GANet: Graph-Aware Network for Point Cloud Completion with Displacement-Aware Point Augmentor
Authors: Hongyu Yan
Haoxi Ran
Li Lu
Venue: Submitted to ICLR 2023 (2023)
Keywords: Point cloud completion
Graph-aware network
Displacements-aware point augmentor

Abstract: Remarkably, real-world data (e.g., LiDAR-based point clouds) is commonly sparse, uneven, occluded, and truncated. The point cloud completion task draws due attention, which aims to predict a complete and accurate shape from its partial observation. However, existing methods commonly adopt PointNet or PointNet++ to extract features of incomplete point clouds. In this paper, we propose an end-to-end Graph-Aware Network (\textbf{GANet}) to effectively learn from the contour information of the partial point clouds. Moreover, we design Displacements-Aware Augmentor (DPA) to upsample and refine coarse point clouds. With our graph-based feature extractors and Displacements-Aware Transformer, our DPA can precisely capture the geometric and structural features to refine the complete point clouds. Experiments on PCN and MVP datasets demonstrate that our GANet achieves state-of-the-art on the task of shape completion.

Under review as a conference paper at ICLR 2023
GANET: GRAPH-AWARE NETWORK FOR POINT
CLOUD COMPLETION WITH DISPLACEMENT-AWARE
POINT AUGMENTOR
Anonymous authors
Paper under double-bling blind review
ABSTRACT
Remarkably, real-world data (e.g. LIDAR-based point clouds) is commonly sparse, uneven, occluded, and truncated. The point cloud completion task draws due attention, which aims to predict complete and accurate shape from its par- tial observation. However, existing methods commonly adopt PointNet or Point- Net++ to extract features of incomplete point clouds. In this paper, we propose an end-to-end Graph-Aware Network (GANet) to effectively learn from the con- tour information of the partial point clouds. Morcover, we design Displacements- Aware Augmentor (DPA) to upsample and refine coarse point clouds. With our graph-based feature extractors and Displacements-AWW can precisely capture the geometric and structural features to refine the complete point clouds. Experiments on PCN and MVP datasets demonstrate that our GANet achieves state-of-the-art on the task of shape completion.
Transformer,
DPA
INTRODUCTION
The rapid development of 3D scanning devices (e.g.. LiDAR) has provided an unprecedented ability to capture point clouds from complex 3D scenes. However, due to limited resolution and occlusion issues, the scanned point clouds are sparse and incomplete, which is why various applications such as 3D detection (Zhang al. 2020b) cannot take full advantage of them.
PointNet (Qi et al. 201 has attracted great attention to the learning methods on raw point clouds.
Inspired by PointNet, PCN (uaan et al. 2018) introduces a coarse-to-fine fashion to learning- -ased
shape completion. Based on this fashion, subsequent work (Yuan et al.) 2018 Tchapmi et al. 2019)
Wang et al. 2020a Liu et al. 2020 Wang et al. 2020b Pan et al. 2021) investigates how to optimize the refinement stage for more detailed results. For example, SnowflakeNet (Xiang et al. 2021al
proposes snowflake point deconvolution to progressively refine coarse point clouds.
Although difficult to discern nizable contours. This observation motivates us to propose Graph-Aware Network (GANet), a novel graph-based network for shape completion. Compared with MI.P-hased methods previous approaches, which rely heavily on inductive learning and may neglect shape awareness as men- tioned in Liu al. (2019b). graph-based methods can extract shape information from the hints of geometric relation more effectively. An overview of our GANet is shown in Figure [ Specifically, design a Multi-scale Edge Aggregator (MEA) extract expressive features with rich geometric information. The MEA first applies set abstraction proposed by PointNet+ (Qi et al., 2017b) to reduce the point number of input data. This operation avoids the effects of noise and repeated points as well as reduces the model's computation complexity. To learn from the outlines of the partial point clouds, we construct the local graphs based on the neighbors of the given centroids. Then we propose novel scalable module, Local Edge Aggregator (LEA) to process the local graphs. This module weights the importance of the edges in the local graphs and then aggregates the features of the edges for the output centroid features. In addition, capture both the local and global structures of the input point clouds, we introduce the philosophy of multi-scaling to our LEA.
