Chenxi Liu¹, Siqi Wang², Matthew Fisher³, Deepali Aneja³, Alec Jacobson^1,3

¹University of Toronto, ²New York University, Courant Institute of Mathematical Sciences, ³Adobe Research, San Francisco

This repository contains the research code for the paper “2D Neural Fields with Learned Discontinuities.” It implements our discontinuous neural field and the end-to-end pipelines to fit images (and depth maps) while recovering unknown discontinuities.

• Linux, NVIDIA GPU recommended
• Python 3.8 (via conda), PyTorch 2.0.1 + CUDA 11.8
• torch-scatter (installed from the PyG wheel index)
• External meshing binary: TriWild

Create and activate the environment:

# From the repo root
conda env create -f environment.yml
conda activate discontinuity2d

Install torch-scatter manually after activating the env:

pip install torch-scatter -f https://data.pyg.org/whl/torch-2.0.1%2Bcu118.html

TriWild must be discoverable; set an explicit path if not on PATH:

export TRIWILD_PATH=/path/to/TriWild

Add the repo root to PYTHONPATH (or call as a module):

export PYTHONPATH="$(pwd):${PYTHONPATH}"

Run the end-to-end pipeline with a PNG (or a depth grayscale image if using --depth). If an SVG is not specified, a default unknown.svg is used:

python launching/run_pipeline.py path/to/your.png --snapshot outputs/run1

Optionally provide an SVG explicitly to define discontinuity locations:

python launching/run_pipeline.py path/to/your.png path/to/your.svg --snapshot outputs/run1

Useful options (see --help for full list):

• --fit selects the representation to optimize:
  • unknown_discontinuity (default): infer edges while fitting
  • discontinuity: use known SVG discontinuities (TriWild “known” mode)
  • per_vertex, per_edge: ablations/baselines
• --config-json: path to a JSON with overrides merged into defaults. Meshing parameters live here (no extra CLI flags):
  • defgrid_config.triwild_edge_r: TriWild target edge-length ratio (e.g., 0.003–0.02)
  • To disable remeshing: set defgrid_config.remesh_epoch to 0 (or omit the key)
• --depth: treat the input as a depth target (grayscale PNG)
• --debug: enables intermediate logs/plots. Default runs are quiet but show tqdm progress bars

Example presets live under inputs/ (e.g., inputs/diffusion_curves/diffusion_curves.json).

Final artifacts are saved under --snapshot:

• fit_final.png: single-sample render (spp = 1) at input resolution
• fit_final_spp.png: anti-aliased render (spp = 16) at input resolution
• fit_final_spp_2x.png: anti-aliased render (spp = 16) at 2× upscaled resolution

• geometry/ — meshing, remeshing, and geometric utilities (TriWild interface, Canny edges)
• learning/ — sampling strategies and data helpers
• neural/ — neural field models and utilities
• pipeline/ — pipeline stages used by the launcher
• launching/run_pipeline.py — top-level entry point
• inputs/ — sample data and JSON configs (e.g., artistic, diffusion_curves, rendering)
• outputs/ — example outputs and snapshots

Sample inputs and configs are provided under inputs/. You can point the launcher to your own image (PNG) and optional SVG. For diffusion-generated depth map cleanup, pass --depth and a grayscale PNG. Artistic inputs are by Oscar Chávez (CC BY-NC-SA 2.0): inputs/artistic/009.jpg, inputs/artistic/014.jpg, inputs/artistic/019.jpg. Other inputs are created by us and can be used under CC0.

• If torch-scatter fails to install, use the PyG index matching your exact Torch/CUDA.
• If TriWild is not found, set TRIWILD_PATH to its binary or add it to PATH.
• CUDA mismatches: ensure your driver/runtime align with pytorch-cuda=11.8 in the environment.

This project is licensed under the Apache License, Version 2.0 — see LICENSE for details.

Notices: see NOTICE for attributions and third-party notices.

@article{discontinuities2d,
	title={2D Neural Fields with Learned Discontinuities},
	author={Liu, Chenxi and Wang, Siqi and Fisher, Matthew and Aneja, Deepali and Jacobson, Alec},
	booktitle={Computer Graphics Forum},
	lccn={2004233670},
	issn={0167-7055},
	year={2025},
	publisher={North Holland},
	volume={44},
	year={2025-05},
	organization={Wiley Online Library}
}