  Point cloud registration for 3D objects is a challenging task due to sparse
and noisy measurements, incomplete observations and large transformations. In
this work, we propose \textbf{G}raph \textbf{M}atching \textbf{C}onsensus
\textbf{Net}work (\textbf{GMCNet}), which estimates pose-invariant
correspondences for full-range Partial-to-Partial point cloud Registration
(PPR) in the object-level registration scenario. To encode robust point
descriptors, \textbf{1)} we first comprehensively investigate
transformation-robustness and noise-resilience of various geometric features.
\textbf{2)} Then, we employ a novel {T}ransformation-robust {P}oint
{T}ransformer (\textbf{TPT}) module to adaptively aggregate local features
regarding the structural relations, which takes advantage from both handcrafted
rotation-invariant ({\textit{RI}}) features and noise-resilient spatial
coordinates. \textbf{3)} Based on a synergy of hierarchical graph networks and
graphical modeling, we propose the {H}ierarchical {G}raphical {M}odeling
(\textbf{HGM}) architecture to encode robust descriptors consisting of i) a
unary term learned from {\textit{RI}} features; and ii) multiple smoothness
terms encoded from neighboring point relations at different scales through our
TPT modules. Moreover, we construct a challenging PPR dataset (\textbf{MVP-RG})
based on the recent MVP dataset that features high-quality scans. Extensive
experiments show that GMCNet outperforms previous state-of-the-art methods for
PPR. Notably, GMCNet encodes point descriptors for each point cloud
individually without using cross-contextual information, or ground truth
correspondences for training. Our code and datasets are available at:
https://github.com/paul007pl/GMCNet.
