HunterLab is similar to Cie-L*ab. Both are based on Xyz but HunterLab's color coordinates are based around a square root transformation rather than a cube.
Hsl is a cylindrical-coordinate representation of the Rgb color model. This representation rearranges the colors in an attempt to be more intuitive and perceptually relevant than the typical Rgb representation. It's frequently used for computer graphics applications like color pickers and image analysis.
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Color conversions performed using the open source ColorMine library.