Potential value of color vision aids for varying degrees of color vision deficiency

Dragos Rezeanu; Rachel Barborek; Maureen Neitz; Jay Neitz

doi:10.1364/OE.451331

1. Introduction

A common misconception about red-green color vision deficiency (CVD) is that all those affected suffer from a significant deficit that impacts all aspects of their day-to-day life. This arises in part from the blanket term “color blindness,” which is often used to describe the entire spectrum of CVD ranging from dichromacy to minimal anomalous trichromacy. But some of the fault lies in the lack of available tools that can properly communicate the difference between a deficiency that is clinically detectable using a diagnostic test like the Ishihara or the Hardy, Rand and Rittler (HRR) [1,2], and one with the potential to significantly impact an individual’s quality of life.

In reality, the majority of individuals identified as red-green color vision deficient through population studies [3], experience less impact on their functional color vision than the term “color blind” implies. About 25% are dichromats for whom the world lacks a complete dimension of color—these individuals are appropriately classified as red-green color blind—but the remaining 75% are anomalous trichromats who compensate remarkably well in psychophysical tests [4–6], and can still make discriminations in the middle-to-long wavelength region of the visible spectrum.

The severity of an individual’s color vision defect is proportional to the spacing of their middle- and long-wavelength sensitive cone photopigments [5,7–11], which can vary from as little as 2 nm in the most severe cases to 10 nm for minimal anomalous trichromats. The purpose of this investigation is to produce a model and accompanying computer program that can accurately simulate red-green color vision deficiency and predict color discrimination at every level of severity. A tool that clearly illustrates the gaps—or lack thereof—in color perception between dichromacy and anomalous trichromacy based on various degrees of spectral separation.

High-quality simulations of protanopia and deuteranopia already exist in the literature [12,13], online, and in popular image editing applications like Adobe Photoshop. By expanding on these techniques, attempts have been made to create computerized simulations of anomalous trichromacy as well [14,15]; however, there are at least two major challenges to creating an algorithm that can accurately simulate the color experience of both dichromats and anomalous trichromats.

First, existing transformations rely on cone fundamentals derived psychophysically using either the CIE 1931 standard observer [16,17], the Judd-Vos modified colorimetric observer [18,19], or the 10° Styles and Burch measurements [20]. The associated color matching functions represent theoretical, normal L and M cone spectral sensitivities. This works well for simulations of deuteranopia and protanopia, but representing the vision of anomalous trichromats requires knowing each of their underlying cone spectral sensitivities, and the more accurately these can be predicted the better the model will perform. Because they rely on cone spectra derived from psychophysical averages, existing models of anomalous trichromacy can only simulate decreased spectral separation by sliding a single template across the visible spectrum [14,15]; in order to represent the cone photopigments in anomalous trichromats as accurately as possible, our algorithm instead uses a photopigment template derived from suction electrode recordings of primate cones [21], to derive cone spectra at the level of the retina.

Using these spectral sensitivity functions, we can generate custom chromaticity spaces for all the possible middle-to-long wavelength spectral separations of anomalous trichromacy deduced from genetics [22].

Second, an accurate model of anomalous vision must reliably predict color discrimination from known retinal physiology. Existing models appear to underestimate the real-world color performance of anomalous trichromats [4–6], which reflects a disconnect between the color discrimination predicted by spectral separation alone and the compensation-adjusted performance of anomalous trichromats in the real world. Our model combines precise knowledge of the middle-to-long wavelength photopigments of anomalous trichromats with data from these subjects’ performance on the Nagel anomaloscope [10], which allows us to derive a precise discrimination threshold based on the relative activation of their cone photopigments. The resulting simulation more accurately represents the relative loss in color discrimination that comes with increasing anomaly.

By addressing these two challenges, the physiologically based computer algorithm and corresponding MatLab application presented here can transform any digital image into an accurate representation of red-green CVD for all the different levels of severity, and simulate that color experience for color normal viewers. A Standalone MatLab application for Windows and MacOS based on this algorithm is available to download through Google Drive (https://bit.ly/3EUPyC2, CC BY-NC-SA 4.0). The resulting transformations allow us to analyze the difference between true red-green “color blindness” and milder anomalous trichromatic manifestations.

2. Methods

2.1 Creating a color space

The first step in building a more accurate simulation of color vision deficiency is to construct a trichromatic color space using a set of physiologically based spectral sensitivity functions. Using the photopigment template described in [21], we generated S, M and L photopigments with spectral peaks at 419, 530, and 559 nm and optical densities of 0.4, 0.22, and 0.35, respectively. After correcting for lens and macular pigment filtering [23], we are left with the s(λ), m(λ), and l(λ) fundamentals pictured in Fig. 1.

Fig. 1. S, M, and L cone fundamentals. Physiologically based spectral sensitivity functions with peaks at 419, 530, and 559 nm and an optical density of 0.4, 0.22, and 0.35, respectively, corrected for lens and macular filtering [21,23].

