Neural Poisson Solver：一种用于自然信号融合的通用连续框架
Neural Poisson Solver: A Universal and Continuous Framework for Natural Signal Blending
AI总结：
针对传统方法用于INR视觉信号融合易产生失真伪影的问题，提出基于连续泊松方程的即插即用通用框架Neural Poisson Solver，含梯度引导解算器与对应损失优化方案，无需额外先验，多任务下鲁棒性获实验验证。
摘要：
隐式神经表征（Implicit Neural Representation, INR）已成为表征视觉信号（例如2D图像和3D场景）的流行方法，在各类下游应用中展现出可观的效果。鉴于其作为视觉信号媒介的潜力，探索利用INR的神经融合方法是自然的发展方向。神经融合指将两个INR合并，生成一个包含两种原始表征信息的全新INR。一种直接方法是将传统图像编辑方法应用于INR渲染流程，但该方法通常会产生融合失真、伪影和色偏，主要原因是底层像素网格的离散化，以及求解变分问题时引入的边界条件。为解决这一问题，我们提出Neural Poisson Solver（神经泊松解算器），这是一个即插即用、可跨不同信号维度通用的框架，用于融合以INR表征的视觉信号。我们的Neural Poisson Solver提供了一种基于连续泊松方程的变分问题求解方法，在多个领域均展现出卓越性能。具体而言，我们提出一种梯度引导的神经解算器来表征变分问题的求解过程，对目标信号进行优化以实现自然的融合效果。我们还设计了基于泊松方程的损失函数与优化方案来训练该解算器，确保其在有效融合输入INR场景的同时，保留场景的固有结构和语义内容。由于无需依赖额外先验知识，我们的方法可轻松适配各类任务场景，凸显了其通用性。全面的实验结果验证了我们的方法在多维度、多融合任务中的鲁棒性。
英文摘要：
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.
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