Hellwig JMh
The Hellwig JMh color space is not registered in Color by default
Properties
Name: hellwig-jmh
White Point: D65 / 2˚
Coordinates:
| Name | Range* |
|---|---|
j | [0, 100] |
m | [0, 105] |
h | [0, 360) |
* Space is not bound to the range and is only used as a reference to define percentage inputs/outputs in relation to the Display P3 color space.
Figure 1. The sRGB gamut represented within the Hellwig JMh color space.
The Hellwig color model is an unofficial name for the CAM16 model with applied "fixes" as published by Luke Hellwig and Mark Fairchild entitled 'Brightness, lightness, colorfulness, and chroma in CIECAM02 and CAM16'. The paper suggests a number of changes to the brightness and lightness properties changing their non-linear relationship to a linear relationship. It also details a reevaluation of chroma, colorfulness, and saturation making some suggestions additional changes.
The model defines numerous different attributes:
| Name | Description |
|---|---|
| J | Lightness |
| C | Chroma |
| h | hue |
| s | saturation |
| Q | Brightness |
| M | Colorfulness |
| H | Hue Quadrature |
A color space can be constructed of using a subset of these attributes: JCh, JMh, Jsh, QCh, QMh, Qsh, etc. You can also construct Lab like spaces taking using the hue and either C, M, or s. The hellwig-jmh color space in ColorAide represents the JMh configuration.
Adjustments for Helmholtz–Kohlrausch Effect
The Hellwig H-K JMh color space is not registered in Color by default
Properties
Name: hellwig-hk-jmh
White Point: D65 / 2˚
Coordinates:
| Name | Range* |
|---|---|
j | [0.0, ~101.560] |
m | [0, 105] |
h | [0, 360) |
* Space is not bound to the range and is only used as a reference to define percentage inputs/outputs in relation to the Display P3 color space.
Figure 2. The sRGB gamut represented within the Hellwig H-K JMh color space.
The Helmholtz–Kohlrausch effect (after Hermann von Helmholtz and V. A. Kohlrausch) is a perceptual phenomenon wherein the intense saturation of spectral hue is perceived as part of the color's luminance. This creates a hue and chroma dependency that affects lightness and brightness.
After the initial paper describing the Hellwig corrections, Luke Hellwig, Dale Stolitzka, and Mark Fairchild published another paper that modified lightness and brightness further to better represent the Helmholtz–Kohlrausch effect in the CAM16 model.
The paper entitled 'Extending CIECAM02 and CAM16 for the Helmholtz–Kohlrausch effect' outlined additional changes to the lightness and brightness calculations of CAM16 and CIECAM02 that allowed the models to better simulate the Helmholtz–Kohlrausch effect. These changes are required to made on top of the original modifications of brightness and lightness as described by in the first Hellwig paper.
Viewing Conditions
Hellwig is a color appearance model and can be configured with different viewing environments. A Hellwig color space will also have an associated environment object. This environment object determines the viewing conditions. Colors will appear different based on the viewing conditions.
| Viewing Conditions | Description |
|---|---|
| White | This is the white point and should be the same as defined in the color class. This is provided as (x, y) chromaticity coordinates. |
| Adapting Luminance | The luminance of the adapting field (La). The units are in cd/m2. |
| Background Luminance | The background luminance (Yb) the relative luminance of the nearby background (out to 10°), relative to the reference white's luminance (Y). Usually 20 providing a gray world assumption. |
| Surround | A description of the peripheral area. Use "dark" for a movie theater, "dim" for e.g. viewing a bright television in a dimly lit room, or "average" for surface colors. |
| Discounting | Discounts the illuminant. If true, the eye is assumed to be fully adapted to the illuminant. Otherwise, the degree of discounting is based on other parameters. When the eye is not fully adapted, it can affect the way colors appear and the chromatic response. |
| Helmholtz–Kohlrausch effect | If true, account for the Helmholtz–Kohlrausch effect by further adjusting lightness and brightness. |
ColorAide must provide some defaults, so Hellwig comes with a default set of viewing conditions that uses a D65 white point, an adapting luminance of 64 lux or a value of ~4 cd/m2, it uses the "gray world" assumption and sets the background to 20, an "average" surround and leaves discounting set to False. The Helmholtz–Kohlrausch effect handling is only enabled for the hellwig-hk-jmh variant.
The default settings do not have to be used and a new Hellwig variant with different viewing conditions can be created. When doing this, the space should be derived from the default.
>>> from coloraide import Color as Base
>>> from coloraide.spaces.hellwig import HellwigJMh, Environment
>>> from coloraide.cat import WHITES
>>> from coloraide import util
>>> import math
>>> class CustomHellwigJMh(HellwigJMh):
... NAME = "hellwig-custom"
... SERIALIZE = ("--hellwig-custom",)
... WHITE = WHITES['2deg']['D65']
... ENV = Environment(
... white=WHITE,
... adapting_luminance=1000 / math.pi,
... background_luminance=20,
... surround='average',
... discounting=False,
... hk=False
... )
...
>>> class Color(Base): ...
...
>>> Color.register([HellwigJMh(), CustomHellwigJMh()])
>>> Color('white').convert('hellwig-jmh')
color(--hellwig-jmh 100 1.0387 209.53 / 1)
>>> Color('white').convert('hellwig-custom')
color(--hellwig-custom 100 0.0606 209.66 / 1)
Note
It can be noted in the above example that white does not have the typical zero chroma. This is because the eye is not assumed as being fully adapted to the environment. Due to the environment, the colors considered achromatic may appear differently.
If discounting was enabled, the eye is then assumed to be fully adapted, and achromatic colors would align better with expectations in other color spaces.
Channel Aliases
| Channels | Aliases |
|---|---|
j | lightness |
m | colorfulness |
h | hue |
Input/Output
The Hellwig JMh space is not currently supported in the CSS spec, the parsed input and string output formats use the color() function format using the custom name --hellwig-jmh. When adjustments for the Helmholtz–Kohlrausch effect are enabled, the custom name --hellwig-hk-jmh is used.
color(--hellwig-jmh j m h / a) // Color function
color(--hellwig-hk-jmh j m h / a) // Color function
The string representation of the color object and the default string output use the color(--hellwig-jmh j m h / a) form. If using the H-K variant, color(--hellwig--hk-jmh j m h / a) is used.
>>> Color("hellwig-jmh", [46.026, 47.347, 27.393], 1)
color(--hellwig-jmh 46.026 47.347 27.393 / 1)
>>> Color("hellwig-jmh", [68.056, 31.228, 71.293], 1).to_string()
'color(--hellwig-jmh 68.056 31.228 71.293)'
>>> Color("hellwig-hk-jmh", [97.726, 33.735, 111.15], 1)
color(--hellwig-hk-jmh 97.726 33.735 111.15 / 1)
>>> Color("hellwig-hk-jmh", [39.201, 27.019, 142.3], 1).to_string()
'color(--hellwig-hk-jmh 39.201 27.019 142.3)'
Registering
Either Hellwig JMh, Hellwig H-K JMh, or both can be registered.
from coloraide import Color as Base
from coloraide.spaces.hellwig import HellwigJMh, HellwigHKJMh
class Color(Base): ...
Color.register([HellwigJMh(), HellwigHKJMh()])