This paper proposes BPNet, a novel end-to-end deep learning framework to
learn B\'ezier primitive segmentation on 3D point clouds. The existing works
treat different primitive types separately, thus limiting them to finite shape
categories. To address this issue, we seek a generalized primitive segmentation
on point clouds. Taking inspiration from B\'ezier decomposition on NURBS
models, we transfer it to guide point cloud segmentation casting off primitive
types. A joint optimization framework is proposed to learn B\'ezier primitive
segmentation and geometric fitting simultaneously on a cascaded architecture.
Specifically, we introduce a soft voting regularizer to improve primitive
segmentation and propose an auto-weight embedding module to cluster point
features, making the network more robust and generic. We also introduce a
reconstruction module where we successfully process multiple CAD models with
different primitives simultaneously. We conducted extensive experiments on the
synthetic ABC dataset and real-scan datasets to validate and compare our
approach with different baseline methods. Experiments show superior performance
over previous work in terms of segmentation, with a substantially faster
inference speed.

本论文提出了 BPNet，一种新颖的端到端深度学习框架，用于学习在 3D 点云上的 Bézier 基元分割。通过将 Bézier 分解应用于点云分割，我们能够实现有限形状类别的广义基元分割。我们提出了一个联合优化框架，在级联架构上同时学习 Bézier 基元分割和几何拟合。通过引入软投票正则化器和自动权重嵌入模块，我们使网络更具鲁棒性和通用性。我们还引入了一个重构模块，通过该模块可以同时处理具有不同基元的多个 CAD 模型。我们在合成的 ABC 数据集和实际扫描数据集上进行了大量实验证实并与不同的基准方法进行了比较。实验证明，我们的方法在分割方面具有卓越的性能，并且推理速度显著得更快。

BPNet：三维点云的贝塞尔基元分割

BPNet: Bézier Primitive Segmentation on 3D Point Clouds

2D image representations are in regular grids and can be processed
efficiently, whereas 3D point clouds are unordered and scattered in 3D space.
The information inside these two visual domains is well complementary, e.g., 2D
images have fine-grained texture while 3D point clouds contain plentiful
geometry information. However, most current visual recognition systems process
them individually. In this paper, we present a \emph{bidirectional projection
network (BPNet)} for joint 2D and 3D reasoning in an end-to-end manner. It
contains 2D and 3D sub-networks with symmetric architectures, that are
connected by our proposed \emph{bidirectional projection module (BPM)}. Via the
\emph{BPM}, complementary 2D and 3D information can interact with each other in
multiple architectural levels, such that advantages in these two visual domains
can be combined for better scene recognition. Extensive quantitative and
qualitative experimental evaluations show that joint reasoning over 2D and 3D
visual domains can benefit both 2D and 3D scene understanding simultaneously.
Our \emph{BPNet} achieves top performance on the ScanNetV2 benchmark for both
2D and 3D semantic segmentation. Code is available at
https://github.com/wbhu/BPNet.

提出一种双向投影网络（BPNet），它包括 2D 和 3D 子网络，通过双向投影模块允许这两个视觉领域之间的互动，实现更好的场景识别。该算法在 2D 和 3D 语义分割方面，取得了 ScanNetV2 基准的最佳性能。