# 2D Neural Fields with Learned Discontinuities

arXiv: https://arxiv.org/abs/2408.00771 · HTML: https://mlsanity.com/paper/2408.00771/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 83 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Repurposing Diffusion-Based Image Generators for Monocular Depth Estimation](https://mlsanity.com/paper/2312.02145/) (2023)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [ACORN: Adaptive Coordinate Networks for Neural Scene Representation](https://mlsanity.com/paper/2105.02788/) (2021)
- [A Multi-Implicit Neural Representation for Fonts](https://mlsanity.com/paper/2106.06866/) (2021)
- [Compact Neural Graphics Primitives with Learned Hash Probing](https://mlsanity.com/paper/2312.17241/) (2023)
- [Inverse Diffusion Curves using Shape Optimization](https://mlsanity.com/paper/1610.02769/) (2016)
- [Differentiable Visual Computing for Inverse Problems and Machine Learning](https://mlsanity.com/paper/2312.04574/) (2023)
- [Field of Junctions: Extracting Boundary Structure at Low SNR](https://mlsanity.com/paper/2011.13866/) (2020)
- [Transforming a Non-Differentiable Rasterizer into a Differentiable One with Stochastic Gradient Estimation](https://mlsanity.com/paper/2404.09758/) (2024)
- [Scalable multi-class sampling via filtered sliced optimal transport](https://mlsanity.com/paper/2211.04314/) (2022)
- [Mumford-Shah Mesh Processing using the Ambrosio-Tortorelli Functional](https://mlsanity.com/paper/1806.05999/) (2018)

## Built on by (most cited first, 2 of 2)

- [SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiability](https://mlsanity.com/paper/2601.19683/) (2026)
- [Soft Anisotropic Diagrams for Differentiable Image Representation](https://mlsanity.com/paper/2604.21984/) (2026)

## Abstract (arXiv)

Effective representation of 2D images is fundamental in digital image processing, where traditional methods like raster and vector graphics struggle with sharpness and textural complexity respectively. Current neural fields offer high-fidelity and resolution independence but require predefined meshes with known discontinuities, restricting their utility. We observe that by treating all mesh edges as potential discontinuities, we can represent the magnitude of discontinuities with continuous variables and optimize. Based on this observation, we introduce a novel discontinuous neural field model that jointly approximate the target image and recovers discontinuities. Through systematic evaluations, our neural field demonstrates superior performance in denoising and super-resolution tasks compared to InstantNGP, achieving improvements of over 5dB and 10dB, respectively. Our model also outperforms Mumford-Shah-based methods in accurately capturing discontinuities, with Chamfer distances 3.5x closer to the ground truth. Additionally, our approach shows remarkable capability in handling complex artistic drawings and natural images.