FloydSteinberg

Floyd–Steinberg is a dithering algorithm used in image processing to convert grayscale or color images to a limited palette, such as black and white or a small set of colors, while preserving perceived tonal detail. It belongs to the family of error diffusion methods, where the quantization error from each processed pixel is distributed to neighboring pixels that have yet to be processed.

The method processes the image in a raster scan order (left to right, top to bottom). For each pixel, the algorithm assigns it the nearest color from the target palette and computes the quantization error as the difference between the original and the quantized value. This error is then distributed to adjacent future pixels using a fixed kernel: 7/16 of the error to the pixel to the right (x+1, y), 3/16 to the bottom-left (x-1, y+1), 5/16 to the pixel below (x, y+1), and 1/16 to the bottom-right (x+1, y+1). The sum of the weights equals 1, ensuring the global brightness is approximately preserved.

Developed by Robert W. Floyd and Louis Steinberg and introduced in 1976, the algorithm became one of the most widely used error-diffusion techniques due to its simplicity and high-quality halftone appearance. While it is computationally efficient and produces smooth gradients, it can produce visible patterns or artifacts in large flat regions or with certain palette choices. It is applicable to both grayscale and color images, with the diffusion applied independently to each color channel or using a perceptually weighted color space.