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Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning
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Proposes dot-controllable neural halftoning that places discrete ink dots on a canvas and moves them via a learned motion predictor, made differentiable by a one-hot dot encoding network (O-Net).
Problem
Deep learning halftoning maps images to near-binary outputs in a black-box, image-level way, giving no direct control over individual ink dots or the dot count, and producing artifacts that are hard to fix locally.
Approach
Treat halftoning as sprinkling a set of discrete ink dots on a canvas: O-Net makes dot coordinates differentiable by mapping them to one-hot encodings whose outer products form each dot's binary matrix (Hadamard product gives the halftone), and P-Net predicts per-dot displacement from the grayscale image and current halftone, with a frozen inverse-halftoning network as a loss.
Key results
- Average PSNR of 43.04 dB on 64x64 test images, versus 41.18 for Ostromoukhov's method and 33.83 for Xia's method.
- Average SSIM of 0.1709, higher than Ostromoukhov's 0.1628 among compared baselines.
- Dot collisions reduce the ink dot count by only about 2-3%, and dot quantity can be controlled directly.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use ink dot-oriented neural halftoning instead of Ostromoukhov | Halftoning · Test images | PSNR (Avg.): 41.18 -> 43.04 | Helped |
| use ink dot-oriented neural halftoning instead of Floyd-Steinberg | Halftoning · Test images | SSIM (Avg.): 0.1687 -> 0.1709 | Helped |
| refine local ink-dot positions to address artifacts | Our method · Local artifact refinement | PSNR: 37.24 -> 44.10 -> 44.43 | Helped |
| refine local ink-dot positions to address artifacts | Our method · Local artifact refinement | SSIM: 0.00756 -> 0.00772 -> 0.00776 | Helped |
Surprising findings
- Learned halftoning achieves higher average PSNR than most classical error-diffusion methods but has the widest min-max spread in PSNR (2.18 std), so not uniformly better.
Limitations
- Dot collisions during movement reduce the dot count slightly (2-3%) and are not yet handled.
- Experiments are limited to 64x64 resolution grayscale images in the main comparison.
- O-Net must be trained to convergence before halftone generation, adding a separate training stage.
Experimental setup
Datasets: DIV2K UTKFace
Benchmarks: DIV2K test images (64x64)
Metrics: PSNR SSIM
Baselines: Ordered Dithering Floyd-Steinberg error diffusion Ostromoukhov's method Xia's Method Jarvis-Judice-Ninke Stucki Atkinson Sierra
Builds on: Xia et al. halftoning network Ostromoukhov error diffusion
Closest papers by meaning
- Conditional Diffusion Process for Inverse Halftoning (NeurIPS 2022 · similarity 0.85)
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- Rethinking Peculiar Images by Diffusion Models: Revealing Local Minima’s Role (AAAI 2024 · similarity 0.80)
- MatFuse: Controllable Material Generation with Diffusion Models (CVPR 2024 · similarity 0.79)
- PixPerfect: Seamless Latent Diffusion Local Editing with Discriminative Pixel-Space Refinement (NeurIPS 2025 · similarity 0.79)
- Image Inpainting via Tractable Steering of Diffusion Models (ICLR 2024 · similarity 0.79)
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