This paper focuses on the statistical analysis of shapes of data objects
called shape graphs, a set of nodes connected by articulated curves with
arbitrary shapes. A critical need here is a constrained registration of points
(nodes to nodes, edges to edges) across objects. This, in turn, requires
optimization over the permutation group, made challenging by differences in
nodes (in terms of numbers, locations) and edges (in terms of shapes,
placements, and sizes) across objects. This paper tackles this registration
problem using a novel neural-network architecture and involves an unsupervised
loss function developed using the elastic shape metric for curves. This
architecture results in (1) state-of-the-art matching performance and (2) an
order of magnitude reduction in the computational cost relative to baseline
approaches. We demonstrate the effectiveness of the proposed approach using
both simulated data and real-world 2D and 3D shape graphs. Code and data will
be made publicly available after review to foster research.

本文通过使用一种新颖的神经网络结构和基于弹性形状度量的无监督损失函数，解决了数据对象形状图之间的点和边的约束注册问题，实现了与基准方法相比具有最先进的匹配性能并且计算成本下降一个数量级。

形态图匹配网络（SGM-net）：统计形态分析的配准

Shape-Graph Matching Network (SGM-net): Registration for Statistical  Shape Analysis

We present a robust method to find region-level correspondences between
shapes, which are invariant to changes in geometry and applicable across
multiple shape representations. We generate simplified shape graphs by jointly
decomposing the shapes, and devise an adapted graph-matching technique, from
which we infer correspondences between shape regions. The simplified shape
graphs are designed to primarily capture the overall structure of the shapes,
without reflecting precise information about the geometry of each region, which
enables us to find correspondences between shapes that might have significant
geometric differences. Moreover, due to the special care we take to ensure the
robustness of each part of our pipeline, our method can find correspondences
between shapes with different representations, such as triangular meshes and
point clouds. We demonstrate that the region-wise matching that we obtain can
be used to find correspondences between feature points, reveal the intrinsic
self-similarities of each shape, and even construct point-to-point maps across
shapes. Our method is both time and space efficient, leading to a pipeline that
is significantly faster than comparable approaches. We demonstrate the
performance of our approach through an extensive quantitative and qualitative
evaluation on several benchmarks where we achieve comparable or superior
performance to existing methods.

提出一种鲁棒的方法，使用简化形状图形和图形匹配技术来找到不同表示方法下的形状区域对应关系，并且可以用于构建点对点的形状之间映射。