A Computational Model for Color Vision Deficiencies, Protanopia, Deuteranopia, and Tritanopia Simulation in MATLAB

Author : Waqas Javaid

Abstract

Color blindness affects millions of people worldwide, presenting significant challenges in digital content perception. This article presents a comprehensive MATLAB framework for simulating and correcting three primary types of color vision deficiencies: Protanopia, Deuteranopia, and Tritanopia. By implementing the Hunt–Pointer–Estevez transformation, we convert images from RGB to the physiologically relevant LMS color space representing long, medium, and short wavelength cone responses [1]. The model incorporates adjustable severity parameters and uses Brettel-Vienot projections to accurately simulate each deficiency type. Furthermore, we implement a Daltonization correction algorithm that redistributes lost color information through contrast-aware error mapping [2]. The system maintains gamma-safe processing for realistic results and generates eight distinct visualizations including simulations, corrected images, and error analyses. This computational approach provides designers, developers, and researchers with valuable tools for accessibility testing and inclusive design practices [3]. The complete MATLAB implementation is presented with practical examples demonstrating its effectiveness for both simulation and correction applications, bridging the gap between color theory and practical digital accessibility solutions [4].

1. Introduction

Human color vision is a remarkable biological achievement, allowing us to perceive a rich spectrum of light, but for approximately 300 million individuals globally, this experience is fundamentally altered by color vision deficiencies, commonly known as color blindness.

This condition, most often genetic and affecting red-green perception, arises from the malfunction or absence of one of the three types of cone photoreceptors in the retina those sensitive to long (L), medium (M), or short (S) wavelengths. In our increasingly digital world, where information is frequently encoded in color, this presents a significant barrier to accessibility, affecting everything from website navigation and data visualization to educational materials and entertainment. To design inclusively and understand these perceptual differences, developers, designers, and researchers require practical tools to simulate how their content appears to colorblind users [5]. This article addresses that need by presenting a robust, computational framework built in MATLAB that models color vision deficiencies with high fidelity [6]. Moving beyond simple RGB filtering, our approach is grounded in the physiological LMS cone response space, implementing the Hunt-Pointer-Estevez transformation to simulate the world as perceived by individuals with Protanopia, Deuteranopia, and Tritanopia [7]. The model features a continuous severity parameter and employs established Brettel-Vienot projection matrices for accurate simulation [8]. Furthermore, we extend the utility of the tool by integrating a Daltonization correction algorithm, which intelligently redistributes lost perceptual information to create images more discernible to colorblind viewers [9]. By detailing this complete pipeline from gamma-corrected input to simulated and corrected outputs we provide a valuable resource for advancing digital accessibility and fostering empathetic, user-centric design [10].

1.1 The Challenge of Color in a Digital World

Our modern world communicates through color. From critical warning signals on dashboards and status indicators in software interfaces to the nuanced data in scientific visualizations and the artistic expression in digital media, color is a fundamental, yet often exclusive, channel of information [11]. For individuals with color vision deficiencies (CVD), this reliance on color can create barriers to understanding, safety, and engagement. An estimated 8% of men and 0.5% of women of Northern European descent experience some form of color blindness, translating to hundreds of millions of people who may struggle with poorly designed content. This presents a profound accessibility challenge for designers, developers, and educators who aim to create inclusive products and materials. Without firsthand experience of these visual perceptions, it is difficult to anticipate where these breakdowns in communication occur [12]. Therefore, the first step toward inclusivity is developing a clear, accurate understanding of how color information is lost or confused, which requires moving beyond anecdote and into empirical, computational modeling of the condition.

1.2 The Biological Basis of Color Vision Deficiencies

To accurately simulate color blindness, we must first understand its biological origin. Normal human color vision is trichromatic, relying on three types of cone cells in the retina that are most sensitive to long (L, red), medium (M, green), and short (S, blue) wavelengths of light. The brain interprets the relative stimulation of these cones to perceive the full spectrum of color [13]. The most common forms of inherited color blindness, Protanopia and Deuteranopia, arise when either the L-cones or M-cones are non-functional, collapsing the red-green discrimination channel. A rarer form, Tritanopia, involves malfunctioning S-cones, affecting blue-yellow discrimination. These are not simple “color swaps” but a fundamental reduction in the dimensionality of color space; the world is not seen in grayscale but through a limited palette where distinct colors to a trichromat become metamers indistinguishable [14]. A faithful simulation must therefore model this physiological loss at the cone-response level, not just apply a superficial filter to the final RGB image, which is the cornerstone of our technical approach.

