Despite technological developments, the colour vision mechanism of converting physical colours into psychological colours remains not clear enough. To fill this void, Chenguang Lu, Associate Professor at Changsha University, has developed the decoding model. Compared with other colour vision zone models, the decoding model can explain colour evolution, colour blindness, and the opponent-process more intuitively. Moreover, it can be applied to colour transformations in computer graphics.
Colour perception has long been a topic of scientific interest. Despite vast technological developments, the colour vision mechanism of converting physical colours into psychological colours remains not clear enough. Solutions to this conundrum would help us understand colour vision and benefit industries including materials (textiles, plastics, etc.), lighting and colour imaging.
A widely accepted theory of colour vision is that colour signals exist in tri-pigments in the zone of visual cones (photoreceptor cells in the retina) and opponent signals (produced by ganglion cells encoding the colour) in the visual nerves’ zone. This theory underpins mathematical models known as zone models. Unfortunately, zone models to date do not easily reveal why colour signals are processed in this way. Furthermore, they do not demonstrate how colour vision has been evolving, nor why different kinds of colour blindness exist. To bridge these knowledge gaps, Chenguang Lu, Associate Professor in the School of Computer Engineering and Applied Mathematics at Changsha University, China, has developed the decoding model, a new version of the zone model. Lu uses his decoding model of colour vision to explain both colour evolution and colour blindness.
Fig. 1: Two zone models get +Red/-Green in different ways, but both use colour components’ addition for yellow: R+G=Y or M+L= Y.
Classical theories of colour vision
The classical theories of the mechanism of colour vision are based on Young and Helmholtz’s trichromatic (or tri-pigment) theory and Herring’s opponent theory. The trichromatic theory affirms that human visual cones receive three primary colour signals (red, green, and blue), which the human brain then decodes into many mental colours. This theory is particularly applicable to computer graphics.
The colour theory underpinning the opponent-process asserts that the human retina produces three pairs of psychological colours, or signals, red-green, blue-yellow, and white-black. This is a better explanation for the negative afterimage phenomenon – that is when the colours you see are inverted from the original, for example if you stare at a red image for a long period of time you will see a green (or cyan) afterimage on a white wall.
“The main reasons behind this problem lie with the existing zone models being asymmetrical and employing colour components’ arithmetic operations.”
Zone models (see fig. 1) combining both theories are widely accepted. In zone models, shortwave, mediumwave, and longwave (S, M, L), or blue, green and red (B, G, R), denote the trichromatic signals. These models advocate that colour signals exist both in trichromatic signals in the cones’ zone, and as opponent pairs in the optic nerve zone between ganglion cells (the projection, or final output, neurons of the vertebrate retina) and the cortex.
Fig. 2: The decoding model first obtains the medium one, M, and then gets three pairs of opponent colours by B, G and R minus M, respectively.
The zone models’ problem
The problem with the current zone models, Lu explains, is in how to convert (B, G, R) or (S, M, L) into three or four pairs of opponent colours and then further into hue, saturation (where white light is combined with a hue), and brightness. Many versions of the zone model have been developed by researchers to date, but not one is suitable for computer graphics’ colour transformations.
Lu believes that the main reasons behind this problem lie with the existing zone models being asymmetrical and employing arithmetic operations so that even if we add some coefficients to them, it is still difficult to obtain a cylindrical colour system with hue, saturation, and brightness. Colour addition should actually be colour vectors’ addition and not the component addition. For example, where the current models use arithmetic operations to add red and green to get yellow, i.e. R+G=Y, they should actually be using vector addition e.g. (0, 0, R)+(0, G, 0)=(0, G, R), which contains yellow, but does not appear yellow, to achieve this purpose. For example, (0, 0.5, 1)=0.5(0, 1, 1)+ 0.5(0, 0, 1) contains 0.5 yellow and 0.5 red and hence is 1 orange instead of 1.5 yellow. Furthermore, he proposes that three pairs of chromatic colours (red-cyan, green-magenta, and blue-yellow) are required with symmetry, instead of the zone models’ two pairs (red-green and blue-yellow).
Fig. 3: The evolution of colour vision.
The decoding model
To solve the problem, Lu has created the decoding model (see fig. 2), a symmetrical zone model of colour vision mechanism, uniting trichromatic theory with opponent theory. Using fuzzy logic, compatible with Boolean Algebra, the decoding model explains the colour vision mechanism as a fuzzy 3-8 decoder, similar to the 3-8 decoder used in electrical circuits that selects one from eight addresses. This novel zone model is symmetrical. Unlike previous asymmetrical zone models employing arithmetic operations with many coefficients, Lu’s model uses analog, or fuzzy, logic operations without any coefficient. The decoding model can explain colour evolution, colour blindness, and the opponent-process more intuitively than other zone models. Moreover, it is more applicable to the colour transformations in computer graphics.
Explaining colour evolution
The decoding model can easily explain the evolution of colour vision by splitting the spectral sensitivity curves of visual cones (see fig.3). If we envisage the red and green curves slowly coming together to form a yellow curve, the red, green, cyan, and magenta fields will gradually disappear. Then, if we imagine the blue and yellow curves gradually approaching one another to form a white curve, the blue and yellow fields will also disappear gradually, leaving only the black and white fields. Reversing this procedure explains the evolution of colour vision. Initially, the human retina had only one kind of visual cones that could only discern two totally different colours, black and white. Then, with the evolution of colour vision, the cones split into two kinds with different spectral sensitivities which meant that that blue and yellow were also perceived. Subsequently, the cones split into three kinds and more colours were perceived.
