  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.
