Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called Flattening-Net to represent irregular 3D point clouds of arbitrary geometry and topology as a completely regular 2D point geometry image (PGI) structure, in which coordinates of spatial points are captured in colors of image pixels. \mr{Intuitively, Flattening-Net implicitly approximates a locally smooth 3D-to-2D surface flattening process while effectively preserving neighborhood consistency.} \mr{As a generic representation modality, PGI inherently encodes the intrinsic property of the underlying manifold structure and facilitates surface-style point feature aggregation.} To demonstrate its potential, we construct a unified learning framework directly operating on PGIs to achieve \mr{diverse types of high-level and low-level} downstream applications driven by specific task networks, including classification, segmentation, reconstruction, and upsampling. Extensive experiments demonstrate that our methods perform favorably against the current state-of-the-art competitors. We will make the code and data publicly available at https://github.com/keeganhk/Flattening-Net.

翻译：点云具有不规则性和非结构化特性，这对高效数据利用和判别性特征提取构成了挑战。本文提出了一种名为Flattening-Net的无监督深度神经网络架构，可将任意几何与拓扑结构的不规则三维点云转化为完全规则的二维点几何图像（PGI）结构——其中空间点的坐标通过图像像素颜色进行编码。直观而言，Flattening-Net隐式模拟了局部平滑的三维到二维曲面展平过程，同时有效保持了邻域一致性。作为一种通用表示模态，PGI天然编码了底层流形结构的内在属性，并促进了曲面风格的点特征聚合。为展示其潜力，我们构建了直接基于PGI的统一学习框架，通过特定任务网络驱动包括分类、分割、重建和上采样在内的多样化高层与低层下游应用。大量实验表明，我们的方法性能优于当前最先进的方法。相关代码与数据将在https://github.com/keeganhk/Flattening-Net 公开。