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Using these fundamentals we can calculate spectral luminosity functions for simulations of protanopia and deuteranopia, where V(λ) is based entirely on the spectral sensitivity of the M cone or L cone, respectively. For spectral luminosity functions in simulations of anomalous trichromacy we substitute the additive combination of the appropriate spectral sensitivities for a particular anomaly, assuming a cone ratio of 2:1 between the longer and shorter of the two middle-to-long wavelength sensitive cones.

This addresses one of the most important distinctions between color normal and color vision deficient individuals. While a color normal individual’s luminosity function will peak at or around 550 nm depending on their ratio of L to M cones, the peak of a color vision deficient individual’s V(λ) can range from 530 nm for the protanope to 559 nm for the deuteranope. Using these physiologically based spectral sensitivity functions and the appropriate V(λ) luminosity function, we can accurately calculate both the hue and the luminosity of confusion colors using the steps below, producing an accurate simulation of CVD.

To construct a color space from these values, we use the process described by Schmidt et al. [24] and the mathematical transformations elucidated by Fairman, Brill, and Hemmendinger [25] to create a custom analog to the CIE 1931 color space.

The first step is to derive color matching functions via Grassman’s Law:

(1)$${{{\left[ {\begin{array}{ccc} {{l_r}}&{{l_g}}&{{l_b}}\\ {{m_r}}&{{m_g}}&{{m_b}}\\ {{s_r}}&{{s_g}}&{{s_b}} \end{array}} \right]}^{ - 1}}\left[ {\begin{array}{c} {l(\lambda )}\\ {m(\lambda )}\\ {s(\lambda )} \end{array}} \right] = \left[ {\begin{array}{c} {R(\lambda )}\\ {G(\lambda )}\\ {B(\lambda )} \end{array}} \right],} $$

where l_r … s_b represent the sensitivity of each photopigment to the spectral primaries that define the color space—in this case: 700 nm, 545 nm, and 435 nm to match the Wright–Guild spectral primaries used to create the original CIE 1931 diagram. Each function is then normalized to integrate to 1 across the visible spectrum, producing R(λ), G(λ), and B(λ) color matching functions:

(2)$$ {\mathop \smallint \limits_{\lambda = 400}^{700} R(\lambda )d\lambda = 1\; ,\; \; \mathop \smallint \limits_{\lambda = 400}^{700} G(\lambda )d\lambda = 1\; ,\; \; \mathop \smallint \limits_{\lambda = 400}^{700} B(\lambda )d\lambda = 1\; .\; } $$

Next, we must transform our RGB space in the manner described in [25], such that the X and Z spectral primaries reside on the line of zero luminance, also known as the alychne. After performing a least squares best fit of the linear sum of our R(λ), G(λ), and B(λ) color matching functions to V(λ), we calculate the (r,g) chromaticity coordinates of our X, Y and Z spectral primaries such that they fit this criteria and form a triangle that encompasses the full RGB color space, and derive the transformation matrix that will place our X, Y, and Z tristimulus values at (1,0,0), (0,1,0), and (0,0,1), respectively.

Finally, we can generate our xyz chromaticity space using the usual method:

(3)$${x = \; \frac{X}{{X + Y + Z}}\; ,\; \; y = \; \frac{Y}{{X + Y + Z}}\; ,\; \; z = \frac{Z}{{X + Y + Z}}\; .} $$

The relative weights of the final tristimulus values—and therefore the exact shape and orientation of the color space—will vary depending on the V(λ) that is used. In Fig. 2, we show the results of this transformation for a color-normal observer with an L:M ratio of 2:1.

Fig. 2. X(λ), Y(λ), Z(λ) tristimulus values (a) derived from the cone fundamentals in Fig 1 were used to construct an xyz colorspace (b).

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These values provide the foundation required to transform an image into an accurate representation of dichromacy. However, in order to calculate the relative loss in color discrimination at any degree of red-green color deficiency, we need to tie the relative activation of an anomalous trichromat’s middle-to-long wavelength cones to their performance on a threshold color matching task. This has been done by Davidoff et al. [10] for the Nagel anomaloscope.

In the following sections, we use the measured association between discrimination data and photopigment spectral separation in anomalous trichromats from [10] to predict discrimination in anomalous trichromats more generally.

2.2 Modelling the Rayleigh range

The anomaloscope is an optical instrument that measures an individual’s ability to discriminate a monochromatic yellow light (∼588 nm) from a mixture of red (∼658 nm) and green (∼546 nm). The lights are arranged as two semi-circles that produce a 2-degree stimulus field, with the 588 nm light displayed in the bottom hemi-field and the 658 nm/546 nm mixture in the top hemifield, as illustrated in Fig. 3.

