PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds

3D Object Recognition with Ensemble Learning --- A Study of Point Cloud-Based Deep Learning Models

In this study, we present an analysis of model-based ensemble learning for 3D point-cloud object classification and detection. An ensemble of multiple model instances is known to outperform a single model instance, but there is little study of the topic of ensemble learning for 3D point clouds. First, an ensemble of multiple model instances trained on the same part of the $\textit{ModelNet40}$ dataset was tested for seven deep learning, point cloud-based classification algorithms: $\textit{PointNet}$, $\textit{PointNet++}$, $\textit{SO-Net}$, $\textit{KCNet}$, $\textit{DeepSets}$, $\textit{DGCNN}$, and $\textit{PointCNN}$. Second, the ensemble of different architectures was tested. Results of our experiments show that the tested ensemble learning methods improve over state-of-the-art on the $\textit{ModelNet40}$ dataset, from $92.65\%$ to $93.64\%$ for the ensemble of single architecture instances, $94.03\%$ for two different architectures, and $94.15\%$ for five different architectures. We show that the ensemble of two models with different architectures can be as effective as the ensemble of 10 models with the same architecture. Third, a study on classic bagging i.e. with different subsets used for training multiple model instances) was tested and sources of ensemble accuracy growth were investigated for best-performing architecture, i.e. $\textit{SO-Net}$. We also investigate the ensemble learning of $\textit{Frustum PointNet}$ approach in the task of 3D object detection, increasing the average precision of 3D box detection on the $\textit{KITTI}$ dataset from $63.1\%$ to $66.5\%$ using only three model instances. We measure the inference time of all 3D classification architectures on a $\textit{Nvidia Jetson TX2}$, a common embedded computer for mobile robots, to allude to the use of these models in real-life applications

3DTI-Net: Learn Inner Transform Invariant 3D Geometry Features using Dynamic GCN

Deep learning on point clouds has made a lot of progress recently. Many point cloud dedicated deep learning frameworks, such as PointNet and PointNet++, have shown advantages in accuracy and speed comparing to those using traditional 3D convolution algorithms. However, nearly all of these methods face a challenge, since the coordinates of the point cloud are decided by the coordinate system, they cannot handle the problem of 3D transform invariance properly. In this paper, we propose a general framework for point cloud learning. We achieve transform invariance by learning inner 3D geometry feature based on local graph representation, and propose a feature extraction network based on graph convolution network. Through experiments on classification and segmentation tasks, our method achieves state-of-the-art performance in rotated 3D object classification, and achieve competitive performance with the state-of-the-art in classification and segmentation tasks with fixed coordinate value

Dynamic Graph CNN for Learning on Point Clouds

Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS

GeoNet: Deep Geodesic Networks for Point Cloud Analysis

Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds. Thus we introduce GeoNet, the first deep learning architecture trained to model the intrinsic structure of surfaces represented as point clouds. To demonstrate the applicability of learned geodesic-aware representations, we propose fusion schemes which use GeoNet in conjunction with other baseline or backbone networks, such as PU-Net and PointNet++, for down-stream point cloud analysis. Our method improves the state-of-the-art on multiple representative tasks that can benefit from understandings of the underlying surface topology, including point upsampling, normal estimation, mesh reconstruction and non-rigid shape classification

Learning to Sample

Processing large point clouds is a challenging task. Therefore, the data is often sampled to a size that can be processed more easily. The question is how to sample the data? A popular sampling technique is Farthest Point Sampling (FPS). However, FPS is agnostic to a downstream application (classification, retrieval, etc.). The underlying assumption seems to be that minimizing the farthest point distance, as done by FPS, is a good proxy to other objective functions. We show that it is better to learn how to sample. To do that, we propose a deep network to simplify 3D point clouds. The network, termed S-NET, takes a point cloud and produces a smaller point cloud that is optimized for a particular task. The simplified point cloud is not guaranteed to be a subset of the original point cloud. Therefore, we match it to a subset of the original points in a post-processing step. We contrast our approach with FPS by experimenting on two standard data sets and show significantly better results for a variety of applications. Our code is publicly available at: https://github.com/orendv/learning_to_sampleComment: CVPR 201

