  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.