1.3 Bridging Perception with Computation: The LMS Framework

The key to a physiologically grounded simulation is operating in the correct color space. Standard digital images are stored in device-dependent RGB values, which do not directly correspond to human cone responses. To bridge this gap, we employ the LMS color space, which aligns with the spectral sensitivities of the Long, Medium, and Short-wavelength cones [15]. Our model uses the Hunt-Pointer-Estevez linear transformation matrix to convert gamma-expanded, linear RGB values into an LMS representation. This transformation provides a computational model of the initial stage of human color vision [16]. By manipulating data in this cone-response space, we can directly simulate the effect of a missing or deficient cone type. This forms the core of our simulation’s accuracy, allowing us to project the three-dimensional LMS data of a normal-sighted viewer onto the two-dimensional plane perceivable by a dichromat, based on established visual science models.

1.4 Implementing Deficiency Simulation with Projection Matrices

Within the LMS space, we simulate specific deficiencies using predefined projection matrices derived from the Brettel-Vienot model, a standard in computational color vision science. For Protanopia (absent L-cones), the LMS values are projected onto a plane defined by the remaining M- and S-cone signals. Separate matrices perform analogous projections for Deuteranopia (absent M-cones) and Tritanopia (absent S-cones) [17]. A crucial feature of our implementation is a continuous “severity” parameter. This allows the simulation to blend linearly between the original, full-color image (severity = 0) and the complete dichromatic projection (severity = 1). This flexibility is valuable for modeling anomalous trichromacy (where cones are shifted in sensitivity, not absent) and for understanding the progressive impact of a deficiency, providing a more nuanced tool than a simple binary simulation [18].

1.5 From Simulation to Solution, The Daltonization Correction Process

Simulation alone highlights problems; the next logical step is to propose solutions. This is where the process of Daltonization named after the scientist John Dalton, who described his own color blindness comes into play [19]. Our correction algorithm works by analyzing the error or difference between the original linear RGB image and the simulated colorblind version. This error represents the perceptual information lost in the simulation. The algorithm then strategically redistributes this lost information into the remaining, discernible color channels of the colorblind viewer. For example, details lost in the red-green channel for a protanope might be shifted into the luminance (brightness) or blue-yellow channel [20]. This is done using a purpose-built error redistribution matrix, creating a corrected image that, while not restoring normal color vision, enhances contrast and detail visibility for the colorblind observer, making the content more accessible.

1.6 Delivering a Complete, Practical MATLAB Toolbox

The culmination of these steps is a fully functional, ready-to-use MATLAB program. The code meticulously handles the image processing pipeline: it linearizes RGB signals to remove display gamma, performs all space conversions and projections, applies the correction, and finally re-encodes the results for proper display. The output is a comprehensive visual analysis consisting of eight figures. These include the original image, the three deficiency simulations, the three corresponding corrected images, and a final diagnostic panel showing error maps and color histograms [21]. This complete package transforms theoretical color science into a practical, hands-on tool. It empowers users whether in academia, software development, or design to not only visualize accessibility barriers but also to actively test and implement strategies to overcome them, fostering a more inclusive digital environment [22].

1.7 Ensuring Visual Fidelity with Gamma-Safe Processing

A critical yet often overlooked aspect of color-accurate image processing is managing gamma correction. Standard images (like JPEGs, PNGs) are stored with a gamma-encoded, non-linear relationship between pixel values and displayed light intensity to match human perceptual sensitivity and optimize storage. Performing linear color space math (like matrix multiplications for LMS conversion) directly on these encoded values introduces significant errors. Our pipeline addresses this by beginning with a gamma expansion step, which converts the non-linear sRGB values back to a linear light intensity space [23]. All core computations LMS transformation, deficiency projection, Daltonization are performed in this linear domain. Finally, a gamma compression step re-encodes the processed linear data back into the standard non-linear format for correct display. This gamma-safe workflow ensures that color shifts and simulations are based on true physical light mixtures, leading to perceptually accurate and mathematically valid results that mirror real-world visual phenomena.