Fig. 4: Different kinds of colour blindness can be described by incomplete separations of the three sensitive curves.
Explaining colour blindness
The decoding model shows that different kinds of colour blindness can be described by incomplete separations of the three sensitive curves (see fig. 4). Monochromatism can be explained under the assumption that the blue, green and red sensitivity curves have not yet separated from a single curve. Red-green blindness can be explained under the assumption that the R-curve and the G-curve have not yet separated from one curve. In addition, red-green blindness can be identified as protanopia or deuteranopia because the peak of the yellow curve has a shorter or longer wavelength. The sufferers can perceive the difference in brightness between red and green, but not the difference in hue.
People with tritanopia can have trouble telling the difference between certain combinations of colours such as blue and green, purple and red, and yellow and magenta. The decoding model illustrates it by assuming that the B-curve has not yet separated from the G-curve. If the G-curve is little far away from the R-curve, then tritanopia becomes tetartanopia so that yellow looks darker.
Fig. 5: The opponent process: changes in colour perception can be caused by different monochromatic lights.
Explaining the opponent-process
Lu uses fuzzy logic compatible with Boolean Algebra to explain the opponent-process. Using this model, we first obtain the medium one, M, of B, G, and R and then get three pairs of opponent-colours blue-yellow, green-magenta, and red-cyan by B, G, and R minus M respectively. The decoding models shows how the opponent-process corresponds to different monochromatic lights and demonstrates how changes in colour perception can also be caused by different monochromatic lights (see fig. 5). This opponent-process ensures that a unique colour can distinctly appear.
“The decoding model can provide more intuitive explanations for colour evolution, colour blindness, and the opponent-process.”
Comparison with another symmetrical colour model
Lu later discovered that his decoding model is also compatible with computer scientist Alvy Ray Smith’s colour transform model for computer graphics. Both models use the same opponent-process and transformation formulae to produce hue, saturation, and brightness from a colour vector (B, G, R). Using the analog logic operations, we can decompose any (B, G, R) into white and two unique colours, which are located at one sector of the colour wheel (see fig. 6), with different proportions. We can obtain hue, saturation, and brightness from the three proportions.
Fig. 6: The colour wheel for colour decomposition.
The models differ in that the decoding model is a colour vision mechanism model, where B, G, and R are three cones’ responses. In contrast, Smith’s model is a colour transform model, where B, G, and R denote three primary colours. The decoding model employs analog logic operations to express the opponent-process and explain the colour vision mechanism. Conversely, Smith’s model deploys if-then statements and arithmetic operations for the opponent-process, without any analog logic interpretation. Moreover, the decoding model can provide more intuitive explanations for colour evolution, colour blindness, and the opponent-process.
Broader implications
The International Commission on Illumination proposed a symmetrical colour model in the early 2000s that was compatible with Smith’s model and with the decoding model. Lu divulges that the decoding model could be used to unify them. In order to achieve this, the decoding model will have to be combined with existing methods in order to obtain an accurate set of three stimulus values to produce better colour transformations.
What led you to study colour vision? How did you develop this colour model?
I have been interested in colour vision since one of my middle school classmates told me that he was red-green colour-blind. When I studied at the university, I found that even if two people innately had two opposite perceptions when they see red flowers and green grasses, they would both call flowers red and grasses green. Later, I found that the opposite perceptions had been called the inverted spectrum in American philosophy in the 1980s; English philosopher Locke had hypothesised about the inverted spectrum earliest. It is for this reason that I wanted to research the colour vision mechanism.
I was able to develop the decoding model because 1) I was familiar with logic circuits and the Venn diagram; 2) I was not satisfied with the popular zone model because I thought it lacked the simplicity and cleverness of scientific laws; 3) I believed that human eyes were similar to electronic devices; colour perceptions were only analog symbols.
Have you been in contact with Professor Alvy Ray Smith?
Yes! I emailed Prof Smith to show him the decoding model about twenty years ago. I said that we could support each other. I remember two sentences in his reply: “Your model is very interesting.” “I did not research colour vision mechanism, I research colour transformations.”
References
Lu C. (2020). Explaining Color Evolution, Color Blindness, and Color Recognition by the Decoding Model of Color Vision. In: Shi Z., Vadera S., Chang E. (eds). Intelligent Information Processing X. IIP 2020. IFIP Advances in Information and Communication Technology, 581. Springer, Cham. Available at: https://doi.org/10.1007/978-3-030-46931-3_27
Lu, C. (2019). Semantic information G theory and logical Bayesian inference for machine learning. Information, 10(8), 261.
Chenguang Lu has developed the decoding model of colour vision to explain colour evolution, colour blindness, and the opponent-process.
Collaborators
Chenguang Lu thanks Professor Peizhuang Wang for his long-term support and encouragement. After seeing Lu’s physical model that demonstrates the decoding model, he let Lu become his visiting scholar to generalise Shannon’s information theory to measure colour vision’s information and semantic information.
Bio
Chenguang Lu graduated from Nanjing University of Aeronautics and Astronautics with a Bachelor’s degree and was trained at Niagara College and Beijing Normal University as a visiting scholar. He has published six books and many articles about colour vision, aesthetics, evolution, semantic information theory, machine learning, portfolio, and philosophy.
Chenguang Lu
Contact
Associate Professor
Changsha University
School of Computer Engineering and Applied Mathematics
21 Hongshan Miao, Kaifu District
Changsha, 410022
China
Guest Professor
Liaoning Technical University
College of Intelligence Engineering and Mathematics
47 Zhonghua Rd, Xihe District
Fuxin, Liaoning, 123000,
China
