Existing point cloud representation learning methods primarily rely on data-driven strategies to extract geometric information from large amounts of scattered data. However, most methods focus solely on the spatial distribution features of point clouds while overlooking the relationship between local information and the whole structure, which limits the accuracy of point cloud representation. Local information reflect the fine-grained variations of an object, while the whole structure is determined by the interaction and combination of these local features, collectively defining the object's shape. In real-world, objects undergo deformation under external forces, and this deformation gradually affects the whole structure through the propagation of forces from local regions, thereby altering the object's geometric features. Therefore, appropriately introducing a physics-driven mechanism to capture the topological relationships between local parts and the whole object can effectively mitigate for the limitations of data-driven point cloud methods in structural modeling, and enhance the generalization and interpretability of point cloud representations for downstream tasks such as understanding and recognition. Inspired by this, we incorporate a physics-driven mechanism into the data-driven method to learn fine-grained features in point clouds and model the structural relationship between local regions and the whole shape. Specifically, we design a dual-task encoder-decoder framework that combines the geometric modeling capability of data-driven implicit fields with physics-driven elastic deformation. Through the integration of physics-based loss functions, the framework is guided to predict localized deformation and explicitly capture the correspondence between local structural changes and whole shape variations.

翻译：现有的点云表示学习方法主要依赖数据驱动策略从大量散乱数据中提取几何信息。然而，大多数方法仅关注点云的空间分布特征，而忽视了局部信息与整体结构之间的关系，这限制了点云表示的准确性。局部信息反映了物体的细粒度变化，而整体结构则由这些局部特征的相互作用与组合所决定，共同定义了物体的形状。在现实世界中，物体在外力作用下会发生变形，这种变形通过力从局部区域的传播逐渐影响整体结构，从而改变物体的几何特征。因此，适当引入物理驱动机制来捕捉局部部件与整体对象之间的拓扑关系，可以有效弥补数据驱动点云方法在结构建模方面的局限性，并增强点云表示在下游理解与识别等任务中的泛化能力和可解释性。受此启发，我们将物理驱动机制融入数据驱动方法中，以学习点云中的细粒度特征，并建模局部区域与整体形状之间的结构关系。具体而言，我们设计了一个双任务编码器-解码器框架，该框架结合了数据驱动隐式场的几何建模能力与物理驱动的弹性变形。通过引入基于物理的损失函数，该框架被引导预测局部化变形，并显式地捕捉局部结构变化与整体形状变化之间的对应关系。