1.8 Enhancing Correction with Contrast-Aware Error Mapping

A simple Daltonization algorithm can sometimes introduce unnatural color shifts or exaggerate noise in low-contrast image regions. To create a more sophisticated and visually pleasing correction, our model incorporates a local contrast-aware scaling mechanism. After calculating the error between the original and simulated images, we analyze the local contrast of the original image. This is done by comparing a grayscale version of the image to a Gaussian-blurred version, highlighting edges and textured areas [24]. The Daltonization error adjustment is then modulated by this contrast map: enhancements are stronger in high-contrast regions and subtler in flat, low-contrast areas. This intelligent, adaptive redistribution prioritizes preserving important visual details and edges that are crucial for object recognition and scene understanding, making the corrected image not just different, but genuinely more intelligible for a colorblind viewer.

1.9 Quantitative Analysis and Performance Metrics

Beyond visual inspection, it is essential to quantitatively assess the impact of both simulation and correction. Our framework includes a metrics module that calculates standard image quality measures. For the simulation stage, we compute the Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) between the original RGB image and each simulated version. These metrics numerically confirm the significant information loss caused by the deficiency [25]. For the correction stage, while a perfect perceptual match is impossible, the diagnostics panel provides crucial insights. The error maps visually pinpoint exactly which colors and regions are most altered by a given deficiency. Simultaneously, RGB channel histograms of the original image reveal the color distribution, helping to explain why certain palettes fail [26]. This quantitative and diagnostic approach transforms the tool from a simple visualizer into an analytical platform for rigorous accessibility testing and design critique.

1.10 Applications and Implications for Inclusive Design

The practical applications of this tool extend across multiple domains. In user experience (UX) and web design, teams can batch-test website themes, charts, and icons to ensure information is not conveyed by color alone. Data visualization scientists can verify that their colormaps (like viridis or plasma) are perceptually uniform and decipherable by all audiences, not just those with normal color vision. Educational content creators can adapt maps, diagrams, and scientific imagery to be effective for students with CVD [27]. In product design, it can be used to check the discernibility of status LEDs or wire color-coding. Furthermore, the tool serves an educational purpose in vision science and computer graphics courses, providing students with hands-on experience in physiological modeling [28]. By making the complex nature of color blindness tangible and correctable, this work underscores a central tenet of universal design: creating environments and products usable by all people to the greatest extent possible, without the need for adaptation or specialized design.

1.11 Future Directions and Extensibility of the Model

The presented framework is a robust foundation that can be extended in several promising directions. One path is the integration of more advanced, individualized correction models that could account for the exact spectral sensitivity of a specific user’s anomalous cones, potentially leveraging data from modern color vision tests [29]. Another is expanding the simulation to model monochromacy (complete color blindness) and acquired color deficiencies from conditions like cataracts or macular degeneration. The algorithm could also be adapted for real-time video processing, enabling live correction for video calls or gaming. From an implementation perspective, the core mathematics could be ported to a web-based JavaScript tool or a plugin for design software like Adobe Photoshop or Figma, dramatically increasing its accessibility to designers [30]. Finally, incorporating machine learning could allow the system to learn optimal correction strategies from paired datasets of original and colorblind-accessible images, potentially discovering novel and more effective enhancement techniques beyond classic Daltonization.

2. Problem Statement

The widespread reliance on color as a primary information carrier in digital media from data visualizations and user interfaces to educational content and safety signage creates significant accessibility barriers for the estimated 300 million individuals with color vision deficiencies (CVD). Current design workflows often lack intuitive, physiologically accurate tools to visualize these perceptual limitations, leading to products that inadvertently exclude users with Protanopia, Deuteranopia, or Tritanopia. Most available simulators operate as simplistic RGB filters, failing to model the true cone-response mechanics of human vision, while correction methods remain underutilized or poorly integrated into standard design practices. This gap necessitates a computational framework that not only accurately simulates CVD in a tunable manner but also provides actionable correction strategies, enabling designers and developers to preemptively identify and resolve color-dependent information loss, thereby bridging the divide between inclusive design intention and practical implementation.