whole, most incomplete point clouds maintain roughly recog-
Furthermore, we design Displacement-Awaar Point Augmentor (DPA), novel upsampling module to refine the coarse output. We leverage a multi-staee strategy to stack DPA blocks. In particular, the LEA as the feature extractor in every DPA block. The LEA can capture the geometric

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Reshape
Edge Aggregator
Global Feature
MLP
MLp
MLP
FPS
No. x
Input
Output
Input
Ng
Point Augmentor
N2 x
Point Augmentor
N₁ x
Point Augmentor
Fine Output
Skip Connection
Skip Connection
Figure 1: The pipeline of our GANet. GANet consists of an edge aggregator (our MEA) extract the global features of a partial point cloud, and MLP to decode the global features for the coarse output, a priori sampling module for stable output, and three cascaded point augmentors (our DPA) with skip connection to upsample and refine the coarse output. Ne is the number of the coarse output points. N1, N2, and Ng the number of the output points from the three point augmentors.
structure information provide better representation compared with regular multi-layer perceptron (MLP). In addition, the current DPA block provides information flow for the next DPA block. This skip connection can help the next block refine a better complete point cloud with information fusion. To effectively utilize previous information, we propose a novel Displacements-Aware Trans- former (DAFFormer). With the cross attention and group ferw-forward network, our DAFormer can learn the precise displacement relation between two point clouds with different resolutions. Finally, our experiments show that GANet outperforms previous methods on PCN dataset (Yuan et al. 2018 and MVP (Pan al., 2021).
Our key contributions are manifold:
We design Graph-Aware Network (GANet) for point cloud completion, which uses the graph-based scalable module to extract local and geometric features of partial point cloud.
We propose Displacements-Awwan Point Augmentor (DAP) to refine coarse com- plete point clouds. Moreover, we introduce a novel Displacements-Are (DAFormer) to aggregate information between two point clouds with different resolution.
Transformer
Our method achieves Nate-of-the-ard on some widely adopted benchmarks including PCN dataset and MVP.
RELATED WORK
2.1 LEARNING ON POINT CLOUDS
Point-based methods (Li et al.
2018a /hao & Tao 2020 Yang et al.
2019 Liu et al.
2019a Zhao
al. 2021 Guo al. 2021 Xiang al. 202 Ma al. 2021 Ran et (022)) have attracted
significant attention for processing on point clouds. PointNet (Qi et al. 201 learns a global view by point-wise MLP followed by max-pooling. Subsequently, PointNet++ (Qi et al. 2017b) intro-
duces hierarchical framework to learn the local features. Afterward, another branch of methods (Dai al.) 2017; Groh et al. 2018 Thomas et al.] 2019: Li et al. 2018b; Xu al., 2018 202T) based on convolution emerged for the local aggregation, using dynamic strategies of transformation for the normal work of convolution on point clouds. PointConv (Wu al., 2019) directly employs the relationship between local centers and their neighbors to learn dynamic weight for convolution.
2.2 GRAPH-BASED METHODS
Groueix et al. 2018 Xu et al. 2020a Hamilton et al. 2017 Kipf Welling 2016 Zhou et al.
2021 achieves notable performance for the local aggregation of geometric features. To capture local
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NCx A
X
Softmax
LEA Ki
Aggregation A
MLP
Group
F'
F
C c++
Mapping
N'x
Nx N'
M' 126
Mean
[1 N131
7 x
N' x
Local Edge Aggregator
Multi-scale Edge Aggregator
Set Abstraction
Concat
product
The design of our Local Edge Aggregator (left) and Multi-scale Edge Aggregator (right,. Local Edge Aggregator (LEA) describes the local geometric structure f by combination of graph aggregation and attention mechanism, and Multi-scale Edge Aggregator (MEA) adopts the philos- ophy of multi-scaling for more expressive features. We first utilize set abstraction block (SA) to extract some key points P' and the corresponding features F² Then, feed F" into LEAs with dif- ferent K (i.e., K1. K2. K3) and obtain the output FK1, FK2, FK3, Finally, through sequence of operations (i.e., concatenation, mapping 7, and aggreation A), our MEA abstracts poal-to-global view of feature g. N is the number of input points. N is the number of key points after SA. K is number of neighbors to queried. and C are the dimensions of the features in J and FK
Figure 2:
geometric features of point clouds, DGCNN (Wang al. 2019) learns edge feature by building the relations between the node and its neighbors. A similar branch of relation-based models learns from relations analogous ric priors equipped with the attention mechanism, while RPNet (Ran et al. 2021) adopts both the geometric and semantic relations in efficient block.
