点云蒙特卡罗卷积网络Monte Carlo Convolution

标题：Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds

作者：Hermosilla, P. and Ritschel, T. and Vazquez, P-P and Vinacua, A. and Ropinski, T.

来源：SIGGRAPH Asia 2018

链接：https://arxiv.org/abs/1806.01759

开源地址：https://github.com/viscom-ulm/MCCNN

介绍

深度学习系统广泛使用卷积运算来处理输入数据。虽然卷积对于结构化数据(如2D图像或3D卷)有明确的定义，但对于其他数据类型(如稀疏点云)则不是这样。以前的技术已经发展到在有限条件下近似卷积。不幸的是，它们的适用性有限，不能用于一般的点云。针对非均匀采样点云，利用现代采集技术，提出了一种高效的卷积学习方法。

网络是由四个创新性的关键部分实现的:首先，将卷积核本身表示为一个多层感知器; 第二，将卷积描述为蒙特卡罗积分问题; 第四，使用泊松磁盘采样（Poisson disk sampling）作为分层点云学习的可伸缩方法。

所有这些贡献的关键思想是从蒙特卡罗的角度保证充分考虑潜在的非均匀样本分布函数。为了使所提出的概念适用于实际任务，我们进一步提出了一个有效的实现，大大减少了训练过程中所需的GPU内存。通过将我们的方法应用于分层网络结构中，我们可以在已建立的点云分割、分类和常规估计基准上超越大多数最先进的网络。此外，与大多数现有的方法相比，我们还证明了我们的方法对采样变化的鲁棒性，即使只使用均匀采样的数据进行训练。

Introduction

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point clouds. Previous techniques have developed approximations to convolutions for restricted conditions. Unfortunately, their applicability is limited and cannot be used for general point clouds. We propose an efficient and effective method to learn convolutions for non-uniformly sampled point clouds, as they are obtained with modern acquisition techniques. Learning is enabled by four key novelties: first, representing the convolution kernel itself as a multilayer perceptron; second, phrasing convolution as a Monte Carlo integration problem, third, using this notion to combine information from multiple samplings at different levels; and fourth using Poisson disk sampling as a scalable means of hierarchical point cloud learning. The key idea across all these contributions is to guarantee adequate consideration of the underlying non-uniform sample distribution function from a Monte Carlo perspective. To make the proposed concepts applicable to real-world tasks, we furthermore propose an efficient implementation which significantly reduces the GPU memory required during the training process. By employing our method in hierarchical network architectures we can outperform most of the state-of-the-art networks on established point cloud segmentation, classification and normal estimation benchmarks. Furthermore, in contrast to most existing approaches, we also demonstrate the robustness of our method with respect to sampling variations, even when training with uniformly sampled data only.