Blue Noise

A comprehensive Rust implementation of Robert Ulichney's void-and-cluster algorithm for generating blue noise textures and applying high-quality dithering to images. Blue noise produces evenly distributed, visually pleasing dithered images without the clustering artifacts of white noise or the repetitive patterns of Bayer dithering.

✨ Features

• 🎨 Generate blue noise textures using the void-and-cluster algorithm
• 🖼️ Dither images with customizable colors and contrast
• ⚡ FFT-optimized Gaussian blur for power-of-two dimensions (~50% faster)
• 🔄 Seamless tiling - all textures use toroidal topology
• 🎲 Reproducible - seeded random number generation
• 📊 Progress indicators for long-running operations
• 🦀 Pure Rust - fast, safe, and dependency-minimal

📦 Installation

From crates.io

cargo install blue-noise

From source

git clone https://github.com/mblode/blue-noise.git
cd blue-noise
cargo build --release

The binary will be in target/release/blue-noise.

🚀 Usage

CLI Tool

Generate Blue Noise Textures

# Generate a 128x128 blue noise texture
blue-noise generate --size 128 --output blue-noise.png

# Generate with custom sigma and seed for reproducibility
blue-noise generate --size 64 --sigma 1.9 --seed 42 --verbose

# Quick 64x64 texture (2-5 seconds)
blue-noise generate -s 64 -o noise-64.png

# Larger 256x256 texture (several minutes)
blue-noise generate -s 256 -o noise-256.png --verbose

Options:

• -s, --size <SIZE> - Texture size (8-512, default: 128)
• -o, --output <PATH> - Output file path (default: blue-noise.png)
• --sigma <SIGMA> - Gaussian sigma (1.0-3.0, default: 1.9)
• --seed <SEED> - Random seed for reproducibility
• -v, --verbose - Show detailed progress

Dither Images

# Basic dithering
blue-noise dither -i input.jpg -o output.png

# Custom colors
blue-noise dither -i photo.jpg -o dithered.png \
  --foreground "#000000" \
  --background "#ffffff"

# Resize and adjust contrast
blue-noise dither -i image.png -o output.png \
  --width 800 \
  --contrast 1.2

# Use custom noise texture
blue-noise dither -i input.jpg -o output.png \
  --noise custom-noise.png \
  --foreground "#1a1a1a" \
  --background "#f0f0f0"

Options:

• -i, --input <PATH> - Input image path (required)
• -o, --output <PATH> - Output image path (required)
• -n, --noise <PATH> - Blue noise texture (default: blue-noise.png)
• -f, --foreground <HEX> - Foreground color (default: #000000)
• -b, --background <HEX> - Background color (default: #ffffff)
• -w, --width <PIXELS> - Output width (maintains aspect ratio)
• --height <PIXELS> - Output height (maintains aspect ratio)
• -c, --contrast <FLOAT> - Contrast adjustment (1.0 = normal)

Library Usage

Add to your Cargo.toml:

[dependencies]
blue-noise = "0.2"

Generate Blue Noise

use blue_noise::{BlueNoiseGenerator, BlueNoiseConfig, save_blue_noise_to_png};

// Create configuration
let config = BlueNoiseConfig {
    width: 128,
    height: 128,
    sigma: 1.9,
    seed: Some(42),
    verbose: true,
    ..Default::default()
};

// Generate texture
let generator = BlueNoiseGenerator::new(config)?;
let result = generator.generate()?;

// Save to file
save_blue_noise_to_png(&result, "blue-noise.png")?;

Apply Dithering

use blue_noise::{
    BlueNoiseTexture,
    Color,
    DitherOptions,
    apply_dithering
};

// Load blue noise texture
let noise = BlueNoiseTexture::load("blue-noise.png")?;

// Configure dithering
let options = DitherOptions {
    foreground: Color::from_hex("#000000")?,
    background: Color::from_hex("#ffffff")?,
    width: Some(800),
    height: None,
    contrast: Some(1.2),
};

// Apply dithering
apply_dithering("input.jpg", "output.png", &noise, options)?;

🎨 Examples

Before and After

Different Colors

# Sepia tone
blue-noise dither -i photo.jpg -o sepia.png \
  --foreground "#704214" --background "#f4e8d8"

# Blue on white
blue-noise dither -i image.jpg -o blue.png \
  --foreground "#0066cc" --background "#ffffff"

# Green matrix style
blue-noise dither -i code.jpg -o matrix.png \
  --foreground "#00ff00" --background "#000000"

🔬 Algorithm

This implementation uses Ulichney's void-and-cluster algorithm, which produces high-quality blue noise with evenly distributed energy at high frequencies and minimal low-frequency content.

Why Blue Noise?

• White noise: Random distribution creates visible clusters and voids
• Bayer dithering: Regular patterns create repetitive artifacts
• Blue noise: Evenly distributed with minimal low-frequency patterns ✓

Generation Process

1. Phase 0: Generate initial binary pattern with random points
2. Phase 1: Serialize initial points by removing from tightest clusters
3. Phase 2: Fill to half capacity by adding to largest voids
4. Phase 3: Invert and fill to completion
5. Phase 4: Convert ranks to threshold map (0-255)

The algorithm uses toroidal topology (wraparound edges) to ensure seamless tiling, making it perfect for dithering large images with small noise textures.

Performance

For power-of-two dimensions, Gaussian blur is performed in the frequency domain using FFT, providing ~50% performance improvement through the convolution theorem:

convolution(A, B) = IFFT(FFT(A) × FFT(B))

Generation times:

• 64×64: ~2-5 seconds
• 128×128: ~30-60 seconds
• 256×256: Several minutes

Tip: Pre-generate textures rather than generating at runtime.

📚 References

• Ulichney, R. (1993). "Void-and-cluster method for dither array generation" Proceedings of SPIE 1913, Human Vision, Visual Processing, and Digital Display IV https://doi.org/10.1117/12.152707

• Ulichney, R. (1988). "Dithering with blue noise" Proceedings of the IEEE, 76(1), 56-79

🛠️ Development

# Build
cargo build --release

# Run tests
cargo test

# Run benchmarks
cargo bench

# Generate documentation
cargo doc --open

📄 License

MIT License - see LICENSE for details

🙏 Acknowledgments

• Robert Ulichney for the void-and-cluster algorithm
• Surma's Ditherpunk for inspiration
• TIGSource discussion

🤝 Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.