the edges of graphs. RSCNN (Liu et al.] 2019c) predefines geomet-
2.3 LEARNING-BASED SHAPE COMPLETION
Various shape completion methods YYng et al., 2018 Vakalopoulou et al. 2018 Tchapmi et al. 2019 Liu et al., 2020; Xie et al., 2020 Huang et al. 20200] Wang et al. [020bb Zhang et al. 2020a) have emerged. PCN Yuan et al. 2018) unprecedentedly introduces deep learning to shape com- pletion by utilizing
coarse-to-fine completion framework. CRN (Wang et al. 2020a) proposes
novel coarse-tee to-fine pipeline to facilitate the decoder with a cascade refinement strategy. Subsequent
work (Yu et al. 2021 Huang al. 202 Zong et al. 2021 Wen et al. 2021a b Lyu et al. 2021
Wang et al. 2222 [ Tang et al. 2022) focuses on how to reconstruct more detailed features.
VRCNet (Pan al. (021) designs Relational Enhancement Network enhance structural rela-
tions for refinement. SnowflakeNet (Xiang et al. (2011a) introduces a snowflake point deconvolution
block generate the detailed complete point cloud.
GRAPH-AWARE NETWORK
In this section, we propose Graph-Aware Network (GANet) for shape completion, following the coarse-to-fine fashion. As shown in Figure GANet firstly extracts the global features by Multi-scale Edge Aggregator (MEA) to predict the coarse output. Afterwards, we upsample the coarse output fine complete point clouds through our Displacements-awarc Point Augmentor modules. Finally, we present our Displacement-awarr Transformer, loss function and the evaluation metrics.
3.1 MULTI-SCALE EDGE AGGREGATION
Prior PointNet-based methods Yang et al. 2018 Vakalopoulou et al. 2018 Tchapmi et al. 2019 Liu et al. 2020 Yuan et al.) 2018 Wang al.) 2020a Pan et al. [021] can hardly learn geomet- ric information as they learn the global and local features from individual points. To tackle this problem, exploit the geometric structures by constructing local graphs. We design a Local Edge Aggregator (LEA), an attention-bart based instead the convolution- like module to aggregate the local graphs. Furthermree we different differenn-definitionn definition----ddee Based LEA, propose novel
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Multi-Scale Edge Aggregation (MEA) to extract global features. As shown in Figure 2 the MEA consists of a set abstraction operation and three Local Edge Aggregators (LEA). The set abstraction is employed to extract key points and their features well as drop the computation complexity.
is the number of the input point clouds. The output of set abstraction (SA) is downsampled point cloud P {Pi.... ..... .'x) } S R-'xx x3 and its corresponding features F" = {fi.... ..... fgx. C R''' N' is the number of points in the downsampled point cloud, and C means the dimension of features F'. We then feed F" into the multi-scale LEAs. Given the i-th point, its output feature through one LEA block can be formulated as:
As shown in Figure 2 we denote the input as P = (PI..... py} C RN*3
K PK Σ j=1
wo O ((E,
(I)
where we define edge ety = f fj. and Wij is the attention weight of egy K represents the number of neighbors to be queried by one LEA. O is element-wise product. [:] is the operation of
concatenation. M is combination of linear and non-linearity function, i.e., {MLP - ReLU 4 MLP). Here Wij is defined as:
Waj = Softoomaa (w (e:;)),
where w is learnable mapping function.
Furthermore, we introduce the philosophy of multi-scale grouping to our edge aggregation. Previous works (Qi al. 2017b; Ran et al., (021) prove the effectiveness multi-scale grouping. Both the local and global structures are essential for a sparse point cloud. Empirical results further show its effectiveness. The global feature of our multi-scale LEAS can be defined as:
g A ([e" , p/0))) l (1, (I....,N'I))
(3)
where K1. K2, K3 and r.K,, F.Ke p.Ks are the predefined numbers of neighbors and the output of different scales of LEAs, respectively. y is linear function. To implement our network, we set K1, K2, K3 10, 20, None (all points neighbors) respectively. A is the function (i.e., max max-pooling, mean-pooling) to aggregate the N' features.
Finally, we utilize the input partial point cloud and the extracted global feature g to generate a coarse complete point cloud through a sequence of operations, i.e., mapping, reshaping, and sampling.
