# Neural Poisson Solver: A Universal and Continuous Framework for Natural Signal Blending

arXiv: https://arxiv.org/abs/2407.08457 · HTML: https://mlsanity.com/paper/2407.08457/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 27 of 27)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Zero-Shot Text-Guided Object Generation with Dream Fields](https://mlsanity.com/paper/2112.01455/) (2021)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [TF-ICON: Diffusion-Based Training-Free Cross-Domain Image Composition](https://mlsanity.com/paper/2307.12493/) (2023)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [StylizedNeRF: Consistent 3D Scene Stylization as Stylized NeRF via 2D-3D Mutual Learning](https://mlsanity.com/paper/2205.12183/) (2022)
- [Stylizing 3D Scene via Implicit Representation and HyperNetwork](https://mlsanity.com/paper/2105.13016/) (2021)
- [ObjectFolder 2.0: A Multisensory Object Dataset for Sim2Real Transfer](https://mlsanity.com/paper/2204.02389/) (2022)
- [Unified Implicit Neural Stylization](https://mlsanity.com/paper/2204.01943/) (2022)
- [Deep Image Blending](https://mlsanity.com/paper/1910.11495/) (2019)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [UPST-NeRF: Universal Photorealistic Style Transfer of Neural Radiance Fields for 3D Scene](https://mlsanity.com/paper/2208.07059/) (2022)
- [Non-line-of-Sight Imaging via Neural Transient Fields](https://mlsanity.com/paper/2101.00373/) (2021)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)
- [RecolorNeRF: Layer Decomposed Radiance Fields for Efficient Color Editing of 3D Scenes](https://mlsanity.com/paper/2301.07958/) (2023)
- [Blended-NeRF: Zero-Shot Object Generation and Blending in Existing Neural Radiance Fields](https://mlsanity.com/paper/2306.12760/) (2023)
- [PaletteNeRF: Palette-based Color Editing for NeRFs](https://mlsanity.com/paper/2212.12871/) (2022)
- [Volumetric Disentanglement for 3D Scene Manipulation](https://mlsanity.com/paper/2206.02776/) (2022)
- [FPM-INR: Fourier ptychographic microscopy image stack reconstruction using implicit neural representations](https://mlsanity.com/paper/2310.18529/) (2023)

## Built on by (most cited first, 1 of 1)

- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)

## Abstract (arXiv)

Implicit Neural Representation (INR) has become a popular method for representing visual signals (e.g., 2D images and 3D scenes), demonstrating promising results in various downstream applications. Given its potential as a medium for visual signals, exploring the development of a neural blending method that utilizes INRs is a natural progression. Neural blending involves merging two INRs to create a new INR that encapsulates information from both original representations. A direct approach involves applying traditional image editing methods to the INR rendering process. However, this method often results in blending distortions, artifacts, and color shifts, primarily due to the discretization of the underlying pixel grid and the introduction of boundary conditions for solving variational problems. To tackle this issue, we introduce the Neural Poisson Solver, a plug-and-play and universally applicable framework across different signal dimensions for blending visual signals represented by INRs. Our Neural Poisson Solver offers a variational problem-solving approach based on the continuous Poisson equation, demonstrating exceptional performance across various domains. Specifically, we propose a gradient-guided neural solver to represent the solution process of the variational problem, refining the target signal to achieve natural blending results. We also develop a Poisson equation-based loss and optimization scheme to train our solver, ensuring it effectively blends the input INR scenes while preserving their inherent structure and semantic content. The lack of dependence on additional prior knowledge makes our method easily adaptable to various task categories, highlighting its versatility. Comprehensive experimental results validate the robustness of our approach across multiple dimensions and blending tasks.