无需重训练，一键编辑隐式神经几何模型的形状。
GENIE: Gram-Eigenmode INR Editing with Closed-Form Geometry Updates
- 利用特征的格拉姆矩阵提取可编辑的形变模式。
- 通过闭式更新实现一次操作完成几何编辑，无需优化。
- 适用于需要快速、精确修改3D形状的研究与工业场景。
隐式神经表示（INRs）能以紧凑形式建模几何结构，但其形状是否可编辑而无需重新训练仍不明确。本文发现，由INR倒数第二层特征诱导的格拉姆算子存在形变本征模式，这些模式可参数化实现实现的SDF零水平集编辑。关键发现是：这些模式并非仅依赖几何本身，只有在从足够丰富的采样分布中估计格拉姆算子时才可稳定恢复。我们推导出一种单步闭式更新方法，利用形变模式实现无需优化的几何编辑。理论分析表明，该方法可行的形变恰好位于这些形变模式的张量空间内，编辑过程在该空间中良定。
原文摘要 · Abstract (English)
Implicit Neural Representations (INRs) provide compact models of geometry, but it is unclear when their learned shapes can be edited without retraining. We show that the Gram operator induced by the INR's penultimate features admits deformation eigenmodes that parameterize a family of realizable edits of the SDF zero level set. A key finding is that these modes are not intrinsic to the geometry alone: they are reliably recoverable only when the Gram operator is estimated from sufficiently rich sampling distributions. We derive a single closed-form update that performs geometric edits to the INR without optimization by leveraging the deformation modes. We characterize theoretically the precise set of deformations that are feasible under this one-shot update, and show that editing is well-posed exactly within the span of these deformation modes.
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