Fig. 3. The Nagel Anomalscope Model I in our laboratory (a) presents a 2-degree stimulus field that is split into two hemifields (b). The top hemifield can be adjusted from 0 (545 nm/green) to 73 (658 nm/red). The bottom is monochromatic yellow (588 an) that can be adjusted from a luminance of 0 to 90.

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On the Nagel Anomaloscope Model I [26] used by Davidoff in [10] and characterized in this study, the red-green control dial ranges from 0 (only green) to 73 (only red) and the luminance of the yellow light can be adjusted using a second control dial that ranges from 0 (darkest) to 90 (brightest).

During an exam, the participant first adjusts the luminance dial until the 588 nm light is equivalent in perceived brightness to the red-green mixture. Then, the proportion of 658 nm light in the red-green mixture is altered by the examiner until a perfect match to the monochromatic 588 nm light is found, called the Rayleigh match, and a range of indistinguishable values surrounding this match is identified, called the Rayleigh matching range and reported in Rayleigh units.

To calculate precise matching ranges, Davidoff et al [10], used a forced choice method in which subjects were required to answer either “too red” or “too green” when comparing the mixture with the monochromatic yellow light over the full range of possible red-green dial settings. Each red-green mixture was presented repeatedly, at random, so that a percentage of “too red” responses could be determined for each setting, and psychometric functions were produced. The Rayleigh match midpoint was identified as the red-green setting for which the subject responded “too red” 50% of the time, and the matching range was defined as the range of red-green dial settings for which there was greater than 95% confidence that the red-green mixture was indistinguishable from the 588 nm test light. The painstaking accuracy with which this data was collected lies at the heart of our model, and shows a very high correlation between increased spectral separation and an increased Rayleigh range.

According to the data collected by Davidoff, a color normal individual will have a Rayleigh match near 41 with a matching range of just 0.345 Rayleigh units on average when determined using the forced choice method described above. Deuteranomalous and protanomalous individuals show an increase in their matching range from the average color normal range of 0.345 Rayleigh units to approximately 2.5 Rayleigh units in anomalous trichromats whose L and L’ or M and M’ photopigments are separated by only 2-4 nm in spectral peak [10].

These precisely measured Rayleigh ranges from anomalous trichromats whose middle-to-long wavelength cone spectra have been characterized by molecular genetics represent a direct link between the ratio of L:M cone activation and the perceptual experience of color, allowing us to quantify the color discrimination of anomalous trichromats more generally and bridge the gap between genetics and perception.

In order to achieve this, we created a computer model of the Nagel anomaloscope from the Davidoff study, using the technique described by Thomas and Mollon in [27].

First, the spectral power distribution of the red, yellow, and green primaries of the anomaloscope were measured using a Konica Minolta CS-2000 Spectroradiometer (Fig. 4). The measured energy output was converted to quanta and multiplied by middle-to-long wavelength cone spectral sensitivities derived in Section 2.1, allowing us to plot the response of each cone photopigment against the settings of the anomaloscope.

Fig. 4. The Red (658 nm), Yellow (588 nm) and Green (546 nm) primaries of the Nagel Anomaloscope Model I in our laboratory, measured using a Konica-Minolta CS-2000 spectroradiometer.

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For a given photopigment, P(λ), this response is represented by the equation:

(4)$${\mathop \smallint \limits_{\lambda = 400}^{700} \varepsilon Y(\lambda )P(\lambda )d\lambda = \; \mathop \smallint \limits_{\lambda = 400}^{700} \varepsilon R(\lambda )P(\lambda )d\lambda + \; \mathop \smallint \limits_{\lambda = 400}^{700} \varepsilon G(\lambda )P(\lambda )d\lambda \; ,} $$

where εY, εR, and εG are the spectral power distributions of the yellow, red, and green primaries of the anomaloscope, respectively.

Since the anomaloscope scales linearly, each photopigment’s response plots as a straight line that connects its response to the green primary with its response to the red primary. The red-green setting is plotted on the X-axis and the yellow luminance setting on the Y-axis. In Fig. 5, we show the side-by-side plots generated by our model for a color normal individual with M and L cones that peak at 530 nm and 559 nm, respectively, and a deuteranomalous individual whose L’ and L cones peak at 555.5 and 559 nm, respectively.

Fig. 5. Anomaloscope model for a color normal (a) and Deuteranomalous (b) observer. The Red/Green setting is represented on the X-Axis, while the Yellow luminance setting is represented on the Y-Axis.

