In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/DeformationBasis.

翻译：在这项工作中,我们提出了一种新颖的方法,通过利用变形场的减少代表来计算非硬性物体之间的对应关系。不同于通过培训通用神经网络来代表变形场的现有工程,我们主张以无网状方法为基础近似。我们让网络在空间的零星位置(节点)学习变形参数,在保证平稳的情况下,以封闭形式重建连续变形场。随着自由度的下降,我们显示数据效率方面的显著改善,从而允许有限的监督。此外,我们的近似提供了直接接触变形场的第一阶衍生物的途径,这有利于有效执行理想的正规化。我们产生的模型具有很高的显性力量,能够捕捉到复杂的变形。我们通过多种变形形状匹配基准的先进结果来展示其有效性。我们的代码和数据在https://github.com/Sententent07/DefreformatBasis上公开提供。