Point Convolutional Neural Networks by Extension Operators

Atzmon, Matan; Maron, Haggai; Lipman, Yaron

doi:10.48550/arxiv.1803.10091

Cited by 65 publications

(111 citation statements)

References 0 publications

Supporting

Mentioning

108

Contrasting

Order By: Relevance

“…Rotation invariant and equivariant point networks. State of the art S n invariant networks, e.g., (Qi et al, 2017a;Atzmon et al, 2018;Xu et al, 2018b; are not invariant/equivariant to rotations/reflections by construction (Chen et al, 2019). Invariance to global or local rotations can be achieved by modifying the 3D convolution operator or modifying the input representation.…”

Section: Previous Workmentioning

confidence: 99%

Frame Averaging for Invariant and Equivariant Network Design

Puny¹,

Atzmon²,

Ben-Hamu³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.

show abstract

Section: Previous Workmentioning

confidence: 99%

Frame Averaging for Invariant and Equivariant Network Design

Puny¹,

Atzmon²,

Ben-Hamu³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Input Acc(%) MVCNN [16] multi-view 90.1 OctNet [22] hybird grid octree 86.5 PointwiseCNN [41] 1K points 86.1 PointNet [6] 1K points 89.2 PCNN [42] 1K points 92.3 PointCNN [30] 1K points 92.5 PointWeb [43] 1K points+normal 92.3 PointConv [29] 1K points+normal 92.5 RS-CNN w/o vot. [37] 1K points 92.4 RS-CNN w vot.…”

Section: Methodsmentioning

confidence: 99%

“…mIoU(%) Ins. mIoU(%) PointNet [6] 80.4 83.7 SynspecCNN [45] 82.0 84.7 PCNN [42] 81.8 85.1 SpiderCNN [46] 82.4 85.3 PointCNN [30] 84.6 86.1 PointConv [29] 82.8 85.7 RS-CNN w/o vot. [37] 84.2 85.8 RS-CNN w/ vot.…”

Section: A Object Classificationmentioning

confidence: 99%

“…We draw these nodes with green of different brightness, the brightness of nodes is related to the weight, bright nodes have high value of weights and dark nodes have low value of weights. Here we visualize a local region with 64 neighboring points from 9 different channels to compare the Method mIoU(%) PointNet [6] 41.1 SegCloud [47] 48.9 TangentConv [48] 52.6 PointCNN [30] 57.3 ParamConv [49] 58.3 SPG [50] 58.0 PointWeb [43] 60.2 PCNN [42] 58.2 FPConv [9] 62.8 Point2Node [44] 62.9 KPConv rigid [8] 65.4 KPConv deform [8] 67.1 PosPool [39] 66.7 PointNet++ [7] 53.5 Ours(*PointNet++) 54.5(1.0 ↑) DGCNN [11] 56. contribution of each point. Fig.…”

Section: Ablation Studiesmentioning

confidence: 99%

See 1 more Smart Citation

PAPooling: Graph-based Position Adaptive Aggregation of Local Geometry in Point Clouds

Wang¹,

Ding³

et al. 2021

Preprint

View full text Add to dashboard Cite

Fine-grained geometry, captured by aggregation of point features in local regions, is crucial for object recognition and scene understanding in point clouds. Nevertheless, existing preeminent point cloud backbones usually incorporate max/average pooling for local feature aggregation, which largely ignores points' positional distribution, leading to inadequate assembling of fine-grained structures. To mitigate this bottleneck, we present an efficient alternative to max pooling, Position Adaptive Pooling (PAPooling), that explicitly models spatial relations among local points using a novel graph representation, and aggregates features in a position adaptive manner, enabling position-sensitive representation of aggregated features. Specifically, PAPooling consists of two key steps, Graph Construction and Feature Aggregation, respectively in charge of constructing a graph with edges linking the center point with every neighboring point in a local region to map their relative positional information to channel-wise attentive weights, and adaptively aggregating local point features based on the generated weights through Graph Convolution Network (GCN). PAPooling is simple yet effective, and flexible enough to be ready to use for different popular backbones like PointNet++ and DGCNN, as a plug-andplay operator. Extensive experiments on various tasks ranging from 3D shape classification, part segmentation to scene segmentation well demonstrate that PAPooling can significantly improve predictive accuracy, while with minimal extra computational overhead. Code will be released.

show abstract

“…SpiderCNN [48] defines its convolution kernel as a family of polynomial functions, relying on the neighbors' order. PCNN [2] designs point kernels based on the spatial coordinates and further KPConv [36] presents a scalable convolution using explicit kernel points. RS-CNN [22] assigns channel-wise weights to neighboring point features according to the geometric relations learned from 10-D vectors.…”

Section: Related Workmentioning

confidence: 99%

Adaptive Graph Convolution for Point Cloud Analysis

Zhou

Feng

Fang³

et al. 2021

Preprint

View full text Add to dashboard Cite

Convolution on 3D point clouds that generalized from 2D grid-like domains is widely researched yet far from perfect. The standard convolution characterises feature correspondences indistinguishably among 3D points, presenting an intrinsic limitation of poor distinctive feature learning. In this paper, we propose Adaptive Graph Convolution (AdaptConv) which generates adaptive kernels for points according to their dynamically learned features. Compared with using a fixed/isotropic kernel, AdaptConv improves the flexibility of point cloud convolutions, effectively and precisely capturing the diverse relations between points from different semantic parts. Unlike popular attentional weight schemes, the proposed AdaptConv implements the adaptiveness inside the convolution operation instead of simply assigning different weights to the neighboring points. Extensive qualitative and quantitative evaluations show that our method outperforms state-of-the-art point cloud classification and segmentation approaches on several benchmark datasets. Our code is available at https://github.com/ hrzhou2/AdaptConv-master.

show abstract

Point Convolutional Neural Networks by Extension Operators

Cited by 65 publications

References 0 publications

Frame Averaging for Invariant and Equivariant Network Design

Frame Averaging for Invariant and Equivariant Network Design

PAPooling: Graph-based Position Adaptive Aggregation of Local Geometry in Point Clouds

Adaptive Graph Convolution for Point Cloud Analysis

Contact Info

Product

Resources

About