3.2 DISPLACEMENT-AWAH POINT AUGMENTATION
The upsampling operation plays a vital role in the point cloud completion task. In this stage, the aim is to refine and upsample coarse point clouds. With a multi-stage strategy, previous methods (Wang) ct 2020at Xiang et al. 202 Tang et al. 2022) can recover local shape details by exploiting local points features. However, these multi-stage methods ignore the importance of the feature extractor. They usually employ MLP-based feature extractor to learn the features of the input, which may fail exploit the geometric and structural features of the input.
To solve the above problems, we propose a Displacement-awaat shown in Figure Following multi-stage strategy, we stack three DPA blocks to generate final complete shape. Each DPA block takes the output of the previous block as input and then refines and upsamples the input with more details. The simple yet effective DPA block consists of a feature extractor, feature fusion, and displacement generator. We adopt one LEA as our feature extractor for the local feature extraction. This process roughly the same as Equation I
Point Augmentation (DPA) block,
In addition, to refine a better point cloud, we aggregate point features of i - 1-th block to the current i-th block. To fuse two different scale features, we construct relation between current features F, and previous point features Fi-1. The relation can guide the DPA block to generate suitable and accurate displacements by aggregating information from P: and P.. To fuse two point features, propose Displacement-awarn Transformer (DAFormer).
Specifically, the input of DPA is point cloud P; = {pi.....
ply) C R NNXx3 where N; is its number
of points. Our goal is to obtain a refined point cloud P++1 = P1
i+1 i+1
1..r. P
PN
C M We
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Next
Max
R
N.
LN
No
Max
MHCA
R.
N.
D
DAForee
Mapping
Shuffie
P
MLP
Pat Nost a
LN
N. X.
Group FFN
X
1
W
N,
DAFormer
Fest
Displacement-awwen Point Augmentor
Repeat
C
Concat
Figure pisplacement-aware Point Augmentator (DPA). Our DPA aims to generate a high- resolution fine output P:+1 from the coarse input P.. We first adopt a LEA extract the local features F. Next, we feed F; with the combination of the feature after max- max-pooling gi and the one from the previous stage g: into an MLP 7 to obtain features F. The pooled feature g will be used in the next DPA block. Then, we leverage DAFormer D along with the mapping function W and the pixel-shuffle- like operation, to generate point displacements with the fusion of F and features from the previous stage F Finally, we use the computed point displacements to obtain the refined output P.+1. R. is upsampling ratio. N; is the number of input points P.. N441 is the number of output points P.+1. N RxNN,
firstly adopt one LEA to extract local features F; = (f....., [......;;]] C RNXD Next, we feed F with the combination of the feature after max-pooling g: and the one from the previous stage g/_ into an MLP 77 to obtain features F/. The pooled feature g will be used in the next DPA block. Then, DAFormer D along with the mapping function W and the pixel-shuffle-ikk operation, utilizes the fusion of F/ and features from the previous stage F to generate point displacements. We define set of point displacements Dj as:
Dj (D ((E)) (....g.....)))) Im E (L......)
Thus, after point augmentation, each point of the input P, will generate R corresponding points (N++1 RXx x No).
Finally, we obtain the refined point cloud P.+1 by the summation of the displacements and their corresponding centroids. Denote djm element of D,. The refined point cloud can be defined
as:
Pi+1 = (p} + dimlf E f1,..., N1, E (1....,
(5)
3.3 ASSPLACEMENT-WARE TRANSFORMER
In the upsampling stage, learn point displacements refine the point cloud. To learn better point displacements, we introduce a novel Transformer, called Displacement-avee Transformer (DAFormer). As shown on the left of Figure 3 the DAFormer is global and local transformer, which consists of a multi-heads cross attention and group feed-forward network.
Cross Attention. The multi-heads cross-attention (MHCA) is used learn global displacement features between P. and P,-1- Denote two inputs with different scales as X and X'. We can express the MHCA as:
= (X)) -('), (XX),,
A = softmarlgh C//h),
(6)
X'') = 0),
where o. 8, and z are linear functions, a is a projection function to align the dimension. C' and the embedding dimension and number of heads, respectively. @ is matrix multiplication.