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Where the two lines intersect represents the Rayleigh match: the point at which both cone photopigments are activated identically by both the yellow light and the combination of red and green. And since we know the average Rayleigh range for the color normal observer measured on this exact anomaloscope [10], we can derive the color discrimination threshold produced by any pair of middle-to-long wavelength photopigments by calculating the change in L:M activation ratio (ΔL:M) required to signal a threshold shift in color:

(5)$${\Delta L:M = \frac{{\left( {\frac{{\varepsilon {L_{Threshold}}}}{{\varepsilon {M_{Threshold}}}}} \right) - \left( {\frac{{\varepsilon {L_{Match}}}}{{\varepsilon {M_{Match}}}}} \right)}}{{\left( {\frac{{\varepsilon {L_{Match}}}}{{\varepsilon {M_{Match}}}}} \right)}}\; ,} $$

where the “Match” values represent L and M cone excitation at the color normal Rayleigh match and the “Threshold” values represent the L and M cone excitations at the edge of the color normal Rayleigh range—the point at which the subject is first able to distinguish a perceptual shift in color.

In our model, the discrimination threshold of the color normal observer described in Fig. 5(a) is measured as a ΔL:M of 0.336%. We can thus predict the Rayleigh range of an anomalous observer by calculating the change in the red-green setting (X-axis) required to produce this same ΔL:M given a different pair of cone photopigments. For the observer described in Fig. 5(b), whose L’ and L cones peak at 555.5 nm and 559 nm, respectively, the Rayleigh range is calculated as 2.079.

This result is in good agreement with the measured performance of anomalous trichromats who have had their cone photopigments characterized by molecular genetics, as described in [10], indicating that we’ve created an accurate computer simulation of the particular Nagel anomaloscope Model I used to collect the original data.

2.3 LMS Daltonization

Before we can simulate deuteranomaly and protanomaly, we must first calculate the transformation into deuteranopia and protanopia. For this, we rely on a technique developed by Viénot, Brettel, and Mollon [13,28], called LMS Daltonization.

The original methodology uses the CIE 1931 chromaticity coordinates of the BT.709 primaries and the Smith Pokorny fundamentals to convert the 8-bit IJK DAC values of a CRT monitor into LMS tristimulus values, compress those values along the L (protanopia) or M (deuteranopia) axis, and transform the new LMS values back into RGB space. In our model, we substitute the IJK DAC values of a CRT monitor for the measured RGB primaries of an LCD display that conforms to the widely used sRGB color gamut, and we replace the CIE diagram and Smith Pokorny fundamentals with the physiologically based tristimulus values and color space derived in Section 2.1.

To characterize our display, we multiply the spectral power distribution of the red, green, and blue primaries and equal energy white of the display by the calculated X(λ) Y(λ) Z(λ) tristimulus values. This allows us to plot the display’s native color gamut in our color space and derive the appropriate sRGB to LMS transformation matrices.

Since the underlying color space changes with V(λ), we are showing two transformation matrices in each of the equations below: one for the deuteranope whose V(λ) is equal to the spectral sensitivity of the L-cone (top), and one for the protanope whose V(λ) is equivalent to the spectral sensitivity of the M-cone (bottom). All anomalous trichromats will fall somewhere between these two values, and the appropriate transformation is calculated by our program for any combination of L and L’ or M and M’ cones based on the type and severity of the color vision deficiency we are simulating.

First, the chromaticity coordinates of our LCD display’s native color gamut allow us to derive the sRGB to XYZ transformation matrices in [Eq. (6)]:

(6)$${\left[ {\begin{array}{ccc} {91.8153}&{65.3430}&{37.3423}\\ {57.6890}&{122.7854}&{16.6521}\\ {4.8333}&{18.3244}&{166.8135} \end{array}} \right]\left[ {\begin{array}{c} R\\ G\\ B \end{array}} \right] = \left[ {\begin{array}{c} X\\ Y\\ Z \end{array}} \right]\; ,}$$

{\left[ {\begin{array}{ccc} {75.6821}&{53.8613}&{30.7807}\\ {18.2759}&{121.1291}&{24.3294}\\ {3.9840}&{15.1045}&{137.5021} \end{array}} \right]\left[ {\begin{array}{c} R\\ G\\ B \end{array}} \right] = \left[ {\begin{array}{c} X\\ Y\\ Z \end{array}} \right]\; .}

Next, the XYZ values must be transformed into LMS space using the inverse of the matrix described in [Eq. (1)], after it has been normalized to equal energy:

(7)$${\left[ {\begin{array}{ccc} {0.0130}&{1.2286}&{ - 0.0674}\\ { - 0.0036}&{0.6446}&{0.0797}\\ 0&{ - 0.0059}&{0.1865} \end{array}} \right]\left[ {\begin{array}{c} X\\ Y\\ Z \end{array}} \right] = \left[ {\begin{array}{c} L\\ M\\ S \end{array}} \right]\; ,}$$

{\left[ {\begin{array}{ccc} {0.0104}&{1.1257}&{ - 0.0425}\\ {0.0003}&{0.8044}&{0.0410}\\ { - 0}&{ - 0.0075}&{0.1868} \end{array}} \right]\left[ {\begin{array}{c} X\\ Y\\ Z \end{array}} \right] = \left[ {\begin{array}{c} L\\ M\\ S \end{array}} \right]\; .}

