Physics-Driven Local-Whole Elastic Deformation Modeling for Point Cloud Representation Learning

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.