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

CVPR, Volume abs/1811.07782, 2019, Pages 998-1008.

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Keywords:
feature extractiongeometric structurepoint setlocal geometric structurepoint cloudMore(7+)
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We address the problem of modeling local geometric structure amongst points with geometric structure by applying a convolutional-like operation operation and a hierarchical feature extraction framework dubbed Geo-convolutional neural networks

Abstract:

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 hie...More

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Introduction
  • With the development of popular sensors such as RGBD cameras and LIDAR, 3D point clouds can be acquired and directly processed in many computer vision tasks [64, 19, 38, 30, 55, 28, 16, 56, 8, 61].
  • To learn 3D representation at high resolution, kd-tree and octree based methods hierarchically partition space to exploit input sparsity [24, 39]
  • Those methods focus more on subdivision of a volume rather than local geometric structure.
  • To improve the ability to handle local feature extraction, PointNet++ [35] aggregates features in local regions hierarchically
  • These methods still ignore the geometric structure amongst points by treating points independently in the global or local point sets
Highlights
  • With the development of popular sensors such as RGBD cameras and LIDAR, 3D point clouds can be acquired and directly processed in many computer vision tasks [64, 19, 38, 30, 55, 28, 16, 56, 8, 61]
  • We propose a novel convolution-like operation geometric structure by applying a convolutional-like operation (GeoConv) to explicitly model the geometric structure amongst points throughout the hierarchy of feature extraction
  • By decomposing the edge feature extraction process into three orthogonal directions, we reduce the variance of the absolute coordinates of the point cloud, and encourage the network to learn edge features along each basis independently; by aggregating the features according to the geometric relationship between the edge vector and the bases, we explicitly model the geometric structure amongst points
  • By learning geometric modeling using GeoConv, we model and preserve the geometric structure of 3D point clouds at every level of our hierarchical feature extraction framework
  • We address the problem of modeling local geometric structure amongst points with GeoConv operation and a hierarchical feature extraction framework dubbed Geo-convolutional neural networks (CNNs)
  • GeoConv explicitly models the geometric structure between two points by decomposing the feature extraction process onto three orthogonal directions, and aggregating the features based on the angles between the edge vector and the bases
Methods
  • PointNet[33] PointNet++[35] DeepSets[62]

    ECC[43] OctNet[39] O-CNN[49] Kd-Net[24] EdgeConv[50] SO-Net[27] SpiderCNN[53] SCN[52] MRTNet[13] SpecGCNN[48] The authors' baseline Geo-CNN Geo-CNN+ MV-Approx.
  • Accuracy Class 86.2 83.2 83.8 88.5 90.2 90.8 87.6 88.2 91.1 91.6 point clouds obtained by sensors, e.g., LIDAR, only contain points from frontal surfaces due to occlusion.
  • To illustrate the effectiveness of Geo-CNN on realworld 3D points, the authors evaluate on 3D object detection using the KITTI dataset [17].
  • For fair comparison with the state-of-the-art detection methods, the authors directly replace the PointNet feature extraction module in the Frustum PointNet v1 [32] detection pipeline with Geo-CNN, and use the 2D bounding box proposals released by [32] in the experiments.
  • Since only train/val proposals of frustum pointnet are published, the authors conduct evaluation using the protocol described in [32, 63] and use their training/testing split
Conclusion
  • The authors address the problem of modeling local geometric structure amongst points with GeoConv operation and a hierarchical feature extraction framework dubbed Geo-CNN.
  • Inspired by the success of exploiting local structure using CNNs on 2D image analysis task, the authors propose to extract features from each point and its local neighborhood with a convolutional-like operation.
  • GeoConv explicitly models the geometric structure between two points by decomposing the feature extraction process onto three orthogonal directions, and aggregating the features based on the angles between the edge vector and the bases.
  • The Geo-CNN with GeoConv operation achieves state-of-the-art performance on the challenging ModelNet40 and KITTI datasets
Summary
  • Introduction:

    With the development of popular sensors such as RGBD cameras and LIDAR, 3D point clouds can be acquired and directly processed in many computer vision tasks [64, 19, 38, 30, 55, 28, 16, 56, 8, 61].
  • To learn 3D representation at high resolution, kd-tree and octree based methods hierarchically partition space to exploit input sparsity [24, 39]
  • Those methods focus more on subdivision of a volume rather than local geometric structure.
  • To improve the ability to handle local feature extraction, PointNet++ [35] aggregates features in local regions hierarchically
  • These methods still ignore the geometric structure amongst points by treating points independently in the global or local point sets
  • Methods:

    PointNet[33] PointNet++[35] DeepSets[62]

    ECC[43] OctNet[39] O-CNN[49] Kd-Net[24] EdgeConv[50] SO-Net[27] SpiderCNN[53] SCN[52] MRTNet[13] SpecGCNN[48] The authors' baseline Geo-CNN Geo-CNN+ MV-Approx.
  • Accuracy Class 86.2 83.2 83.8 88.5 90.2 90.8 87.6 88.2 91.1 91.6 point clouds obtained by sensors, e.g., LIDAR, only contain points from frontal surfaces due to occlusion.
  • To illustrate the effectiveness of Geo-CNN on realworld 3D points, the authors evaluate on 3D object detection using the KITTI dataset [17].
  • For fair comparison with the state-of-the-art detection methods, the authors directly replace the PointNet feature extraction module in the Frustum PointNet v1 [32] detection pipeline with Geo-CNN, and use the 2D bounding box proposals released by [32] in the experiments.
  • Since only train/val proposals of frustum pointnet are published, the authors conduct evaluation using the protocol described in [32, 63] and use their training/testing split
  • Conclusion:

    The authors address the problem of modeling local geometric structure amongst points with GeoConv operation and a hierarchical feature extraction framework dubbed Geo-CNN.
  • Inspired by the success of exploiting local structure using CNNs on 2D image analysis task, the authors propose to extract features from each point and its local neighborhood with a convolutional-like operation.
  • GeoConv explicitly models the geometric structure between two points by decomposing the feature extraction process onto three orthogonal directions, and aggregating the features based on the angles between the edge vector and the bases.
  • The Geo-CNN with GeoConv operation achieves state-of-the-art performance on the challenging ModelNet40 and KITTI datasets
Tables
  • Table1: ModelNet40 Shape Classification Results. We sort the previous methods by time
  • Table2: Performance Comparison in 3D Object Detection: average precision (in %) on KITTI validation set. Geo-CNN achieves significantly better performance when compared with the baseline, which demonstrates the effectiveness of our decomposition-aggregation method on modeling local geometry. Our Frustum Geo-CNN is implemented based on Frustum PointNet v1, and it outperforms both Frustum PointNet v1 and v2
  • Table3: Ablation Study: Different Geometric Modeling Methods. We study different ways to model local geometry amongst points using ModelNet40 dataset. "Baseline + 3D Coords" directly learns the geometric structure with 3D coordinates of the two points at every layer of the network; "GeoConv - Learned-Agg"
  • Table4: Ablation Study: Model Complexity. We add channels to the weight matrix of the reduction layer of the baseline method
  • Table5: Overall Accuracy on ModelNet40 with Different Multiview Augmentations. "Data Aug." and "MV-Approx." refer to input-level augmentation and our feature-level multi-view approximation
Download tables as Excel
Related work
  • Motivated by the recent development in 3D sensor technology, increasing attention has been drawn to developing efficient and effective representations on 3D point clouds for shape classification, shape synthesis and modeling, indoor navigation, 3D object detection, etc.[47, 53, 54, 44, 22, 57, 46, 40, 1, 25, 52, 37, 9, 12]. Some earlier works constructed hand-crafted feature descriptors to capture local geometric structure and model local similarity between shapes [2, 6, 3, 20, 42, 41]. More recently, deep neural networks have been used to learn representations directly from data. One intuitive way to model the unstructured geometric data is voxelization, which represents a point cloud as a regular 3D grid over which 3D ConvNets can be easily applied [63, 34, 51, 31, 5, 4, 10, 29]. However, volumetric methods usually produce 3D grids which are sparsely occupied in the space. Their exponentially growing computational cost associated with making the grid finer limits the resolution in each volumetric grid, and leads to quantization artifacts. Due to its regular structures and scalability compared to uniform grids, some indexing techniques such as kd-tree and octree have also been applied to model point clouds [24, 39], but those methods still focus more on subdivision of a volume rather than modeling local geometric structure.
Funding
  • This research was partially supported by National Key R&D Program of China (No 2017YFA0700800). The research was partially supported by the Office of Naval Research under Grant N000141612713: Visual Common Sense Reasoning for Multi-agent Activity Prediction and Recognition
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