Perceptually-Minimal Color Optimization for Web Accessibility: A Multi-Phase Constrained Approach

Web accessibility guidelines require sufficient color contrast between text and backgrounds; yet, manually adjusting colors often necessitates significant visual deviation, compromising vital brand aesthetics. We present a novel, multi-phase optimization approach for automatically generating WCAG-compliant colors while minimizing perceptual change to original design choices. Our method treats this as a constrained, non-linear optimization problem, utilizing the modern perceptually uniform OKLCH color space. Crucially, the optimization is constrained to preserve the original hue ($\text{H}$) of the color, ensuring that modifications are strictly limited to necessary adjustments in lightness ($\text{L}$) and chroma ($\text{C}$). This is achieved through a three-phase sequence: binary search, gradient descent, and progressive constraint relaxation. Evaluation on a dataset of 10,000 procedurally generated color pairs demonstrates that the algorithm successfully resolves accessibility violations in $77.22\%$ of cases, with $88.51\%$ of successful corrections exhibiting imperceptible color difference ($\Delta E_{2000} < 2.0$) as defined by standard perceptibility thresholds. The median perceptual change for successful adjustments is only $0.76\ \Delta E_{2000}$, and the algorithm achieves this with a median processing time of $0.876\text{ms}$ per color pair. The approach demonstrates that accessibility compliance and visual design integrity can be achieved simultaneously through a computationally efficient, perceptually-aware optimization that respects brand identity. The algorithm is publicly implemented in the open-source cm-colors Python library.