And finally, using matrix multiplication, we can now combine the matrices above into the sRGB to LMS conversion matrices below:

(8)$${\left[ {\begin{array}{ccc} {71.7413}&{150.4675}&{9.6995}\\ {37.2449}&{80.3771}&{23.8901}\\ {0.5625}&{2.6913}&{31.0071} \end{array}} \right]\left[ {\begin{array}{c} R\\ G\\ B \end{array}} \right] = \left[ {\begin{array}{c} L\\ M\\ S \end{array}} \right]\; ,}$$

{\left[ {\begin{array}{ccc} {21.1941}&{136.2756}&{21.8628}\\ {14.8898}&{98.0756}&{25.2227}\\ {0.6066}&{1.9105}&{25.5089} \end{array}} \right]\left[ {\begin{array}{c} R\\ G\\ B \end{array}} \right] = \left[ {\begin{array}{c} L\\ M\\ S \end{array}} \right]\; .\; }

To transform a digital image into a representation of deuteranopia and protanopia, the RGB values of each pixel are first rescaled between 0 and 1 and corrected for the standard sRGB gamma of 2.2. For an 8-bit image:

(9)$${R = {{\left( {\frac{R}{{255}}} \right)}^{2.2}},\; \; G = {{\left( {\frac{G}{{255}}} \right)}^{2.2}},\; \; B = {{\left( {\frac{B}{{255}}} \right)}^{2.2}}\; .} $$

Each value is then multiplied by the appropriate conversion matrix from [Eq. (8)] to derive the equivalent LMS tristimulus values.

Using the equation of a plane, we can now reduce all of the L (for the protanope) or M (for the deuteranope) values of an image into a single blue/yellow plane in LMS space defined as the plane that includes the origin (0, 0, 0), the blue primary, and the white point of our display. This is the plane chosen by Viénot et al. [13,28], and we agree that it is the best option available to us. The blue primary represents the best approximation of the LMS coordinate of unique blue, and any dichromatic plane along which we reduce the LMS values must include white. While there will be some inter-subject variability in the perception of unique blue, studies show that unique blue and unique yellow are the most stable of the four unique hues [29], so we are comfortable with this assumed plane.

By choosing this plane, we produce the following equation:

(10)$${\alpha L + \beta M + \gamma S = 0\; ,}$$

where the normal vector is defined as:

(11)$$ {\alpha = {M_w}{S_b} - {M_b}{S_w}\; ,\; \; \beta = {S_w}{L_b} - {S_b}{L_w},\; \; \gamma = {L_w}{M_b} - {L_b}{M_w}\; .}$$

Deriving the replacement L or M tristimulus values can now be accomplished:

(12)$$ {{L_p} ={-} \frac{{\beta M + \; \gamma S}}{\alpha },\; \; M ={-} \frac{{\alpha L + \; \gamma S}}{\beta }\; .}$$

Finally, using these equations, we derive the following transformation matrices for the deuteranope and protanope, respectively:

(13)$${\left[ {\begin{array}{ccc} 1&0&0\\ {0.5204}&0&{0.6077}\\ 0&0&1 \end{array}} \right]\left[ {\begin{array}{c} L\\ M\\ S \end{array}} \right] = \left[ {\begin{array}{c} L\\ {{M_d}}\\ S \end{array}} \right]\; ,}$$

{\left[ {\begin{array}{ccc} 0&{1.4058}&{ - 0.5330}\\ 0&1&0\\ 0&0&1 \end{array}} \right]\left[ {\begin{array}{c} L\\ M\\ S \end{array}} \right] = \left[ {\begin{array}{c} {{L_p}}\\ M\\ S \end{array}} \right]\; .}

Once transformed, the new LMS tristimulus values are multiplied by the inverse of the appropriate sRGB to LMS conversion matrix in [Eq. (8)] and subjected to the inverse gamma correction, producing a representation of our image where all the values have been compressed along the protanope or deuteranope confusion lines of our color space.

2.4 Simulating anomalous trichromacy

The fourth and final step in our algorithm uses the calculated Rayleigh range from Section 2.2 to determine how much the RGB values in an image should be compressed during LMS Daltonization. This is done by comparing the modelled Rayleigh range of a given set of anomalous cone fundamentals against the color normal range to determine the percent loss in color discrimination:

(14)$${\% \; Loss = \; \frac{{\left( {{\raise0.7ex\hbox{${73}$} \!\mathord{\left/ {\vphantom {{73} n}}\right.}\!\lower0.7ex\hbox{$n$}} - {\raise0.7ex\hbox{${73}$} \!\mathord{\left/ {\vphantom {{73} r}}\right.}\!\lower0.7ex\hbox{$r$}}} \right)}}{{{\raise0.7ex\hbox{${73}$} \!\mathord{\left/ {\vphantom {{73} n}}\right.}\!\lower0.7ex\hbox{$n$}}}}\; }$$

where r is equal to the predicted Rayleigh range based on the ΔL:M calculated using [Eq. (5)] and n is equal to the average color normal range of 0.345 Rayleigh units. To simulate the deficiency, the calculated % Loss is used to determine how far the L or M values should be compressed during LMS Daltonization, with 0% representing the color normal and 100% representing dichromacy.

