Color To Grayscale By Quantization and Integration

The conversion of color images to grayscale involves reducing the three-dimensional color space into a single luminance dimension, resulting in a one-to-many mapping. Although the number of colors in an image vastly exceeds what can be represented in grayscale, the number of visually distinguishable colors in a scene is often limited. Building on this observation, we propose a four-step approach to grayscale conversion. First, the color data are clustered using k-means into a limited number of centroids. Second, the luminance of each centroid is computed and distributed evenly across the luminance space. Third, these luminance values are optimized to maximize the overall gradient in the image. When the centroids and their corresponding pixel groups are mapped back to the image, the result is a quantized grayscale version that preserves distinctions between the color regions in the original image. However, this quantization introduces visual artifacts. To address these, we iteratively adjust the Laplacian of the grayscale image to approximate that of the original color image, ultimately achieving an artifact-free result with enhanced local and global contrast.