Point cloud registration is to estimate a transformation to align point
clouds collected in different perspectives. In learning-based point cloud
registration, a robust descriptor is vital for high-accuracy registration.
However, most methods are susceptible to noise and have poor generalization
ability on unseen datasets. Motivated by this, we introduce SphereNet to learn
a noise-robust and unseen-general descriptor for point cloud registration. In
our method, first, the spheroid generator builds a geometric domain based on
spherical voxelization to encode initial features. Then, the spherical
interpolation of the sphere is introduced to realize robustness against noise.
Finally, a new spherical convolutional neural network with spherical integrity
padding completes the extraction of descriptors, which reduces the loss of
features and fully captures the geometric features. To evaluate our methods, a
new benchmark 3DMatch-noise with strong noise is introduced. Extensive
experiments are carried out on both indoor and outdoor datasets. Under
high-intensity noise, SphereNet increases the feature matching recall by more
than 25 percentage points on 3DMatch-noise. In addition, it sets a new
state-of-the-art performance for the 3DMatch and 3DLoMatch benchmarks with
93.5\% and 75.6\% registration recall and also has the best generalization
ability on unseen datasets.

点云配准研究中，引入了 SphereNet 以学习一个对噪音具有鲁棒性且适用于未知数据集的描述符。通过球体体素化和球面插值等方法，提取特征，并在新的 3DMatch-noise 基准测试中得到了 25% 以上的特征匹配召回率的提升，同时在 3DMatch 和 3DLoMatch 基准测试中取得了最佳性能，具有出色的泛化能力。

SphereNet: 学习点云配准的噪声鲁棒性和通用描述器

SphereNet: Learning a Noise-Robust and General Descriptor for Point  Cloud Registration

We consider representation learning of 3D molecular graphs in which each atom
is associated with a spatial position in 3D. This is an under-explored area of
research, and a principled message passing framework is currently lacking. In
this work, we conduct analyses in the spherical coordinate system (SCS) for the
complete identification of 3D graph structures. Based on such observations, we
propose the spherical message passing (SMP) as a novel and powerful scheme for
3D molecular learning. SMP dramatically reduces training complexity, enabling
it to perform efficiently on large-scale molecules. In addition, SMP is capable
of distinguishing almost all molecular structures, and the uncovered cases may
not exist in practice. Based on meaningful physically-based representations of
3D information, we further propose the SphereNet for 3D molecular learning.
Experimental results demonstrate that the use of meaningful 3D information in
SphereNet leads to significant performance improvements in prediction tasks.
Our results also demonstrate the advantages of SphereNet in terms of
capability, efficiency, and scalability. Our code is publicly available as part
of the DIG library (this https URL).

本文提出了一种基于球面坐标系的球面消息传递（SMP）算法和 SphereNet 模型，在可以区分几乎所有分子结构的同时提高了预测性能，证明其在大规模分子中具有高效性和可扩展性的优势。

3D 图形网络的球形消息传递

Spherical Message Passing for 3D Graph Networks

Convolution as inner product has been the founding basis of convolutional
neural networks (CNNs) and the key to end-to-end visual representation
learning. Benefiting from deeper architectures, recent CNNs have demonstrated
increasingly strong representation abilities. Despite such improvement, the
increased depth and larger parameter space have also led to challenges in
properly training a network. In light of such challenges, we propose
hyperspherical convolution (SphereConv), a novel learning framework that gives
angular representations on hyperspheres. We introduce SphereNet, deep
hyperspherical convolution networks that are distinct from conventional inner
product based convolutional networks. In particular, SphereNet adopts
SphereConv as its basic convolution operator and is supervised by generalized
angular softmax loss - a natural loss formulation under SphereConv. We show
that SphereNet can effectively encode discriminative representation and
alleviate training difficulty, leading to easier optimization, faster
convergence and comparable (even better) classification accuracy over
convolutional counterparts. We also provide some theoretical insights for the
advantages of learning on hyperspheres. In addition, we introduce the learnable
SphereConv, i.e., a natural improvement over prefixed SphereConv, and
SphereNorm, i.e., hyperspherical learning as a normalization method.
Experiments have verified our conclusions.

本文提出了基于超球面的学习框架 ——SphereConv，以及其在超球面上的深度学习网络 SphereNet，使用广义角 softmax 损失函数实现监督。实验证明，SphereNet 能够有效编码具有辨别力的特征表示并缓解训练困难，使优化更容易，收敛更快，并且分类准确度（甚至更好）与基于传统卷积的网络相当。