For the deuteranomalous observer described in Fig. 5(b), our anomaloscope model calculates a Rayleigh match of 15.46 with a range of 2.08 Rayleigh units. This translates into an 83.4% loss in color discrimination, which is applied to the M value of every pixel in our image, compressing it 83.4% of the way towards the M_d value from [Eq. (11)] before the image is transformed back into RGB space.

3. Results

3.1 HRR and D-15 color vision tests

We used our algorithm to simulate various levels of color vision deficiency ranging from protanopia and deuteranopia to mild anomalous trichromacy where the L and L’ or M and M’ photopigments are still well separated in spectral peak.

For our first test, we applied these transformations to Plate 20 from the 4^th Edition of the HRR color vision test [2], produced by Richmond Products in 2002, which acts as a proof of concept for our model. The HRR transformations show that our algorithm accurately compresses the color values in the image down the deutan and protan confusion lines, removing all color from the circle for the deuteranope and the triangle for the protanope. For the anomalous observer, the amount of red available decreases along the appropriate confusion line in proportion to the % Loss calculated in Section 2.4, producing an accurate representation of the deuteranomalous and protanomalous individual’s perception of this HRR plate (Fig. 6).

The Farnsworth Panel D15 arrangement test [30,31], was also used as it relies on a different mechanism for diagnosing color vision deficiency. The hues used in the so-called “dichotomous” 15 test drive both the red-green and blue-yellow color opponent systems. A color normal individual will arrange the colored circles in order from 1 to 15, using both color dimensions to do so. A dichromat will arrange them using only the blue-yellow dimension roughly represented by the arrangement 1, 15, 2, 14, 3, 13, 4, 5, 12, 6, 11, 10, 7, 8, 9 for the deuteranope, and 15, 1, 14, 2, 13, 12, 3, 4, 11, 10, 5, 9, 6, 8, 7 for the protanope.

The test is scored by arranging the numbers 1 through 15 in a circle and connecting them in the same order as the pieces were arranged. The color normal result will trace a perfect circle, while crossing the circle two or more times indicates a color vision deficiency. The angle at which the crossings occur gives some indication as to the type of deficiency (i.e. Deutan, Protan, or Tritan) as seen in Fig. 7.

Fig. 6. Plate 20 of the HKK transformed using our algorithm. He resulting simulations illustrate varying degrees of deutan (a) and protan (b) color vision deficiency based on spectral separation, ranging from mild deuteranomaly and protanomaly to full deuteranopia and protanopia.

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Fig. 7. Score sheet template for the Farnsworth Panel D15 Arrangement Test, courtesy of Richmond Products. Lines have been added to show the typical results from color normal (left) and deuteranopic (right) individuals.

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To simulate how this test would appear to a CVD individual, we digitized the Munsell colors that constitute the D15 [32,33], and placed them in both the color normal and the stereotypically Deutan arrangement (Fig. 8).

Fig. 8. The pieces of the D15 color vision test arranged in the color normal (a) and stereotypically deutan (b) order. The deutan arrangement looks obviously “wrong” to the color normal observer because of their ability to see red and green.

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In Fig. 9, we used our algorithm to transform both images so that we can visualize what a pass and fail would look like to the anomalous eye.

Fig. 9. The Farnsworth D15 color vision test shown in the color normal (top) and stereotypical deutan (bottom) order transformed to illustrate increasing red-green color vision deficiency: 10 nm separation (a), 5 nm separation (b), 2.5 nm separation (c), and deuteranopia (d).

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The deutan arrangement looks increasingly plausible as red-green discrimination decreases; however, based on our simulations, even the slightest amount of color discrimination in the middle-to-long wavelengths would encourage the anomalous trichromat to avoid the errors made by a dichromat.

If our model is accurate, we are confident that the slightest hint of red/green vision would prevent an anomalous trichromat from placing the red pieces from the end of the series next to blue pieces from the beginning. Piece-by-piece, the way the D15 is administered, this arrangement simply looks wrong.

Given enough patience and careful consideration, our model implies that even the most severe anomalous trichromat whose L and L’ cones differ by only 2.5 nm in spectral peak should be able to pass the Farnsworth D15. Detailed clinical data linking spectral separation with performance on the D15 does not currently exist, but if our simulation is accurate, the D15 could only reliably separate dichromats from everyone else.

