Notes

Real Life Color Perception

The spectral composition of illumination represents the set of wavelengths present in light source. Each surface has a particular reflectance spectrum, not all surfaces reflect light in the same way. The product of illumination and reflectance gives us the color signal, i.e., the color that arrives at the eye, which is a combination of which wavelengths are generated by the source of illumination and which wavelengths are reflected by the surface. The color signal that reaches the eye is then filtered by the three populations of cones receptors present in the retina. Hence, the signal representing colors that is propagated as information in the brain can be summarized by three numbers, i.e., how much activity the signal generated in the Long (Red), Medium (Green) /Short (Blue) wavelength sensitive cones. Keep in mind, that the wavelength composition of the color signal is not sufficient to assess with certainty the color appearance in the eye. Indeed, adaptation, context, background and various factors affect the color perception.

Photoreceptors Sensitivity Profiles The picture below shows the same concept as before. The curves show the relative absorbance of wavelengths depending on the cones/rods type. It is important that also the rods are wavelength selective, even though they are mostly used in low-lighting settings. Since we only have three cones type, our vision is defined trichromatic. Side note: computer screens feature only three types of pixels matching the three wavelengths preferences of cones photoreceptors.

About 10% of human population suffers from color blindness. People with color blindness have a restricted spectrum of colors. Color blindness occurs when one or more types of cone cells in the retina are absent, non-functioning, or have an altered response to light. In a person with normal color vision, each cone type is most sensitive to a specific range of wavelengths. When light enters the eye and stimulates these cones, the brain integrates the signals from each cone type to perceive color. In individuals with color blindness, one or more of the cone types are either absent or have an altered response to light. This can result in an inability to distinguish certain colors or a reduced ability to see certain color combinations. Color blindness can be inherited or acquired. Inherited color blindness is usually due to a genetic mutation that affects the development or function of the cone cells. Acquired color blindness can occur due to certain diseases or conditions that damage the retina or optic nerve, or due to exposure to certain chemicals or medications that can affect the function of the cone cells.

Cone Mosaic

The cone mosaic refers to the pattern of cones across the retina, which varies across the retina and between individuals. In the fovea, which is the central region of the retina responsible for high-resolution vision, the cone cells are densely packed and arranged in a regular pattern. This regular arrangement of cone cells is important for high visual acuity, as it allows for precise and detailed information to be transmitted to the brain. In this area, as it can be seen from the figure, we have close-to-none blue cones and an higher density of red cones over green ones. In the peripheral retina, the cone cells are more widely spaced and arranged in a less regular pattern. This arrangement is not as critical for high-resolution vision, as the peripheral retina is more specialized for detecting motion and changes in brightness. The second image shows the inter-individual variability in the cones distribution among human subjects with normal color vision.

Color Matching Experiments

The color matching experiment (Maxwell) is a common technique used to study color vision and color perception. In this experiment, a subject is presented with a test color and is asked to adjust the intensity of three primary lights (usually red, green and blue) to match the color of the test stimulus. The primary lights are mixed together in varying intensities until the subject perceives a color that matches the test stimulus. The process is repeated for several test stimuli, each of which has a different wavelength. The resulting data can be plotted as a color matching function, which shows how the intensities of the primary lights change to match different test stimuli. This experiment provides information about the sensitivity and response properties of the three types of cone cells in the retina. By analyzing the data, researchers can estimate the relative sensitivity of each type of cone cell to different wavelengths of light. They can also identify any anomalies or deficiencies in color vision, such as color blindness or abnormal color discrimination.

Two Metameric Spectral Distributions Color matching experiments reveal two metameric colors, i.e., colors that are different from a physical point of view, but appear identical to us. Referring to the figure below, these two spectral compositions give rise to the same color perception when filtered through the three cones types.

Receptive Fields of LGN Neurons

M-cells and Ganglion cells show very similar receptive fields. Approximately 50% of these cells have an on-center, where the cell strongly responds to an increase of light intensity. While the other 50% shows off-center, where the cell strongly responds to a decrease in light intensity. This type of receptive field is great to detect contrast. P-cells also have round receptive fields, but rather than discriminating light intensity, they discriminate between middle and long wavelengths. Furthermore, the size of the centers of the receptive fields changes depending on the location of the cell in the retina. Finally, K-cells show again round receptive fields which distinguish among short wavelengths.

