# DGANet: A Dilated Graph Attention-Based Network for Local Feature Extraction on 3D Point Clouds

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- We utilize an improved k-nearest neighbor (K-NN) search algorithm to construct a local dilated graph for each point, which models the long-range geometric correlation between each point and its neighbors to help the point neural network learn more local features of each point with a larger receptive field when conducting the convolution operation.
- We embed an offset–attention mechanism into a designed module called dilated graph attention module (DGAM), which can dynamically learn local discriminative attention features on the constructed dilated graph-like data, and employ a graph attention pooling to aggregate the most significant features and better capture the local geometric details of each point.
- We propose a novel DGANet for local feature extraction on point clouds and carry out extensive experiments on two competitive benchmark datasets. The experimental results demonstrate that our method achieves considerable performance and outperforms several existing state-of-the-art methods in both 3D object classification and segmentation tasks.

## 2. Related Work

#### 2.1. Projection-Based Methods

#### 2.2. Voxel-Based Methods

#### 2.3. Point-Based Methods

#### 2.4. Graph-Based Methods

#### 2.5. Attention-Based Methods

## 3. Methods

#### 3.1. Network Architecture

_{C}object categories at object-level. Firstly, the point feature (N × 1024) generated by the encoder is processed by the max-pooling operation to achieve a global feature (1 × 1024). Next, the global feature is successively fed into two shared multi-layer perceptron (MLP) layers to predict the classification score of the point cloud belonging to N

_{C}object categories. The convolutional kernel size of the two shared MLP layers are 512 and 256, respectively, and the final classification result is determined by the category with the maximal score.

#### 3.2. Spatial Transformation Embedding

#### 3.3. Local Dilated Graph Construction

#### 3.3.1. Dilated K-NN Search

_{0}, p

_{1}, ..., p

_{n}} with p

_{i}ϵ R

^{C}, where n represents the number of points and C represents the feature dimension of each point. The point p

_{i}= {x

_{i}, y

_{i}, z

_{i}} is represented by its 3D coordinates, hence the C = 3. The goal is to select k dilated points m

_{i}= {p

_{i}

_{1}

^{[d]}, p

_{i}

_{2}

^{[d]}, …, p

_{ik}

^{[d]}} in the dilated scope d to calculate the edges of the next step.

#### 3.3.2. Edge Calculation

_{i}and its dilated points m

_{i}denote a local dilated graph G

_{d}= (V

_{d}, E

_{d}), where V

_{d}= {p

_{i}, m

_{i}} and E

_{d}= {e

_{i}

_{1}

^{[d]}, e

_{i}

_{2}

^{[d]}, …, e

_{ik}

^{[d]}}. The V

_{d}and E

_{d}represent a set of vertices and edges, respectively. We endeavor to construct the local dilated graph G

_{d}of each point p

_{i}with its multi-scope neighboring points m

_{i}for the representation of geometric correlations between local point clouds. The edges of the local dilated graph can be formulated using the general mathematical operation between the central point and its dilated points in a 3D local coordinate space. Each edge in the dilated graph G

_{d}can be calculated as follows:

_{ij}

^{[d]}denotes the j-th dilated point of the central point p

_{i}in the dilated scope d, and k denotes the selected number of the dilated neighborhood points. To make the edge features efficiently learnable and avoid gradient vanishing during the edge convolution, we utilize the concatenation operation to fuse the central point with the edge in feature dimension to enhance the edge feature. This inspiration comes from DGCNN [17].

#### 3.4. Dilated Graph Attention Module

#### 3.4.1. Dilated Edge Attention Convolution

_{i}, p

_{i}

_{1}, p

_{i}

_{2}, …, p

_{ik}}, h ϵ R

^{C}, where p

_{i}is the central point, and other points {p

_{i}

_{1}, p

_{i}

_{2}, …, p

_{ik}} are its k dilated neighbors. We consider a constructed local dilated graph G

_{d}= (V

_{d}, E

_{d}) and its directed edges E

_{d}= {e

_{i}

_{1}

^{[d]}, e

_{i}

_{2}

^{[d]}, …, e

_{ik}

^{[d]}}. Denote F = {f

_{1}, f

_{2}, …, f

_{n}} as a set of input–edge features and each feature f

_{i}ϵ R

^{C}is associated with a corresponding graph edge, where C is the number of feature dimensions. The designed DEACov aims to learn a function g: R

^{C}→ R

^{K}to transform the input–edge features into a new set of edge features F’ = {f’

_{1}, f’

_{2}, …, f’

_{n}} with f’

_{i}ϵ R

^{K}.

_{i}= {α

_{i}

_{1}, α

_{i}

_{2}, …, α

_{ik}} ϵ R

^{K}represents the attention–weight feature vector of k constructed edges of the central point, e

_{ij}

^{[d]}ϵ R

^{C}represents the j-th edge of the central point, and d represents the dilated scope rate which is used to adjust the receptive field of the constructed dilated graph. ||, e

_{ij}

^{[d]}, p

_{ij}

^{[d]}and p

_{i}are the same as mentioned above, and the mechanism a can be implemented by using a single multilayer perceptron (MLP), which can be formulated as follows:

_{a}: R

^{C}→ R

^{K}represents the shared multilayer perceptron (shared MLP) layer which realizes the mapping of input–edge features into higher-level features. E

_{ij}

^{[d]}is same as mentioned above.