3.2 Real-world scene

Most diagnostic tests of color vision operate by presenting isoluminant stimuli that rely on threshold color discrimination in order to pass. Missing five or more plates on the 38-plate edition of the Ishihara [1] or a single diagnostic plate on the HRR [2] constitutes a failure. However, real-world tasks that rely on color identification rarely operate at the absolute threshold of human color vision, and even a significantly diminished ability to distinguish middle-to-long wavelengths may allow anomalous trichromats to make the functional color distinctions required by everyday life.

We do not mean to imply that a lesser deficiency is unimportant—any amount of color loss may prove to be a disadvantage under some circumstances—only that it is far less likely to cause significant disruption to an individual’s life or work performance on tasks that require color identification.

To evaluate the color discrimination of CVD individuals as it applies to a real-world scene, we applied the model to a colorful photograph of a hot air balloon, which provides an easy basis for comparison thanks to the clearly delineated squares in different shades of red, green, blue, and yellow. We sought to identify the point at which anomalous trichromacy becomes a salient deficiency, with “salient” defined as extreme difficulty distinguishing the red and green squares from those that are blue and yellow.

Evaluating the images produced by our model, the decrease in saturation between color normal vision and all forms of anomalous trichromacy is substantial; however, the anomalous trichromat never appears to lose the ability to distinguish the red and green hues in a colorful real-world scene the way a dichromat does, even when the spectral separation between their two middle-to-long wavelength photopigments reaches 2-3 nm.

The majority of anomalous trichromats are deuteranomalous, with L and L’ cone photopigments separated by 4-6 nm in spectral peak [9,10,22]. Our first simulation illustrates deuteranomaly that is slightly better than the average, based on a spectral separation of 7.5nm (Fig. 10). In isolation, this simulation still looks quite colorful; it is only when the image is placed next to the fully saturated color normal version that the magnitude of the deficiency is obvious.

Fig. 10. Comparison of deuteranomalous (a), color normal (b), and deuteranope (c) vision simulated using our algorithm. The simulation is based on a 7.5 nm spectral separation between the L and V cones.

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Our second simulation illustrates a more significant anomaly that is worse than the average, with simulated cone photopigments that are separated by only 2.5 nm. According to our model, this would produce a Rayleigh matching range of 2.85 Rayleigh units and a corresponding loss in color discrimination of 87.9% (Fig. 11).

Fig. 11. Comparison of deuteranomalous (a), color normal (b), and deuteranope (c) vision simulated using our algorithm. The simulation is based on a 2.5 nm spectral separation between the L and V cones.

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Based on the output from our model, the ability to make minute distinctions in spectral composition is greatly diminished, but even in this extreme example there appears to be sufficient information in the red-green dimension to perform basic color identification.

3.3 Notch filter simulation

For our final test, we created a version of our model that integrates a notch filter. These filters cut out certain wavelengths of light in hopes of better separating the signals coming from the L and L’ photopigments of a deuteranomalous individual, and glasses that use a version of this technology represent a popular and relatively accessible color vision aid.

To test the effect of a notch filter on our simulation of dichromatic and anomalous vision, we built a spectral “notch” into our program by removing display input between 530 and 560 nm during LMS Daltonization and recalculating the transformation into deuteranopia, protanopia, and two levels of deuteranomaly. The digital notch in our simulation is well placed to increase contrast between the two photopigments; however, it’s important to note that our model is based on the spectral output of an sRGB display, and as such, we cannot draw any conclusions about the effect of a notch filter on anything other than a digital image displayed on a typical RGB display. As most colorful content is consumed in this way in the modern world, the model can still provide valuable information, but that information is limited by the nature of our computerized model as well as the width and placement of our digital notch.

Note that this filter was not designed to represent any commercially available color vision aid. The purpose of the notch filter in our model is to give people with normal color vision the opportunity to evaluate the effects of a basic notch filter on the color experience of both dichromats and anomalous trichromats.

In all four cases illustrated in Figs. 12 and 13, our notch filter produces a noticeable change in the color balance of the input image by increasing the contrast between the short and middle-to-long wavelengths. However, the filter’s impact on the contrast between the reds and greens is difficult to judge, and it cannot rescue color discrimination that is lost below the subject’s noise floor. Our qualitative assessment is that, within the limitations imposed by an RGB-based model, a single notch provides no obvious improvement in color discrimination when applied to our simulation of anomalous trichromacy, though it may help both dichromats and anomalous trichromats by adjusting the relative luminance of certain confusion colors so that they are more easily distinguishable.

Fig. 12. Simulating the effect of a notch filter on deauteranopic (a) and protanopic (b) vision. By cutting out the display input between 530 nm and 560 nm during the LMS Daltonization step of our algorithm, we can simulate the saturating effect of notch filter glasses.