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3. Mathematical Approach

The mathematical approach is anchored in a linear algebraic framework operating within the LMS color space. It begins with the Hunt–Pointer–Estevez matrix transformation, to convert gamma-linearized RGB values to physiological cone responses.

Specific dichromatic vision is then simulated via severity-weighted blending between the identity and a Brettel-Vienot projection matrix (P) yielding.

For correction, the perceptual error is redistributed using a predefined matrix (R) and scaled by a local contrast map (C) resulting in the Daltonized output where all operations enforce gamma-safety and perceptual uniformity.

The mathematical model transforms an image through a series of color space conversions and linear projections. First, it removes the screen’s gamma encoding to work with linear light values. These linear RGB values are then mapped to the Long, Medium, and Short cone response space of the human eye using a standardized transformation matrix. To simulate a deficiency, a projection matrix specific to Protanopia, Deuteranopia, or Tritanopia is applied. This matrix effectively collapses the three-dimensional cone space along the axis of the missing cone type. The model allows for adjustable severity by creating a weighted blend between the original full cone response and this collapsed projection. For correction, the process first recalculates how the simulated image would appear in standard RGB. The difference between this simulated version and the original linear image is computed as the perceptual error. This error represents the color information lost to the viewer. A predefined redistribution matrix then intelligently shifts this lost information into the color channels that remain discernible to the colorblind viewer, such as enhancing luminance or blue-yellow contrast. Finally, this adjustment is intelligently scaled by a local contrast map, amplifying corrections in detailed edges while suppressing them in flat regions, before the entire image is re-encoded with gamma for proper display.

4. Methodology

The methodology is structured as a sequential, modular image-processing pipeline that transforms an input RGB image into simulated and corrected outputs via physiologically grounded operations.

Table 1: Core Mathematical Components

It commences with a crucial pre-processing step: gamma expansion linearizes the standard non-linear image data, ensuring all subsequent mathematical operations are performed on values proportional to physical light intensity. This linear RGB data is then converted to the LMS color space using the Hunt–Pointer–Estevez transformation matrix, representing the image in terms of human Long, Medium, and Short-wavelength cone responses [31]. Three distinct projection matrices derived from the Brettel-Vienot model are defined to mathematically collapse this three-dimensional cone space for Protanopia, Deuteranopia, and Tritanopia simulations. A continuous severity parameter enables a tunable linear blend between the original LMS data and the fully projected dichromatic state, allowing modeling of both complete absence and partial deficiency of cone function. Each resulting simulated LMS representation is converted back to linear RGB using the inverse transformation matrix, then gamma-compressed for standard display, producing the final visual simulations. Parallel to simulation, the correction pathway implements the Daltonization algorithm. This begins by comparing the original linear RGB image to the linear RGB version reconstructed from the simulated LMS data, calculating a precise error map of lost perceptual information. A fixed redistribution matrix then transforms this error, strategically translating lost red-green information, for instance, into modulations in luminance or the intact blue-yellow channel [32]. This raw correction is then refined by a local contrast-scaling module, which uses a Gaussian-blurred grayscale image to create a spatial mask. This mask amplifies corrections in high-contrast edge regions critical for detail recognition while attenuating them in uniform areas to prevent noise amplification. The scaled correction is added back to the original linear RGB image, and the result is clamped to the valid intensity range before final gamma compression [33]. The entire process is validated through a comprehensive output suite, generating eight figures that include the original, three simulations, three corrected versions, and a diagnostic panel with error maps and color histograms for quantitative and qualitative analysis [34].

5. Design Matlab Simulation and Analysis

The simulation process is a systematic linear algebraic transformation of color information grounded in human cone physiology. It begins by loading and normalizing a standard RGB image, then critically removes the non-linear gamma encoding to work with linear light values.

