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What is the basic practical difference between CIE Lab and CIE Lch (aka HCL, right?) color models?

All I have found about them on Google is that they are two different ways to represent the same color space. But there are no explanations about why the two different ways are necessary at all, and there are also no examples to see where one model is better than another.

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This direct screenshot from Wikipedia shows the conversion between Lab and HCL.

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HCL is only for convenience, it doesn't change the color space (except in case the numbers are limited to sparse integer values)

What convenience?

For ex. I like to use HCL version because I can imagine the color changes more easily beforehand by adjusting hue and chroma of HCL. Trying to guess how to change a and b in Photoshop's Lab system for a wanted change is much more trial and error than using HCL which is available in GIMP.

Fortunately in Photoshop I can also adjust hue and chroma. The hue/saturation adjustment works with hue and chroma in Lab mode, but the colors are in the color picker shown as Lab-numbers.

I prefer HCL over Lab if I can choose because the bones of my head are too thick for intuitive handling of Lab-numbers. But there exists people who have things differently. See for ex this old case:

Is there a way to remove lens flare?

Hopefully you have already noticed that Lab and HCL are made to present the colors which humans can see so that the luminance, chroma and hue are visually separated from each other. Actually in Lab hue and chroma are mangled together in a and b, but L is independent.

RGB and its polar variations (which are made also for covenience) present commands for colored light production machinery in computer screens and what RGB sensors in a camera output. The visual effect of the saturation in polar RGB systems like Photoshop's HSB depends drastically on hue and brightness. In HCL the factors are much more visually independent. That has an unfortunate consequence: It's far too easy to select in Lab or HCL a color which cannot be produced in RGB screens. Fortunately the programs have options to switch out of gamut warning ON.

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    One could also add that HCL sort of is to Lab what HSB/HSV is to RGB.
    – Wolff
    Dec 6, 2021 at 17:19
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    Both of them may be available when you tweak colors in programs, but someone can tell to you a color in Lab or you must tell the color in Lab. That's nothing neverbeforeheard, because Lab tells something of the visual look of a colored material, not what a computer does. HCL, of course does the same, but I have never seen the colors of materials told in HCL
    – user82991
    Dec 6, 2021 at 18:03
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    @johnc.j. the axes of Lab coincide with how the adversarial nature of human senses work. By working in Lab its easier to boost certain aspects and deal with colorblindness issues. You can easily do this with curves in Lab but not curves in LCH. On the otherhand Lch is better at picking colors for certain uses.
    – joojaa
    Dec 6, 2021 at 21:57
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    I guess you can regard HCL and HSB as tools for selecting colors in Lab and RGB. Not color modes in their own right.
    – Wolff
    Dec 6, 2021 at 22:27
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    @johnc.j. User Wolff presented it as a guess, but what he wrote above is a perfect fact. HCL is a color numbering method in Lab color system and HSB is the same in RGB system. HCL and HSB are developed for more intuitive color adjustments and selections.
    – user82991
    Dec 7, 2021 at 0:01
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Short Answer:

It's only a difference of coordinates.

CIELAB uses cartesian coordinates, that is, xyz-type coordinates. LCh is only a conversion from cartesian coordinates to polar coordinates, but the underlying color model is the same.

Longer Answer

The 1931 CIE "standard observer" is a device independent "virtual eye" that is based on studies of human perception of color. The related color space is the XYZ space, which uses cartesian coordinates and is essentially linear in regards to light in the real world.

Human Perception

Human perception of light is not linear as light exists in the real world. In an effort to create a model that was perceptually uniform, meaning linear to perception as opposed to light, in 1976 the CIE released CIELAB

Cartesian

CIELAB is defined as cartesian coordinates in a euclidian space, i.e. xyz coordinates. However, as there are other color spaces referred to as XYZ and xyY, LAB uses L* for perceptual lightness (100) to darkness(0), a± for red/green opponent colors and b± for yellow/blue opponent colors.

  • L* is perceptual lightness, from 0 (black) to full white (100).
    • It is a perception and not a measure of light (i.e. it is not luminance, it is the perception of luminance).
  • positive a* values are redder, negative a* values are greener
  • positive b* values are yellower, negative b* values are bluer

Polar

LCh is only a conversion from the L*a*b* cartesian coordinates to polar coordinates, wherein the L* values remains exactly the same, but the a*b* coordinates are converted to a hue and a colorfulness (chroma) correlate.

  • hue is a value from 0° to 360° (361° = 1°)
  • Chroma is a value from 0 (achromatic grey) to over 133 (for sRGB blue).

It should be noted that CIELAB is not truly perceptually uniform, but is substantially more uniform than RGB or HSB/HSV/HSL etc.

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