colour.appearance.atd95 Module¶

ATD (1995) Colour Vision Model¶

Defines ATD (1995) colour vision model objects:

ATD95_Specification
XYZ_to_ATD95()

Notes

According to CIE TC1-34 definition of a colour appearance model, the ATD95 model cannot be considered as a colour appearance model. It was developed with different aims and is described as a model of colour vision.

References

[1]	Mark D. Fairchild, Color Appearance Models, 3nd Edition, The Wiley-IS&T Series in Imaging Science and Technology, published June 2013, ASIN: B00DAYO8E2, Locations 5841-5991.

[2]	S. Lee Guth, Further applications of the ATD model for color vision, IS&T/SPIE’s Symposium on Electronic Imaging: Science & Technology, International Society for Optics and Photonics, pages 12-26, DOI: https://doi.org/10.1117/12.206546

class colour.appearance.atd95.ATD95_ReferenceSpecification[source]¶

Bases: colour.appearance.atd95.ATD95_ReferenceSpecification

Defines the ATD (1995) colour vision model reference specification.

This specification has field names consistent with Mark D. Fairchild reference.

Parameters:

Parameters:	H (numeric) – Hue angle $H$ in degrees. C (numeric) – Correlate of saturation $C$ . Guth (1995) incorrectly uses the terms saturation and chroma interchangeably. However, $C$ is here a measure of saturation rather than chroma since it is measured relative to the achromatic response for the stimulus rather than that of a similarly illuminated white. Br (numeric) – Correlate of brightness $Br$ . A_1 (numeric) – First stage $A_1$ response. T_1 (numeric) – First stage $T_1$ response. D_1 (numeric) – First stage $D_1$ response. A_2 (numeric) – Second stage $A_2$ response. T_2 (numeric) – Second stage $A_2$ response. D_2 (numeric) – Second stage $D_2$ response.

H (numeric) – Hue angle $H$ in degrees.
C (numeric) – Correlate of saturation $C$ . Guth (1995) incorrectly uses the terms saturation and chroma interchangeably. However, $C$ is here a measure of saturation rather than chroma since it is measured relative to the achromatic response for the stimulus rather than that of a similarly illuminated white.
Br (numeric) – Correlate of brightness $Br$ .
A_1 (numeric) – First stage $A_1$ response.
T_1 (numeric) – First stage $T_1$ response.
D_1 (numeric) – First stage $D_1$ response.
A_2 (numeric) – Second stage $A_2$ response.
T_2 (numeric) – Second stage $A_2$ response.
D_2 (numeric) – Second stage $D_2$ response.

class colour.appearance.atd95.ATD95_Specification[source]¶

Bases: colour.appearance.atd95.ATD95_Specification

Defines the ATD (1995) colour vision model specification.

This specification has field names consistent with the remaining colour appearance models in colour.appearance but diverge from Mark D. Fairchild reference.

Notes

This specification is the one used in the current model implementation.

Parameters:

Parameters:	h (numeric) – Hue angle $H$ in degrees. C (numeric) – Correlate of saturation $C$ . Guth (1995) incorrectly uses the terms saturation and chroma interchangeably. However, $C$ is here a measure of saturation rather than chroma since it is measured relative to the achromatic response for the stimulus rather than that of a similarly illuminated white. Q (numeric) – Correlate of brightness $Br$ . A_1 (numeric) – First stage $A_1$ response. T_1 (numeric) – First stage $T_1$ response. D_1 (numeric) – First stage $D_1$ response. A_2 (numeric) – Second stage $A_2$ response. T_2 (numeric) – Second stage $A_2$ response. D_2 (numeric) – Second stage $D_2$ response.

h (numeric) – Hue angle $H$ in degrees.
C (numeric) – Correlate of saturation $C$ . Guth (1995) incorrectly uses the terms saturation and chroma interchangeably. However, $C$ is here a measure of saturation rather than chroma since it is measured relative to the achromatic response for the stimulus rather than that of a similarly illuminated white.
Q (numeric) – Correlate of brightness $Br$ .
A_1 (numeric) – First stage $A_1$ response.
T_1 (numeric) – First stage $T_1$ response.
D_1 (numeric) – First stage $D_1$ response.
A_2 (numeric) – Second stage $A_2$ response.
T_2 (numeric) – Second stage $A_2$ response.
D_2 (numeric) – Second stage $D_2$ response.

colour.appearance.atd95.XYZ_to_ATD95(XYZ, XYZ_0, Y_0, k_1, k_2, sigma=300)[source]¶

Computes the ATD (1995) colour vision model correlates.