_{i}, we utilize the Softmax function to normalize the obtained edge attention coefficients. Each edge attention score can be normalized as follows:

_{iu}represents the attention score of each edge and α

_{iu}represents the u-th unnormalized edge–attention weight of the attentional weight vector α

_{i}.

_{iu}and α’

_{iu}represent the attention–weight feature of the edge e

_{iu}

^{[d]}and its corresponding attention score, respectively. M

_{a}and * are the same as mentioned above.

#### 3.4.2. Graph Attention Pooling

_{i}represent the significant features of input local points and reference point p

_{i}, respectively, and e’

_{ij}represents the j-th enhanced edge of p

_{i}.

#### 3.5. Comparison with Existing Methods

_{i}which selects k local points near it, we define the local feature function of the reference point p

_{i}as follows:

_{ij}is the j-th corresponding neighboring point of reference point p

_{i}.

_{ij}. Thus, the local feature function in PointNet++ can be denoted as follows:

_{i}, and p

_{ij}are the same as mentioned above.

_{i}and its corresponding edge (p

_{ij}− p

_{i}). The local feature function can be defined as follow:

_{i}, and p

_{ij}are the same as mentioned above.

_{ij}represents the attentional score of j-th edge (p

_{ij}− p

_{i}) of the reference point p

_{i}, and mlp(.) and p

_{ij}are the same as mentioned above.

_{i}in our DGANet can be defined as follows:

_{i}, and p

_{ij}are the same as mentioned above.

## 4. Experiments

#### 4.1. Classification on the ModelNet40 Dataset

#### 4.1.1. Dataset

#### 4.1.2. Task and Metrics

_{i}represents the mean accuracy of the category i, N(TP)

_{i}and N

_{i}represent the number of 3D meshed models that correctly classified into category i and the number of 3D meshed models belonging to category i, respectively, and N

_{c}and N

_{T}represent the number of categories and number of total 3D meshed models, respectively.

#### 4.1.3. Implementation Details

#### 4.1.4. Results and Discussion

#### 4.1.5. Ablation Studies and Analysis

#### 4.2. Part Segmentation on the ShapeNet Part Dataset

#### 4.2.1. Dataset

#### 4.2.2. Task and Metrics

_{i}represents the averaged IoUs for all parts that fall into the same category I, N(TP)

_{i}represents the number of 3D models belonging to the category i and the parts of each 3D model that are correctly classified into their corresponding part categories, N(FP)

_{i}represents the number of 3D models belonging to category i and the wrong parts of each 3D model that are wrongly classified into correct part categories, N(FN)

_{i}represents the number of 3D models belonging to category i and the correct parts of each 3D model that are wrongly classified into wrong part categories, and N

_{c}represents the number of categories for all 3D models.

#### 4.2.3. Implementation Details

#### 4.2.4. Results and Discussion

#### 4.2.5. Ablation Studies and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The 3D illustration of the local feature extraction with different methods: (

**a**) With PointNet ++; (

**b**) With DGCNN; (

**c**) With our proposed DGANet.

**Figure 4.**The schematic illustration of the local graph construction: (

**a**) The construction of the local graph using normal K-NN; (

**b**) The construction of the local graph using our dilated K-NN.

**Figure 8.**The illustration of random input dropout in point cloud: (

**a**) Results of our network with random input dropout; (

**b**) Test samples with different numbers of points.

**Figure 9.**Visual comparison of part segmentation results on ShapeNet part dataset: (

**a**) Input point clouds; (

**b**) Ground truth labels; (

**c**) Results of PointNet; (

**d**) Results of DGCNN; (

**e**) Results of our DGANet. Red circles in this figure represent the local detailed segmentation results of the tested 3D models.

Method | Input | Points | mA (%) | OA (%) | Params (Million) | FLOPs (10^{8}) |
---|---|---|---|---|---|---|

3DShapeNets [7] | C | 1 k | 77.3 | 84.7 | - | - |

VoxNet [12] | C | 1 k | 83 | 85.9 | 0.77 | - |

PointNet [14] | C | 1 k | 86.2 | 89.2 | 3.48 | 1.88 |

Kc-Net [37] | C | 1 k | - | 91 | 0.9 | - |

Kd-Net [27] | C | 32 k | 88.5 | 91.8 | 2 | - |

PointNet++ (ssg) [15] | C | 1 k | - | 90.7 | 1.47 | 1.37 |

PointNet++ (msg) [15] | C, N | 5 k | - | 91.9 | 1.74 | 6.41 |

PointCNN [29] | C | 1 k | 88.1 | 92.2 | 0.45 | - |

SpiderCNN [38] | C, N | 1 k | - | 92.4 | - | - |

DGCNN [17] | C | 1 k | 89.5 | 91.9 | 1.84 | 4.63 |

PointCov [23] | C, N | 1 k | - | 92.2 | 1.96 | 1.87 |

Ours | C | 1 k | 89.4 | 92.3 | 1.72 | 4.31 |

Number of Neighbors (k) | Search Method of Local Graph Construction | mA (%) | OA (%) |
---|---|---|---|

