Being able to learn an effective semantic representation directly on raw
point clouds has become a central topic in 3D understanding. Despite rapid
progress, state-of-the-art encoders are restrictive to canonicalized point
clouds, and have weaker than necessary performance when encountering geometric
transformation distortions. To overcome this challenge, we propose PointTree, a
general-purpose point cloud encoder that is robust to transformations based on
relaxed K-D trees. Key to our approach is the design of the division rule in
K-D trees by using principal component analysis (PCA). We use the structure of
the relaxed K-D tree as our computational graph, and model the features as
border descriptors which are merged with pointwise-maximum operation. In
addition to this novel architecture design, we further improve the robustness
by introducing pre-alignment -- a simple yet effective PCA-based normalization
scheme. Our PointTree encoder combined with pre-alignment consistently
outperforms state-of-the-art methods by large margins, for applications from
object classification to semantic segmentation on various transformed versions
of the widely-benchmarked datasets. Code and pre-trained models are available
at this https URL

PointTree 是一个基于松弛 K-D 树，采用主成分分析作为分割规则的点云通用编码器，通过前向预对准进一步提高其鲁棒性，结合点描述符和点最大化操作达到优足以处理变形的点云数据的目标，在各种基准数据集上，其表现优于现有最先进方法。

PointTree：具有松弛 k-d 树的鲁棒变换点云编码器

PointTree: Transformation-Robust Point Cloud Encoder with Relaxed K-D  Trees

Recent theory work has found that a special type of spatial partition tree -
called a random projection tree - is adaptive to the intrinsic dimension of the
data from which it is built. Here we examine this same question, with a
combination of theory and experiments, for a broader class of trees that
includes k-d trees, dyadic trees, and PCA trees. Our motivation is to get a
feel for (i) the kind of intrinsic low dimensional structure that can be
empirically verified, (ii) the extent to which a spatial partition can exploit
such structure, and (iii) the implications for standard statistical tasks such
as regression, vector quantization, and nearest neighbor search.

本研究通过理论与实验结合的方法，探讨了更广泛的树类组合，以了解空间划分可以利用数据的内在低维结构的程度，对于回归、向量量化和最近邻搜索等标准统计任务的影响，并证实了随机投影树是适应数据固有维数的。