Image quality metrics for restricted gamut images produced by laser-induced printing on plasmonic films | Journal of the European Optical Society-Rapid Publications

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Table 2

List of the twenty metrics considered.

Designation	Metrics	Definition
M1	Normalized density	$M 1 = \sum_{s = 0}^{35} \| p_{s}^{(i)} - p_{s}^{(g)} \| .$ $M1=\sum_{s=0}^{35}\left\|{p}_s^{(i)}-{p}_s^{(g)}\right\|.$ Where $p_{s}^{(i)}$ ${p}_s^{(i)}$ is the proportion of pixels in the original image that belong to the hue sector s of the CIE LCh* color space. The hue sector s contains the points whose hue is between 10s and 10(s + 1). $p_{s}^{(g)}$ ${p}_s^{(g)}$ is the proportion for the gamut p.
M2	Maximum luminance [16]	Difference between the highest luminance value in the palette and the highest luminance value in the image in absolute value.
M3	Minimum luminance	Difference between the lowest luminance value in the gamut and the lowest luminance value in the image in absolute value.
M4	Delta luminance	Difference between the highest and the lowest luminance values in the gamut. This value is independent of the image.
M5	Maximum chroma [16]	$M 5 = \sum_{s = 1}^{6} \| {\max (C)}_{s}^{(i)} - {\max (C)}_{s}^{(g)} \| .$ $M5=\sum_{s=1}^6\left\|{\mathrm{max}\left(\mathrm{C}\right)}_s^{(i)}-{\mathrm{max}\left({C}\right)}_s^{(g)}\right\|.$ Here the sectors are chosen to be: s = 1 for h ∈ [−10, 40[(red color), s = 2 for h ∈ [40, 75[(orange color), s = 3 for h ∈ [75, 100[(yellow color), s = 4 for h ∈ [100, 200[(green color), s = 5 for h ∈ [200, 290[(blue color) and s = 6 for h ∈ [290, 350[(purple color).
M6	Minimum chroma	Same as M5 but with the difference of minimum chroma in each sector for the image and the gamut.
M7	Average chroma	Same as M5 but with the average chroma value rather than the maximum chroma value.
M8	Standard deviation of chroma	Same as M5 but with the difference of the standard deviation values of the chroma.
M9	Convex hull area of ab [21]	Convex hull area of the gamut when projected on the ab plane. This value is independent of the image.
M10	Image center of mass	Euclidian distance in Lab* space between the barycenter of the ensembles of color points present in the gamut and image.
M11	Image colorfulness [34]	Ratio of the computed Hasler colorfulness of the simulated image and the Hasler colorfulness of the original image.
M12	Image complexity [38]	The complexity of the pattern within the image using the average spatial frequency of the image.
M13	Capacity to infer colors from the semantic content of the image	1 if the content of the image gives a lot of information on the expected image (e.g. color of the tree leaves, …), 0 otherwise.
M14	Pixel delta RGB volume	For all pixels of the original and simulated images, the difference of the red, green and blue channels is calculated. All these differences can be plotted in a “RGB difference” solid whose convex hull has a volume that can be calculated.
M15	Pixel delta Lab* volume	Same but the pixel differences are calculated in L, a, b*.
M16	Distance of the white point selected to the image gamut [39]	Distance between the white point selected and the center of mass of the image gamut.
M17	Gamut centers hue difference	Difference of hue values between the center of mass of the image gamut and the center of mass of palette gamut.
SSIM	Structure Similarity Index Measure	Comparison image structures, luminance, and contrast to assess visual similarity.
MSE	Mean Square Error	Measures the average squared difference between original and reproduction images as the mean squared difference (done on each channel here).
PSNR	Peak Signal to Noise Ratio	Measures the average squared difference between original and reproduction images.

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