Color space and the illusion of color

Just as the universe is not bound to the human construct of three dimensions, the universe does not have color. As Peter Gouras states in "Webvision: The organization of the Retina and Visual System":

"Color vision is an illusion created by the interactions of billions of neurons in our brain. There is no color in the external world; it is created by neural programs and projected onto the outer world we see. It is intimately linked to the perception of form where color facilitates detecting borders of objects."

Cones do not see color. Cone opsins merely respond to the chemical reaction of the chromophore pigment. To call the cones red, green, and blue is actually a misnomer. While not completely accurate, the terms Long, Medium, and Short (LMS) are better. The reality is that the three different types of cones respond to three different ranges of wavelengths. This information is relayed via the optic nerve bundle to the left and right visual corti. Information from the left side of the retina goes to the left visual cortex. Conversely, information from the right side of the retina goes to the right cortex. The visual corti assemble the color image.

What are the wavelength ranges for each cone type? It varies depending on the study, and the methodology used to measure the wavelength and sensitivity. While the following diagram appears in a number of color vision articles, the source of the associated study is not given:

A 1995 study by Williams & Cummins show the following wavelength ranges:

Just think, 12% of women are tetrachromatic, but with a different wavelengths for the fourth cone type. The following diagram is from The Neurosphere:

Since a very small percentage of women have a distinctly different curve for the fourth cone type, we can safely use trichromacy for the general population.

As we look at the wavelength curves for each cone type, we can see that the names red, green, and blue are misnomers. The peak receptivity for the Long (red) wavelength cone is closer to yellow than it is to red. The green cone has a peak sensitivity in the dark green wavelengths, while the peak sensitivity for the blue  is closer to violet. The trap is using color models, such as RGB, to define CVD.

Simulation of CVD requires the use of models that reflect the color space of the human eye, or the LMS color space. in 1931, the International Commission on Illumination (CIE) created one of the first mathematical models of the human color space (CIE 1931 color space). This is known as the CIE XYZ color space and is based on the experiments done by William David Wright and John Guild in the late 1920s. Their experiments resulted in the CIE RGB color space. The CIE XYZ color space is a derivative of the CIE RGB color space. The Y component is the luminance. The Z component is quasi-equal to the S cone response, while the X component is a linear combination cone response curves chosen to be non-negative. For any given Y (luminance), the XZ plane will provide all chromaticities at that luminance. It is important to remember that the perceived color depends on the luminance.

From the CIE XYZ color space there are transforms to the LMS color space. Given the complex nature of human color vision, there is not a universally accepted transform. Instead, Chromatic Appearance Models (CAMs) provide Chromatic Adaptation Transform (CAT) matrices. These matrices (M) are the basis of modern simulation models.

The following is a brief summary of the common CAMs. If you are interested in reviewing the actual CAT matrices, you can find them in LMS color space.

1. CIELAB
   It wasn't until 1976 that CIE released a CAM to replace the many existing, and incompatible, color difference models. CIELAB became the first color appearance model, and became one of the most widely used models. The major weakness of CIELAB is that it performs the von Kries transform before converting to LMS color space. The LLAB CAM was released to correct this error.
2. Hunt and RLAB CAMs
   Both the Hunt and RLAB CAMs use the Hunt-Pointer-Esteves transformation matrix. Since this matrix was originally used von Kries transform method, it  is also known as the von Kries transform matrix.
3. CIECAM97s and LLAB CAMs
   Both the CIECAM97s and the LLAB CAMs use the Bradford transformation matrix. With the Bradford transformation matrix, the L and M cone curves are narrower. The narrower curves create a "spectrally sharpened" transformation matrix. The Bradford transformation matrix is also used with the linear von Kries method. There is also a revised CIECAM97s CAM that uses a linear transformation matrix.
4. CIECAM02
   Released in 2002, the CIECAM02 CAM is a replacement to CIECAM97s. CIECAM02 has better performance and is easier to implement than CIECAM97s. CIECAMO2 comes close to being an internationally agreed upon standard for a comprehensive color appearance model.
5. ICAM
   Also released in 2002, ICAM was developed by Mark D. Fairchild and Garrett M. Johnson. The goals included simple implementation for images, handling of HDR images, and tone mapping.

The CIE XYZ color space is a virtual space that acts as a reference model for color models. Color models are the subject of the next two articles in this series. These articles provide the necessary background for understanding CVD simulation models, which will be the last article of this series.

Color is an illusion, but it is a fascinating illusion.