10 | normal K-NN (d = 1) | 87.6 | 91.2 |

10 | dilated K-NN (d = 3) | 88.7 | 91.9 |

10 | dilated K-NN (d = 5) | 87.2 | 90.7 |

20 | normal K-NN (d = 1) | 88.6 | 91.9 |

20 | dilated K-NN (d = 2) | 89.4 | 92.3 |

20 | dilated K-NN (d = 3) | 88.4 | 91.1 |

30 | normal K-NN (d = 1) | 88.2 | 91.6 |

30 | dilated K-NN (d = 2) | 89.3 | 91.8 |

30 | dilated K-NN (d = 3) | 88.1 | 90.9 |

Method | pIoU | Air | Bag | Cap | Car | Cha. | Ear | Gua. | Kin. | Lam. | Lap | Mot. | Mug | Pis. | Roc. | Ska. | Tab. |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Kd-Net [27] | 82.3 | 80.1 | 74.6 | 74.3 | 70.3 | 88.6 | 73.5 | 90.2 | 87.2 | 81.0 | 94.9 | 57.4 | 86.7 | 78.1 | 51.8 | 69.9 | 80.3 |

Kc-Net [37] | 83.7 | 82.8 | 81.5 | 86.4 | 77.6 | 90.3 | 76.8 | 91.0 | 87.2 | 84.5 | 95.5 | 69.2 | 94.4 | 81.6 | 60.1 | 75.2 | 81.3 |

PointNet [14] | 83.7 | 83.4 | 78.7 | 82.5 | 74.9 | 89.6 | 73.0 | 91.5 | 85.9 | 80.8 | 95.3 | 65.2 | 93.0 | 81.2 | 57.9 | 72.8 | 80.6 |

3DmFV [39] | 84.3 | 82.0 | 84.3 | 86.0 | 76.9 | 89.9 | 73.9 | 90.8 | 85.7 | 82.6 | 95.2 | 66.0 | 94.0 | 82.6 | 51.5 | 73.5 | 81.8 |

PCNNet [40] | 85.1 | 82.4 | 80.1 | 85.5 | 79.5 | 90.8 | 73.2 | 91.3 | 86.0 | 85.0 | 95.7 | 73.2 | 94.8 | 83.3 | 51.0 | 75.0 | 81.8 |

DGCNN [17] | 85.1 | 84.2 | 83.7 | 84.4 | 77.1 | 90.9 | 78.5 | 91.5 | 87.3 | 82.9 | 96.0 | 67.0 | 93.3 | 82.6 | 59.7 | 75.5 | 82.0 |

SpiderCNN [38] | 85.3 | 83.5 | 81.0 | 87.2 | 77.5 | 90.7 | 76.8 | 91.1 | 87.3 | 83.3 | 95.8 | 70.2 | 93.5 | 82.7 | 59.7 | 75.8 | 82.8 |

SGPN [41] | 85.8 | 80.4 | 78.6 | 78.8 | 71.5 | 88.6 | 78.0 | 90.9 | 83.0 | 78.8 | 95.8 | 77.8 | 93.8 | 87.4 | 60.1 | 92.3 | 89.4 |

Ours | 85.2 | 84.6 | 85.7 | 87.8 | 78.5 | 91.0 | 77.3 | 91.2 | 87.9 | 82.4 | 95.8 | 67.8 | 94.2 | 81.1 | 59.7 | 75.7 | 82.0 |

Method | STE | DGAM | pIoU (%) | OA (%) |
---|---|---|---|---|

Network A | × | × | 83.7 | 93.6 |

Network B | √ | × | 84.1 | 93.8 |

Network C | × | √ | 84.7 | 94.0 |

Ours | √ | √ | 85.2 | 94.3 |

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## Share and Cite

**MDPI and ACS Style**

Wan, J.; Xie, Z.; Xu, Y.; Zeng, Z.; Yuan, D.; Qiu, Q.
DGANet: A Dilated Graph Attention-Based Network for Local Feature Extraction on 3D Point Clouds. *Remote Sens.* **2021**, *13*, 3484.
https://doi.org/10.3390/rs13173484

**AMA Style**

Wan J, Xie Z, Xu Y, Zeng Z, Yuan D, Qiu Q.
DGANet: A Dilated Graph Attention-Based Network for Local Feature Extraction on 3D Point Clouds. *Remote Sensing*. 2021; 13(17):3484.
https://doi.org/10.3390/rs13173484

**Chicago/Turabian Style**

Wan, Jie, Zhong Xie, Yongyang Xu, Ziyin Zeng, Ding Yuan, and Qinjun Qiu.
2021. "DGANet: A Dilated Graph Attention-Based Network for Local Feature Extraction on 3D Point Clouds" *Remote Sensing* 13, no. 17: 3484.
https://doi.org/10.3390/rs13173484