PointHop: An Explainable Machine Learning Method for Point Cloud Classification

An explainable machine learning method for point cloud classification, called the PointHop method, is proposed in this work. The PointHop method consists of two stages: 1) local-to-global attribute building through iterative one-hop information exchange, and 2) classification and ensembles. In the attribute building stage, we address the problem of unordered point cloud data using a space partitioning procedure and developing a robust descriptor that characterizes the relationship between a point and its one-hop neighbor in a PointHop unit. When we put multiple PointHop units in cascade, the attributes of a point will grow by taking its relationship with one-hop neighbor points into account iteratively. Furthermore, to control the rapid dimension growth of the attribute vector associated with a point, we use the Saab transform to reduce the attribute dimension in each PointHop unit. In the classification and ensemble stage, we feed the feature vector obtained from multiple PointHop units to a classifier. We explore ensemble methods to improve the classification performance furthermore. It is shown by experimental results that the PointHop method offers classification performance that is comparable with state-of-the-art methods while demanding much lower training complexity.Comment: 13 pages with 9 figure

Local Spectral Graph Convolution for Point Set Feature Learning

Feature learning on point clouds has shown great promise, with the introduction of effective and generalizable deep learning frameworks such as pointnet++. Thus far, however, point features have been abstracted in an independent and isolated manner, ignoring the relative layout of neighboring points as well as their features. In the present article, we propose to overcome this limitation by using spectral graph convolution on a local graph, combined with a novel graph pooling strategy. In our approach, graph convolution is carried out on a nearest neighbor graph constructed from a point's neighborhood, such that features are jointly learned. We replace the standard max pooling step with a recursive clustering and pooling strategy, devised to aggregate information from within clusters of nodes that are close to one another in their spectral coordinates, leading to richer overall feature descriptors. Through extensive experiments on diverse datasets, we show a consistent demonstrable advantage for the tasks of both point set classification and segmentation

Modeling Local Geometric Structure of 3D Point Clouds using Geo-CNN

Recent advances in deep convolutional neural networks (CNNs) have motivated researchers to adapt CNNs to directly model points in 3D point clouds. Modeling local structure has been proven to be important for the success of convolutional architectures, and researchers exploited the modeling of local point sets in the feature extraction hierarchy. However, limited attention has been paid to explicitly model the geometric structure amongst points in a local region. To address this problem, we propose Geo-CNN, which applies a generic convolution-like operation dubbed as GeoConv to each point and its local neighborhood. Local geometric relationships among points are captured when extracting edge features between the center and its neighboring points. We first decompose the edge feature extraction process onto three orthogonal bases, and then aggregate the extracted features based on the angles between the edge vector and the bases. This encourages the network to preserve the geometric structure in Euclidean space throughout the feature extraction hierarchy. GeoConv is a generic and efficient operation that can be easily integrated into 3D point cloud analysis pipelines for multiple applications. We evaluate Geo-CNN on ModelNet40 and KITTI and achieve state-of-the-art performance

MOPS-Net: A Matrix Optimization-driven Network forTask-Oriented 3D Point Cloud Downsampling

This paper explores the problem of task-oriented downsampling over 3D point clouds, which aims to downsample a point cloud while maintaining the performance of subsequent applications applied to the downsampled sparse points as much as possible. Designing from the perspective of matrix optimization, we propose MOPS-Net, a novel interpretable deep learning-based method, which is fundamentally different from the existing deep learning-based methods due to its interpretable feature. The optimization problem is challenging due to its discrete and combinatorial nature. We tackle the challenges by relaxing the binary constraint of the variables, and formulate a constrained and differentiable matrix optimization problem. We then design a deep neural network to mimic the matrix optimization by exploring both the local and global structures of the input data. MOPS-Net can be end-to-end trained with a task network and is permutation-invariant, making it robust to the input. We also extend MOPS-Net such that a single network after one-time training is capable of handling arbitrary downsampling ratios. Extensive experimental results show that MOPS-Net can achieve favorable performance against state-of-the-art deep learning-based methods over various tasks, including classification, reconstruction, and registration. Besides, we validate the robustness of MOPS-Net on noisy data.Comment: 15 pages, 16 figures, 10 table