  Point Cloud Registration is a fundamental and challenging problem in 3D
computer vision. Recent works often utilize the geometric structure information
in point feature embedding or outlier rejection for registration while
neglecting to consider explicitly isometry-preserving constraint ($e.g.,$ point
pair linked edge's length preserving after transformation) in training. We
claim that the explicit isometry-preserving constraint is also important for
improving feature representation abilities in the feature training stage. To
this end, we propose a \underline{G}raph \underline{M}atching
\underline{O}ptimization based \underline{Net}work (GMONet for short), which
utilizes the graph-matching optimizer to explicitly exert the isometry
preserving constraints in the point feature training to improve the point
feature representation. Specifically, we exploit a partial graph-matching
optimizer to optimize the super point ($i.e.,$ down-sampled key points)
features and a full graph-matching optimizer to optimize fine-level point
features in the overlap region. Meanwhile, we leverage the inexact proximal
point method and the mini-batch sampling technique to accelerate these two
graph-matching optimizers. Given high discriminative point features in the
evaluation stage, we utilize the RANSAC approach to estimate the transformation
between the scanned pairs. The proposed method has been evaluated on the
3DMatch/3DLoMatch benchmarks and the KITTI benchmark. The experimental results
show that our method performs competitively compared to state-of-the-art
baselines.
