image-compare

Simple image comparison in rust based on the image crate

Note that this crate is still work in progress. Algorithms are not cross-checked. Everything is implemented in plain CPU with rayon multithreading and seems to perform just fine on modern processors. Neither memory optimizations nor SIMD seemed to provide any remarkable improvement.

Supported now:

• Comparing grayscale and rgb images by structure
  • By RMS - score is calculated by: $1-\sqrt{\frac{\sum_{x,y=0}^{x,y=w,h}\left(f(x,y)-g(x,y)\right)^2}{w*h}}$
  • By MSSIM
    • SSIM is implemented as described on wikipedia: $\mathrm{SSIM}(x,y)={\frac{(2\mu_{x}\mu_{y}+c_{1})(2\sigma_{xy}+c_{2})}{(\mu_{x}^{2}+\mu_{y}^{2}+c_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+c_{2})}}$
    • MSSIM is calculated by using 8x8 pixel windows for SSIM and averaging over the results
  • RGB type images are split to R,G and B channels and processed separately.
    • The worst of the color results is propagated as score but a float-typed RGB image provides access to all values.
    • As you can see in the gherkin tests this result is not worth it currently, as it takes a lot more time
    • It could be improved, by not just propagating the individual color-score results but using the worst for each pixel
    • This approach is implemented in hybrid-mode, see below
  • "Hybrid Comparison"
    • Splitting the image to YUV colorspace according to T.871
    • Processing the Y channel with MSSIM
    • Comparing U and V channels via RMS
    • Recombining the differences to a nice visualization image
    • RGB Score is calculated as: $\mathrm{score}=\mathrm{avg}_{x,y}\left(\mathrm{min}\left[\Delta \mathrm{MSSIM}(Y,x,y),\sqrt{(\Delta RMS(U,x,y))^2 + (\Delta RMS(V,x,y))^2}\right]\right)$
    • For RGBA the $\alpha$ channel is also compared using MSSIM and taken into account.
    • The average alpha of each pixel $\bar{\alpha}(x,y) = 1/2 (\alpha_1(x,y) + \alpha_2(x,y))$ is then used as a linear weighting factor
    • RGBA Score is calculated as: $\mathrm{score}=\mathrm{avg}_{x,y}\left(1/\bar{\alpha} \cdot \mathrm{min}\left[\Delta \mathrm{MSSIM}(Y,x,y),\sqrt{(\Delta RMS(U,x,y))^2 + (\Delta RMS(V,x,y))^2}, \Delta \mathrm{MSSIM}(\alpha,x,y)\right]\right)$
    • Edge cases RGBA: $\mathrm{score} \in (0, 1)$ and $\mathrm{score} = 1.0$ if $\bar{\alpha} = 0.0$
    • This allows for a good separation of color differences and structure differences for both RGB and RGBA
    • Interpretation of the diff-images:
      • RGB: Red contains structure differences, Green and Blue the color differences, the more color, the higher the diff
      • RGBA: Same as RGB but alpha contains the inverse of the alpha-diffs. If something is heavily translucent, the alpha was so different, that differentiating between color and structure difference would be difficult. Also, minimum alpha is clamped at 0.1, so you can still see all changes.
• Comparing grayscale images by histogram
  • Several distance metrics implemented see OpenCV docs:
    • Correlation $d(H_1,H_2) = \frac{\sum_I (H_1(I) - \bar{H_1}) (H_2(I) - \bar{H_2})}{\sqrt{\sum_I(H_1(I) - \bar{H_1})^2 \sum_I(H_2(I) - \bar{H_2})^2}}$
    • Chi-Square $d(H_1,H_2) = \sum _I \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)}$
    • Intersection $d(H_1,H_2) = \sum _I \min (H_1(I), H_2(I))$
    • Hellinger distance $d(H_1,H_2) = \sqrt{1 - \frac{1}{\sqrt{\int{H_1} \int{H_2}}} \sum_I \sqrt{H_1(I) \cdot H_2(I)}}$

Changelog: 0.3.0:

• An error was found in hybrid RGB compare in 0.2.x that over-weighted color differences. Numbers in tests were adjusted
  • Influence was very small for most images but noticeable for the color-filtered one which yields much higher similarity now
• Added an idea for RGBA comparison
• Added GitHub inline latex for equations instead of embedded images - fixes dark theme rendering