Parameters:	XYZ (array_like, (3,)) – CIE XYZ colourspace matrix of test sample / stimulus in domain [0, 100]. XYZ_0 (array_like, (3,)) – CIE XYZ colourspace matrix of reference white in domain [0, 100]. Y_0 (numeric) – Absolute adapting field luminance in $cd/m^2$ . k_1 (numeric) – Application specific weight $k_1$ . k_2 (numeric) – Application specific weight $k_2$ . sigma (numeric, optional) – Constant $\sigma$ varied to predict different types of data.
Returns:	ATD (1995) colour vision model specification.
Return type:	ATD95_Specification

Warning

The input domain of that definition is non standard!

Notes

Input CIE XYZ colourspace matrix is in domain [0, 100].
Input CIE XYZ_0 colourspace matrix is in domain [0, 100].
For unrelated colors, there is only self-adaptation, and $k_1$ is set to 1.0 while $k_2$ is set to 0.0. For related colors such as typical colorimetric applications, $k_1$ is set to 0.0 and $k_2$ is set to a value between 15 and 50 Guth (1995).

Examples

>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_0 = np.array([95.05, 100.00, 108.88])
>>> Y_0 = 318.31
>>> k_1 = 0.0
>>> k_2 = 50.0
>>> XYZ_to_ATD95(XYZ, XYZ_0, Y_0, k_1, k_2)  
ATD95_Specification(h=1.9089869..., C=1.2064060..., Q=0.1814003..., A_1=0.1787931... T_1=0.0286942..., D_1=0.0107584..., A_2=0.0192182..., T_2=0.0205377..., D_2=0.0107584...)

colour.appearance.atd95.luminance_to_retinal_illuminance(XYZ, absolute_adapting_field_luminance)[source]¶

Converts from luminance in $cd/m^2$ to retinal illuminance in trolands.

Parameters:	XYZ (array_like, (3,)) – CIE XYZ colourspace matrix. absolute_adapting_field_luminance (numeric) – Absolute adapting field luminance in $cd/m^2$ .
Returns:	Converted CIE XYZ colourspace matrix in trolands.
Return type:	ndarray

Examples

>>> XYZ = np.array([19.01, 20., 21.78])
>>> Y_0 = 318.31
>>> luminance_to_retinal_illuminance(XYZ, Y_0)  
array([ 479.4445924...,  499.3174313...,  534.5631673...])

colour.appearance.atd95.XYZ_to_LMS_ATD95(XYZ)[source]¶

Converts from CIE XYZ colourspace to LMS cone responses.

Parameters:	XYZ (array_like, (3,)) – CIE XYZ colourspace matrix.
Returns:	LMS cone responses.
Return type:	ndarray, (3,)

Examples

>>> XYZ = np.array([19.01, 20., 21.78])
>>> Y_0 = 318.31
>>> luminance_to_retinal_illuminance(XYZ, Y_0)  
array([ 479.4445924...,  499.3174313...,  534.5631673...])

colour.appearance.atd95.opponent_colour_dimensions(LMS_g)[source]¶

Returns opponent colour dimensions from given post adaptation cone signals matrix.

Parameters:	LMS_g (array_like, (3,)) – Post adaptation cone signals matrix.
Returns:	Opponent colour dimensions.
Return type:	tuple

Examples

>>> from pprint import pprint
>>> LMS_g = np.array([6.95457922, 7.08945043, 6.44069316])
>>> pprint(opponent_colour_dimensions(LMS_g))  
(0.1787931...,
 0.0286942...,
 0.0107584...,
 0.0192182...,
 0.0205377...,
 0.0107584...)

colour.appearance.atd95.final_response(value)[source]¶

Returns the final response of given opponent colour dimension.

Parameters:	value (numeric) – Opponent colour dimension.
Returns:	Final response of opponent colour dimension.
Return type:	numeric

Examples

>>> final_response(43.54399695501678)  
0.1787931...