Threshold matrices and dithering — dither • gghalftone

The threshold matrices behind levels = k quantisation. bayer_matrix() is the ordered-dither matrix of size n (a power of two); blue_noise_matrix() is a void-and-cluster matrix (cached, seeded) whose thresholds are evenly spread with no periodic structure. dither_bayer() and dither_blue_noise() quantise a tone matrix z in [0, 1] to levels steps and dither the remainder with the tiled matrix.

Usage

bayer_matrix(n = 4)

blue_noise_matrix(n = 32, sigma = 1.5)

dither_blue_noise(z, levels = 1, n = 32)

dither_bayer(z, levels = 1, n = 4)

Arguments

n: Matrix size (Bayer: 2, 4, 8, ...; blue noise: 32 by default).
sigma: Gaussian width, in cells, of the energy filter used to build the blue-noise matrix.
z: Numeric matrix of tone in [0, 1].
levels: Number of quantisation steps.

Value

A numeric matrix of thresholds in (0, 1) (matrices), or a quantised tone matrix (dither functions).

Details

Use Bayer for graded tone and blue noise for a binary stipple (levels = 1). You rarely need to call these functions directly. Pass levels and algorithm to geom_halftone() or with_halftone() instead. By default, tone is continuous and no dithering takes place.

References

Bayer, B. E. (1973). An optimum method for two-level rendition of continuous-tone pictures. IEEE International Conference on Communications, 26, 11-15. Floyd, R. W., and Steinberg, L. (1976). An adaptive algorithm for spatial greyscale. Proceedings of the Society for Information Display, 17(2), 75-77. Ulichney, R. (1993). The void-and-cluster method for dither array generation. Proceedings of SPIE, 1913, 332-343. doi:10.1117/12.152707

Examples

bayer_matrix(2)
#>       [,1]  [,2]
#> [1,] 0.125 0.625
#> [2,] 0.875 0.375
range(blue_noise_matrix(32))
#> [1] 0.0004882812 0.9995117188