This paper presents an innovative enhancement to the Sphere as Prior
Generative Adversarial Network (SP-GAN) model, a state-of-the-art GAN designed
for point cloud generation. A novel method is introduced for point cloud
generation that elevates the structural integrity and overall quality of the
generated point clouds by incorporating topological priors into the training
process of the generator. Specifically, this work utilizes the K-means
algorithm to segment a point cloud from the repository into clusters and
extract centroids, which are then used as priors in the generation process of
the SP-GAN. Furthermore, the discriminator component of the SP-GAN utilizes the
identical point cloud that contributed the centroids, ensuring a coherent and
consistent learning environment. This strategic use of centroids as intuitive
guides not only boosts the efficiency of global feature learning but also
substantially improves the structural coherence and fidelity of the generated
point clouds. By applying the K-means algorithm to generate centroids as the
prior, the work intuitively and experimentally demonstrates that such a prior
enhances the quality of generated point clouds.

本研究提出了一种改进的 Sphere as Prior Generative Adversarial Network (SP-GAN) 模型，用于点云生成。该方法使用 K-means 算法将点云分割成聚类并提取质心，然后将质心作为先验用于 SP-GAN 的生成过程，以提高生成点云的结构完整性和质量。生成器的训练过程中还使用了与质心相关的相同点云，以确保连贯一致的学习环境。实验证明，使用 K-means 算法生成质心作为先验能够提高生成点云的质量。

利用拓扑先验增强点云生成技术

Exploiting Topological Prior for Boosting Point Cloud Generation

We present an approach to inform the reconstruction of a surface from a point
scan through topological priors. The reconstruction is based on basis functions
which are optimized to provide a good fit to the point scan while satisfying
predefined topological constraints. We optimize the parameters of a model to
obtain likelihood function over the reconstruction domain. The topological
constraints are captured by persistence diagrams which are incorporated in the
optimization algorithm promote the correct topology. The result is a novel
topology-aware technique which can: 1.) weed out topological noise from point
scans, and 2.) capture certain nuanced properties of the underlying shape which
could otherwise be lost while performing surface reconstruction. We showcase
results reconstructing shapes with multiple potential topologies, compare to
other classical surface construction techniques, and show the completion of
real scan data.

本文提出了一种基于拓扑先验的表面重建方法，该方法利用基函数来优化点云拟合，并通过持久图捕获拓扑约束，以实现去除拓扑噪声和捕获底层形状的特定属性。作者展示了在多种可能的拓扑情况下的表面重建结果，并将其与其他传统表面构建技术进行了比较。