. Conversely, a small error averaged over a huge image may conceal one damaged scratch that matters to the inspection. Squaring errors changes how a score responds to an outlier. An error twice as large contributes four times as much squared error. That is useful to remember when a single damaged pixel or registration error dominates a comparison. Check that the two arrays line up before calculating. Show a crop of the largest error beside the mean value; otherwise a small average over a large image can hide damage exactly where an inspector cares most. Now check the idea on a concrete example: For pixel errors of two and four, their squares are four and sixteen; the mean squared error is ten. The answer follows from that evidence: Mean squared error averages squared pixel-by-pixel differences on aligned arrays. Shift a reference image by one pixel and calculate again. The resulting error can rise at edges even though the objects have not changed. That contrast makes the importance of alignment concrete.
Limits and next step
Report the range and reference used for the calculation, and inspect critical crops beside the score. Next, we'll turn this error into a logarithmic quality number and avoid treating it as a universal verdict.
Worked example
For errors of 2 and 4, the mean squared error is (4 + 16) / 2 = 10.
Quick check: test your understanding
Try it yourself: Consider this case: For errors of 2 and 4, the mean squared error is (4 + 16) / 2 = 10. Explain how you would check the result. In your answer, address this limitation: MSE does not tell where an error occurred or whether it matters perceptually.
Check the reasoning
Mean squared error averages squared pixel-by-pixel differences on aligned arrays. MSE does not tell where an error occurred or whether it matters perceptually.
What is the main idea behind calculate mean squared pixel error?
Mean squared error averages squared pixel-by-pixel differences on aligned arrays.
How is it used in the example?
For errors of 2 and 4, the mean squared error is (4 + 16) / 2 = 10.
What limitation should be checked?
MSE does not tell where an error occurred or whether it matters perceptually.
Further reading
Digital Image Processing, 4th edition — Rafael C. Gonzalez and Richard E. Woods.
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Accessible referenceLesson 73 transcript320 words · Narration ready for the upcoming videoOpen transcript
Two restored versions of a photograph look nearly alike. How different are their pixel measurements from a chosen reference? Mean squared error gives one straightforward answer. For corresponding pixels, subtract one value from the other, square the difference, and average those squares.
Try just two pixel errors: two and four. Their squares are four and sixteen; their average is ten. Squaring makes a larger error contribute more strongly. But the number is only meaningful when the images have the same shape, alignment, channel interpretation, and numeric range.
Shift an otherwise identical image by one pixel and see how the error changes around its edges. The score can become large even though the scene content is nearly unchanged. Conversely, a small error averaged over a huge image may conceal one damaged scratch that matters to the inspection. Squaring errors changes how a score responds to an outlier. An error twice as large contributes four times as much squared error. That is useful to remember when a single damaged pixel or registration error dominates a comparison. Check that the two arrays line up before calculating. Show a crop of the largest error beside the mean value; otherwise a small average over a large image can hide damage exactly where an inspector cares most. Now check the idea on a concrete example: For pixel errors of two and four, their squares are four and sixteen; the mean squared error is ten. The answer follows from that evidence: Mean squared error averages squared pixel-by-pixel differences on aligned arrays. Shift a reference image by one pixel and calculate again. The resulting error can rise at edges even though the objects have not changed. That contrast makes the importance of alignment concrete.
Report the range and reference used for the calculation, and inspect critical crops beside the score. Next, we'll turn this error into a logarithmic quality number and avoid treating it as a universal verdict.