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

TL;DR

The paper introduces the Neural Poisson Solver, a universal neural framework for blending visual signals represented by Implicit Neural Representations, addressing artifacts and distortions in traditional methods through a continuous variational approach.

Contribution

It presents a novel neural blending framework based on the continuous Poisson equation, enabling natural and artifact-free merging of INRs across different signal domains.

Findings

Achieves superior blending quality with minimal artifacts.

Demonstrates versatility across multiple signal types and tasks.

Outperforms traditional image editing methods in preserving structure.

Abstract

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.