The "DKL" Color Space

It is a color space defined on the base of cone pigments and sensitivity of cones in macaque monkeys. They represent the colors in a tridimensional space based on cones excitation. This space has three axis:

• Luminance (L + M), represents the overall brightness of a color, which is determined by the combined responses of the long-wavelength (L) and medium-wavelength (M) sensitive cones in the retina.
• Chromaticity "Red -- Green" (L - M), represents the difference in the responses of the long-wavelength (L) and medium-wavelength (M) sensitive cones, which corresponds to the red-green axis of color perception.
• Chromaticity "Blue -- Yellow" (S - (L + M)), represents the difference in the responses of the short-wavelength (S) sensitive cones and the combined responses of the long-wavelength (L) and medium-wavelength (M) sensitive cones, which corresponds to the blue-yellow axis of color perception.

Any color perceived by humans can be represented as a point in this system. In this coordinates system, azimuth and elevation are defined as follows:

• Azimuth (also called hue angle, is the angle on the horizonal plane) represents the hue of the color in the chromatic plane. It is the angle formed between the red-green axis (L - M) and the color's chromaticity vector projected onto the chromatic plane.
• Elevation (also called saturation angle, is the angle on the vertical plane) represents the saturation or chroma of the color. It is the angle formed between the luminance axis (L + M) and the color's chromaticity vector.

Preferred Color of pLGN neurons

If you plot the preferred colors of LGN neurons based on this coordinates system, you obtain a figure like the one above. We can notice that the points distribution is condensed in four main "columns" approximately 90 degrees from one another. The 0 and 180 deg populations are the red and green cells, while the 90 and 270 deg are the blue and yellow cells. This demonstrates that LGN cells come in the two families we have discussed except few outliers (which are very unusual). In addition, we can draw some analyses based on the cell position in the plot, e.g., a cell positioned at high-levels of elevation indicates a cell that strongly response to high-levels of light. On the other side, cells positioned at low-levels of elevation indicates cells that strongly respond to colors regardless of illumination.

The World Seen through the LGN

The image above gives us an idea of how color vision at the early stages of visual processing might look like. Indeed, superimposing the three subfigures to the right and to the bottom, we obtain the top-left subfigure. Thus, we can notice one channel indicating the red-green information, another the blue-yellow information and one channel describing the light variation information.

There are several studies suggesting that this represents an efficient way of encoding color information, thus explaining why the brain evolved and developed this technique.

Color Contrasts of Natural Objects

In the figure above, we have excitation in the long-wavelength sensitive cones as horizontal axis, against the excitation in medium-wavelength sensitive cones. The points represent the excitation of these two types of cones to the pixels of a "natural" image. The most efficient way to transmit this information in the brain is by taking these two orthogonal diagonals, which represent (L + M) and (L - M).

Preferred Color of Cortical Cells

The same exact experiment discussed above is performed in V2 and V3. Here, we see major differences. We do not have any more a red-green and a blue-yellow channel, but we have an almost-equal distribution across the azimuth axis. There is a much more widespread distribution over color preferences. In addition, we notice that there is more density in high-levels of elevation, thus indicating that cells are more "interested" in luminance rather than color. Overall, the cells become more specialized with intermediate color preferences and stronger responses to higher levels of illumination.

Examples of Cortical Cells' Responses to Color Variations

At earlier levels, by varying the azimuth of the stimulus (i.e., changing the color) you will observe plots like the ones above. Indeed, the cell will respond differently depending on its color preference. While ganglion cells and LGN cells are pretty much the same, they linearly combine cones' inputs in the same way (red-green cells and blue-yellow cells), when you reach the cortex level of information processing things get more complicated, all the color spectrum is considered, and cells can become selective to extremely specific colors.

Three Stages of Color Processing

What we discussed in color vision can be summarized by the figure below, where we have the cones tuned to the three wavelengths associated with red, blue and green. Then, at the level of LGN, we have colors opponents with red-green, blue-yellow and luminance opponency. Finally, in higher order areas (e.g., V1, V2, V3) we have a wide plethora of possibilities, with cells tuned to specific colors.

Other major areas of research are color constancy and color appearance. Color constancy is the ability of humans of maintaining unchanged color appearance of objects even when varying illumination or context. Our brain is capable of discerning the contribution of illumination and reflectance in the color signal perceived, such that we are capable of interpreting different color signals as equal when varying conditions. This level of information processing takes place in extrastriate areas.