We introduce a novel data-driven approach aimed at designing high-quality shape deformations based on a coarse localized input signal. Unlike previous data-driven methods that require a global shape encoding, we observe that detail-preserving deformations can be estimated reliably without any global context in certain scenarios. Building on this intuition, we leverage Jacobians defined in a one-ring neighborhood as a coarse representation of the deformation. Using this as the input to our neural network, we apply a series of MLPs combined with feature smoothing to learn the Jacobian corresponding to the detail-preserving deformation, from which the embedding is recovered by the standard Poisson solve. Crucially, by removing the dependence on a global encoding, every \textit{point} becomes a training example, making the supervision particularly lightweight. Moreover, when trained on a class of shapes, our approach demonstrates remarkable generalization across different object categories. Equipped with this novel network, we explore three main tasks: refining an approximate shape correspondence, unsupervised deformation and mapping, and shape editing. Our code is made available at https://github.com/sentient07/LJN

翻译：本文提出一种新颖的数据驱动方法，旨在基于粗糙的局部输入信号设计高质量的形状形变。与以往需要全局形状编码的数据驱动方法不同，我们发现在某些场景下，无需任何全局上下文信息即可可靠地估计出细节保持形变。基于这一观察，我们利用单环邻域内定义的雅可比矩阵作为形变的粗糙表示。以此作为神经网络的输入，我们应用一系列结合特征平滑处理的多层感知机来学习对应于细节保持形变的雅可比矩阵，随后通过标准泊松求解恢复嵌入表示。关键的是，通过消除对全局编码的依赖，每个\textit{点}都成为一个训练样本，使得监督过程特别轻量化。此外，当在某一类形状上进行训练时，我们的方法在不同物体类别间展现出卓越的泛化能力。借助这一新型网络，我们探索了三个主要任务：近似形状对应的精细化、无监督形变与映射，以及形状编辑。我们的代码公开于 https://github.com/sentient07/LJN。