Table 2: Color Blindness Simulator & Corrector

This linear RGB data is converted into the LMS color space using the Hunt-Pointer-Estevez matrix, representing pixel colors as the theoretical stimulations of the eye’s Long, Medium, and Short-wavelength cone types. For each target deficiency Protanopia, Deuteranopia, and Tritanopia a specific Brettel-Vienot projection matrix is applied. This matrix mathematically collapses the three-dimensional LMS data by removing or blending the dimension corresponding to the non-functioning cone, projecting the full-color information onto a two-dimensional plane perceivable by a dichromat. A continuous severity parameter allows for a tunable linear blend between the original LMS data and the fully projected state, modeling both total absence and partial deficiency of cone function. The core operation reshapes the three-channel LMS image into a large matrix where each column is a pixel’s LMS vector, enabling efficient bulk matrix multiplication. The projection is applied, and the result is reshaped back into image form [35]. This simulated LMS data is then converted back to the linear RGB color space using the inverse transformation matrix. The resulting linear RGB values represent how the original colors would be perceived after the simulated cone loss. Finally, the image undergoes gamma re-compression to match standard display expectations and is clamped to the valid zero-to-one intensity range. This complete pipeline, executed separately for each deficiency type, produces a perceptually accurate simulation that shows not just which colors are confused, but how the entire color composition of the image shifts due to the physiological constraint, providing a direct visual understanding of the accessibility barrier.

This figure presents the unaltered, full-color input image in its standard RGB format, serving as the essential visual baseline and reference point for all subsequent analyses. The peppers provide a rich, diverse palette of reds, greens, yellows, and purples, making it an ideal test subject for evaluating color transformations. Every simulation and correction process described in this work begins from this exact set of pixel data. It represents the world as perceived by a typical trichromat with normal color vision. The accuracy and perceptual fidelity of all following simulations are judged by their deviation from this ground truth. This baseline is critical for understanding the specific color information that becomes compromised for individuals with color vision deficiencies and for quantifying the effectiveness of the applied corrections.

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This visualization depicts how the original image is perceived by an individual with Protanopia, a deficiency where the long-wavelength (L) cones responsible for red light perception are absent or non-functional. The simulation uses a physiological projection matrix to collapse the LMS color space, effectively removing the red-sensitive dimension. Consequently, colors that rely on red differentiation such as the vibrant red and green peppers lose their distinctiveness and appear as shades of yellow, brown, and olive. The overall scene retains luminance detail but suffers a severe loss in chromatic contrast in the red-green axis, demonstrating a common accessibility failure in content that uses these colors to convey separate information.

This figure illustrates the simulated view for Deuteranopia, a condition involving the absence of medium-wavelength (M) cones, which are sensitive to green light. While similar in effect to Protanopia from a perceptual standpoint, the underlying mathematical projection targets a different axis in the LMS cone-response space. The result is again a collapse of the red-green color channel, causing confusion between reds and greens, but with a subtly different mapping that often renders reds as dimmer, muddier tones compared to the Protanopic simulation. This subtlety underscores the importance of modeling each deficiency type with its unique transformation matrix rather than a generic “red-green” filter.

This output simulates Tritanopia, a rarer blue-yellow color blindness caused by missing short-wavelength (S) cones. The projection matrix here collapses color information along the blue-sensitive axis. The effect is profoundly different from red-green deficiencies; blues become desaturated and shift towards gray or green, while yellows and violets lose their defining chromatic components. In the test image, purple areas may blend with blues, and the yellow pepper’s vibrancy is diminished. This simulation highlights that color accessibility challenges are not limited to red-green confusion and must be considered across the entire spectrum for truly inclusive design.

This image is the result of applying the Daltonization correction algorithm specifically optimized for a Protanopic viewer. The algorithm analyzes the perceptual error between the original and simulated images and strategically redistributes the lost red-green information into the luminance (brightness) channel and the intact blue-yellow channel. The correction enhances edge contrast and textural details that were lost in the simulation, such as the boundary between the red and green peppers, without attempting to restore the “true” red color. The goal is not normal vision but improved intelligibility, making the content more accessible by providing alternative visual cues.

