标题： 预条件变形网格 显示英文标题

标题： Preconditioned Deformation Grids

摘要： 从点云序列中对物体进行动态表面重建是计算机图形学中的一个具有挑战性的领域。 现有方法要么需要多个正则化项，要么需要大量训练数据，然而这会导致重建精度的妥协以及过度平滑或对未见过的物体和运动的泛化能力差。 为了解决这些限制，我们引入了预条件变形网格，这是一种新颖的技术，可以直接从无结构点云序列中估计一致的变形场，而无需要求或形成显式对应关系。 我们方法的关键在于使用多分辨率体素网格，以在不同空间尺度上捕捉整体运动，从而实现更灵活的变形表示。 结合将基于网格的Sobolev预条件引入基于梯度的优化，我们证明在输入点云以及不断演变的模板网格之间应用Chamfer损失就足以获得准确的变形。 为了确保物体表面上的时间一致性，我们在网格边线上包含了一个弱等距损失，这在不约束变形保真度的情况下补充了主要目标。 广泛的评估表明，与最先进的技术相比，我们的方法在长序列上取得了更优的结果。 显示英文摘要

摘要： Dynamic surface reconstruction of objects from point cloud sequences is a challenging field in computer graphics. Existing approaches either require multiple regularization terms or extensive training data which, however, lead to compromises in reconstruction accuracy as well as over-smoothing or poor generalization to unseen objects and motions. To address these lim- itations, we introduce Preconditioned Deformation Grids, a novel technique for estimating coherent deformation fields directly from unstructured point cloud sequences without requiring or forming explicit correspondences. Key to our approach is the use of multi-resolution voxel grids that capture the overall motion at varying spatial scales, enabling a more flexible deformation representation. In conjunction with incorporating grid-based Sobolev preconditioning into gradient-based optimization, we show that applying a Chamfer loss between the input point clouds as well as to an evolving template mesh is sufficient to obtain accurate deformations. To ensure temporal consistency along the object surface, we include a weak isometry loss on mesh edges which complements the main objective without constraining deformation fidelity. Extensive evaluations demonstrate that our method achieves superior results, particularly for long sequences, compared to state-of-the-art techniques.