We present SyNoRiM, a novel way to jointly register multiple non-rigid shapes
by synchronizing the maps relating learned functions defined on the point
clouds. Even though the ability to process non-rigid shapes is critical in
various applications ranging from computer animation to 3D digitization, the
literature still lacks a robust and flexible framework to match and align a
collection of real, noisy scans observed under occlusions. Given a set of such
point clouds, our method first computes the pairwise correspondences
parameterized via functional maps. We simultaneously learn potentially
non-orthogonal basis functions to effectively regularize the deformations,
while handling the occlusions in an elegant way. To maximally benefit from the
multi-way information provided by the inferred pairwise deformation fields, we
synchronize the pairwise functional maps into a cycle-consistent whole thanks
to our novel and principled optimization formulation. We demonstrate via
extensive experiments that our method achieves a state-of-the-art performance
in registration accuracy, while being flexible and efficient as we handle both
non-rigid and multi-body cases in a unified framework and avoid the costly
optimization over point-wise permutations by the use of basis function maps.

利用 SyNoRiM，我们提供一种新的方法，通过同步点云上定义的学习功能的映射以联合注册多个非刚性形状，以既处理非刚性形状，又处理多体情况为特点，避免了点对点排列的昂贵优化。