Similar to the Protanopia correction, this figure shows the Daltonized result for Deuteranopia. Using the same error redistribution principle but accounting for the different spectral loss profile, the algorithm amplifies discernible contrasts for the Deuteranopic visual system. Corrections often involve subtle boosts in luminance variation and strategic shifts in the blue-yellow spectrum to compensate for the missing green-sensitive data. Comparing this corrected version to Figure 3 demonstrates how information originally encoded in the lost channel can be partially recovered and presented in a perceivable form, mitigating the confusion present in the raw simulation.

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This corrected image addresses the unique challenges of Tritanopia. The Daltonization process here redirects the lost blue-yellow information primarily into the red-green and luminance channels, which remain functional for this deficiency type. The result often introduces subtle magenta or reddish tinges to areas that were confused blues or purples in the simulation, and enhances the contrast of yellow features against their backgrounds. This correction exemplifies the algorithm’s adaptability, using a different error redistribution strategy tailored to the specific cone-type absence, proving the framework’s versatility across the spectrum of color vision deficiencies.

This composite diagnostic panel provides quantitative and qualitative insights into the simulation process. The three error maps (top-left, top-right, bottom-left) visually encode the absolute pixel-wise difference between the original image and each simulation, with brighter areas indicating greater perceptual change. These maps clearly show that red and green regions generate the most error for Protanopia and Deuteranopia, while blue and yellow areas dominate the error for Tritanopia. The bottom-right histogram plots the distribution of red, green, and blue pixel intensities in the original image, revealing the color composition that the simulations must transform. Together, these subplots offer a comprehensive analytical summary of the transformations’ localized impact and the original image’s color statistics.

6. Results and Discussion

The results from the MATLAB implementation provide both a compelling visual demonstration and quantitative validation of the color vision deficiency model. The three primary simulations Protanopia, Deuteranopia, and Tritanopia visibly confirm the expected perceptual collapses, with the peppers image showing characteristic confusions: reds and greens blending into muddy yellows and browns for the first two, and blues and yellows losing vibrancy for the latter [36]. The high MSE values and correspondingly low PSNR scores quantitatively underscore the significant information loss inherent in these conditions, formally validating the simulations’ deviation from the original [37]. The subsequent corrected images demonstrate the practical efficacy of the Daltonization algorithm, where reintroduced contrast and strategically shifted hues create clearer separations between previously confused regions, such as the edges of the red and green peppers. This visual improvement confirms the core hypothesis that lost color information can be partially recovered through intelligent remapping into preserved perceptual channels. Discussion of these results highlights several key insights. First, the physiological accuracy achieved by operating in the LMS space, as opposed to simpler RGB filtering, is evident in the nuanced differences between Protanopic and Deuteranopic simulations, which generic models often treat identically. The success of the contrast-aware correction emphasizes that enhancing local luminance variation is frequently more critical than attempting to restore original colors, aligning with known visual processing where edge detection precedes color interpretation [38]. However, the corrections also introduce unavoidable, sometimes unnatural, color shifts (e.g., magenta tints in the Tritanopia correction), revealing a fundamental trade-off between accessibility and aesthetic fidelity. This underscores that algorithmic correction is an assistive tool, not a perfect solution, and should complement not replace inherently accessible design principles like using patterns, labels, or high luminance contrast. The framework’s modularity, with its tunable severity and separate correction pathway, makes it a versatile platform for both educational demonstration and practical design testing, bridging theoretical color science and applied digital accessibility.

7. Conclusion

In conclusion, this work successfully demonstrates a comprehensive, physiologically grounded MATLAB framework for simulating and correcting color vision deficiencies. By leveraging the LMS color space and Brettel-Vienot projections, the model provides accurate, tunable simulations of Protanopia, Deuteranopia, and Tritanopia, moving beyond simplistic filters [39]. The integrated Daltonization algorithm with contrast-aware error redistribution effectively enhances image discernibility for colorblind viewers, addressing real-world accessibility challenges. The results confirm that while perfect color restoration is impossible, intelligent remapping of lost information can significantly improve visual intelligibility [40]. This tool serves as a vital bridge between color theory and practical application, empowering designers, developers, and educators to create more inclusive digital content. Ultimately, it underscores the importance of embedding accessibility considerations directly into the design and development workflow.

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