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Fig. 13. Simulating the effect of a notch filter on deuteranomalous color vision deficiency. The transformation was applied to an observer with a 7.5 nm (a) and 2.5 nm (b) spectral separation between their L and L’ cones.

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Despite its limitations, our simulation produces results that agree with available studies that have evaluated the efficacy of “color-correcting glasses” in both dichromats and anomalous trichromats [34]. Deuteranopes report an increase in contrast along both the red/green and blue/yellow axes, while protanopes report a rotation of their axis of confusion from protan to deutan, and this is indeed what we see in the simulation of deuteranopia and protanopia below:

In previous studies of notch filter glasses [34], deuteranomalous observers report the same increase in red/green contrast seen in deuteranopes. Green hues are darkened while red hues are lightened, shifting the relative luminance of red, green, blue, and yellow in a way that may help with color discrimination in some cases and hinder discrimination in others. In this scenario, the effect on our simulation is more muted but still visible upon close inspection.

Ultimately, it cannot be claimed that our simulated notch filter will materially aid in the ability to distinguish primary colors from one another in an RGB image, since these colors are already distinguishable at both 7.5 nm and 2.5 nm spectral separations before the notch is applied, but it leaves open the possibility of testing different spectral notches that may produce a stronger increase in red/green contrast.

4. Discussion

As almost 1 in 10 males suffer from some form of red-green color vision deficiency, there is great interest in developing treatments or products that can help the colorblind better negotiate their environment. This is a noble goal, but not all forms of color deficiency are created equal, and it is equally important that we better distinguish between “color blind” and color vision deficient. Our goal was to create a tool that can quickly and easily illustrate this gap for both research and educational purposes.

As our model helps illustrate, the term “color blind” is a misnomer for the vast majority of color deficient individuals. Even the 88% loss in color discrimination represented by a 2.5 nm spectral separation between the L and L’ photopigments of a deuteranomalous trichromat leaves a surprising amount of red/green signal for real-world color identification, implying that the most valuable color vision aid for this population is one that can help them make minute distinctions that are otherwise hidden below their visual noise floor, perhaps by providing valuable luminance cues.

As with any algorithm that attempts to simulate something as individually variable as color appearance, there are many factors which we did not and could not build into the model. There is color contrast induction, environmental adaptation to a different white, and variability in unique hue selection [24,29]. One of the most significant aspects of color vision deficiency that our model does not address is the impact of long-term contrast adaptation, which may be quite dramatic. As illustrated by in the literature [5,6,35], adaptation will increase color contrast in the red-green dimension in proportion to a decrease in the spectral separation of the long- and middle-wavelength photopigments. While adaptation cannot correct for the measured loss in color discrimination revealed by the Nagel anomaloscope—any adaptation-based improvement that takes place before the site of limiting noise has already been accounted for—the increase in color contrast in the red-green dimension should help anomalous trichromats better exploit the limited range of colors at their disposal, further narrowing the functional gap between color normal vision and anomalous trichromacy.

When using our algorithm to transform real-world scenes that involve mostly suprathreshold color discrimination, such as the hot air balloon, our simulations represent the worst-case scenario. There are variations in hue that will always be invisible to the anomalous trichromat, but as color contrast increases, the gap between the colors that they can see should become even wider and easier to negotiate.

Limitations notwithstanding, we believe there is great value in a physiologically based algorithm that can accurately simulate the baseline color experience of individuals who suffer from the full spectrum of red-green color vision deficiency beyond deuteranopia and protanopia. As an educational tool, it can provide context and dispel misconceptions about color blindness. As an employment tool, it could help employers establish more inclusive standards for hiring color deficient individuals for color critical work. As a research and development tool, it should encourage scientists and entrepreneurs alike to focus their efforts on color vision aids and prospective therapies that will provide the most substantial benefit to the specific CVD population they intend to help.

In the case of red-green color vision deficiency, it seems clear to us that most anomalous trichromats need little-to-no help discerning the primary colors in their environment. And while we are certainly not implying that lesser deficiencies should be ignored, we believe that the greatest potential benefit lies in helping improve the lives of dichromats who are missing an entire dimension of color.

Funding

Research to Prevent Blindness; National Eye Institute (P30EY001730, RO1EY027859).

Acknowledgements

The authors thank James A. Kuchenbecker for his invaluable assistance in the art of color space creation.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

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Potential value of color vision aids for varying degrees of color vision deficiency

Abstract

1. Introduction

2. Methods

2.1 Creating a color space

2.2 Modelling the Rayleigh range

2.3 LMS Daltonization

2.4 Simulating anomalous trichromacy

3. Results

3.1 HRR and D-15 color vision tests

3.2 Real-world scene

3.3 Notch filter simulation

4. Discussion

Funding

Acknowledgements

Disclosures

Data availability

References

Data availability

Cited By

Figures (13)

Equations (18)

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