用泊松方程实现表面学习的局部全局融合,兼顾精度与效率。
PoissonNet: A Local-Global Approach for Learning on Surfaces
- 以泊松方程为机制,结合局部特征变换与全局传播
- 在语义分割和动画表面参数化上达到当前最优性能
- 对网格剖分不敏感,计算开销小,适合大规模数据
现有网格上的网络架构在学习高频特征、感受野不足、对离散化敏感及计算开销大之间存在权衡。受经典网格处理中局部-全局方法启发,我们提出PoissonNet,一种新型神经架构,通过构建局部-全局学习框架克服上述缺陷。核心设计是:在网格梯度域应用可学习的局部特征变换,再求解泊松系统实现标量特征的全局传播。该框架保留特征全频谱,提供真正全局感受野,且对网格三角剖分保持不变性。构造高效,相比同类方法计算开销显著降低,支持数据集规模和单个样本尺寸的扩展。实验验证表明,在语义分割和高细节动画表面参数化任务中优于先前内在架构,达到最新水平。作为核心应用,PoissonNet在学习形变方面表现优异,显著超越现有表面学习架构。
原文摘要 · Abstract (English)
Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient computational overhead. Drawing from classic local-global approaches in mesh processing, we introduce PoissonNet, a novel neural architecture that overcomes all of these deficiencies by formulating a local-global learning scheme, which uses Poisson's equation as the primary mechanism for feature propagation. Our core network block is simple; we apply learned local feature transformations in the gradient domain of the mesh, then solve a Poisson system to propagate scalar feature updates across the surface globally. Our local-global learning framework preserves the features's full frequency spectrum and provides a truly global receptive field, while remaining agnostic to mesh triangulation. Our construction is efficient, requiring far less compute overhead than comparable methods, which enables scalability -- both in the size of our datasets, and the size of individual training samples. These qualities are validated on various experiments where, compared to previous intrinsic architectures, we attain state-of-the-art performance on semantic segmentation and parameterizing highly-detailed animated surfaces. Finally, as a central application of PoissonNet, we show its ability to learn deformations, significantly outperforming state-of-the-art architectures that learn on surfaces.
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