Image Quality Assessment | Sahithyan's Notes

Image processing aims to reproduce a real-world scene at the same perceptual level as the original, not to judge artistic quality. Quality assessment measures how much an image has changed from its source state.

Sources of Change

Artefacts

Unwanted details from side-effects of capture, quantization and processing. Known ahead of time in most instances. Easy to estimate and quantify.

Noise

Unwanted details from internal or external sources, mostly from analog stages. Random in most instances, though it may follow a known probability model. Difficult to quantize and estimate.

Objective Assessment

Based on mathematical formulae comparing an image to a reference source. Independent of human judgment. May not align with artistic or perceptual judgment

\text{mean squared error} = \frac{1}{MN}\sum_{x=1}^{M}\sum_{y=1}^{N}(p(x,y) - r(x,y))^2

Here:

$M, N$: image dimensions
$p(x,y)$: pixel value in the processed image
$r(x,y)$: pixel value in the source image

A higher MSE means more change between the images, but this isn’t necessarily aligned with subjective quality. A restoration process, for instance, deliberately changes pixel values to improve perceived quality.

Size Independence

A sum of squared errors grows with the pixel count. MSE divides by $MN$ , so it is a per-pixel value and is comparable across image sizes.

\text{PSNR} = 10\log_{10}\frac{\text{MAX}^2}{\text{MSE}}

Here:

$\text{MAX}$: maximum possible pixel value

PSNR is relative to the dynamic range, so 8-bit and 16-bit images share one scale. SSIM compares local windows and averages the results over the image, so it is also independent of size.

Aligning Different Sizes

Full-reference metrics compare $p(x,y)$ with $r(x,y)$ pixel by pixel. Both images must have the same dimensions.

Resample to the reference size
Interpolation adds its own error. Use the same interpolation method for every process being compared.
Crop to the overlap
Register the images first when the geometry changed. Compare only the overlapping region.

For downscaling or compression pipelines, resample the output back to the source size before comparing.

No-Reference Metrics

Used when no source image exists. They score how far local patch statistics deviate from those of natural images, for example NIQE and BRISQUE. They work on any image size. They are less reliable than full-reference metrics.

Subjective Assessment

Based on human perception, expressed as a textual description of image quality.

Different observers may disagree. The same observer may disagree with themselves at different times.
Requires multiple assessments, from multiple subjects and images, to avoid bias
Needs a normalized rating scale

Each observer rates an image with a value from a scale. The ratings of all observers are averaged into a mean opinion score.

Goodness scale rates the overall quality of the image. A higher value is better.

Value	Description
5	Excellent
4	Good
3	Fair
2	Poor
1	Unsatisfactory

Impairment scale rates how visible and how annoying the degradation is. A higher value is worse, so it runs opposite to the goodness scale.

Value	Description
5	Extremely objectionable
4	Definitely objectionable
3	Impairment, but not objectionable
2	Just noticeable
1	Not noticeable

Worked Example

MSE and PSNR

An 8-bit image has squared errors $0$ , $4$ , $9$ and $1$ over a $2 \times 2$ region. Find its MSE and PSNR.

Solution Reveal Hide

\text{MSE} = \frac{0 + 4 + 9 + 1}{4} = 3.5

\text{PSNR} = 10\log_{10}\frac{255^2}{3.5} \approx 42.69\text{ dB}

The region has an MSE of $3.5$ and a PSNR of approximately $42.69\text{ dB}$ .