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Group Feed-forward Network. Different from the vanilla Transformer proposed by ViossVit (Chen et al. 2021). we employ a group feed-forward network (FFN) to introduce non- linear operation. Compared with regular FFN based MLP, group FFN can aggregate the regional information by the grouping operation. Specifically, we first leverage a linear function to map the input channel into the hidden space, which is able reduce the computing complexity. Next, group the neighbors by the k-nearest neighbors (KNN) algorithm in the geometric space. Then, use the relation between the center point and its neighbors learn the displacement features. Finally, back projection function is used to align the dimensions for the following residual connec- tion. Note that, position encoding not necessary for our DAFormer because we use group FFN to update the features. The output of the Group FFN can be formulated as:
G(F)= = T E
(((M(
j=1
where Φ, 3 are linear function. series of MLP. The G denotes the number of neighbors.
back projection function. M mapping function with
Benefiting from the cross attention and group FFN, our DAFormer can learn global and local dis- placements change to help following point shuffle operation to generate better displacements, The output of DAFormer can designed as follows:
F MHCA (-E LN(F--))
Fout = F' + G(LN(F))
where G is group feed-forward network. LN is the layer normalization
(Ba et al. 2016
3.4 Loss FUNCTION AND EVALUATION METRICS
We use the Chamfer Distance (CD) and Fl-score to evaluate the quality of the reconstructed point clouds.
CD calculates the average closest point distances between the output X and the ground truth Y, which can be defined as follows:
CD
Σ
min ||
ull2 +
min |l zeX yEY
Σ
x/12.
X
Y
xEX
For an end-to-ent training on our GANet, we design the total loss function, which is as follows:
-= CD( Σ CD().)))
(10)
where P' and P. denote the coarse and fine output of DPA block, respectively. Q is the ground truth. n is the number of GAP blocks.
4 EXPERIMENTS
Implementation Details. We build our network with PyTorch and CUDA. We train our models using an Adam optimizer (Kingma Ba 2014) with B1 0.9 and 83 0.999 on NVIDIA V100 16G GPU. The initial learning rate is set to 10 with a decay of 0.1 every 50 epochs, and the batch size is 32.
4.1 RESULTS ON MVP DATASET
Dataset. Pan et al. 2222 proposes high-quality multi-view partial point cloud dataset (MVP) for the task point cloud completion. utilizes Poisson Disk Sampling (PDS) to generate the ground truth point clouds, and has multiple camera views (26 uniformly distributed camera poses unit sphere) and various categories. addition, the MVP dataset provides different resolutions (i.c., 2048, 4096, 8192, and 16384) of ground truth for more accurate evaluation.

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Table 1: Quantitative results the MVP dataset (Pan al.
2021
with different resolutions. sop
means additional data augmentation.
2048
4096
8192
16384
Method
CD (
(T))
(D)
(f)
CD (L)
(
CD())
(.)
(1)
PCN Yuan et al. 2018
9.77
0.320
7.96
0.458
6.99
0.563
6.02
0.638
TopNer Tehapmi et al. 2019
10.11
0.308
8.20
0.440
7.00
0.533
6.36
0.601
MSN (Liu al. 2020
0.432
6.17
0.585
5,42
0.659
4.90
0.710
CRN Wang ei al. 2020a
7.25
0.434
0.569
4.90
4.30
VRCNet (Pan et al. 2021
5.96
0.499
4.70
0.636
3.64
0.727
3.12
0.791
SnowflakeNet (Xtang cl u..
2021u
5.76
0.513
4,42
0.671
3.50
0.746
2.74
PoinTr Yuu al. 2021
5.18
0.606
3.94
0.724
3.08
0.767
PDR paradigm (Lyu 2021
0.499
4,26
0.649
3.35
0.754
2.61
0,817
GAN (ours)
4.99
0.527
3.81
0.679
2.87
0.776
2.28
Input
PCN
VRCNet
PoinTr
Snow
Ours
GT
Figure 4: Visualization on MVP Pan et al. 2021). From left to right, each column of images is incomplete point clouds (Input), the results PCN
Yuan et al. 2018). PoinTr (Yu et al. 202T) SnowflakeNet (Xiang et al., 2021a), VRCNet (Pan et al. 2021), our GANet and ground truth (GT).
Results. To verify the effectiveness of our GANet, evaluate our GANet the MVP dataset and compare it with the previous methods Table Our method achieves ofate-of-the-art results on all of the resolutions in the metries of CD and F score. Compared with state-of-the method PDR paradigm (Lyu et al. 2021), we reduce the 1.8% CD and improve 5,6% Fl-score in the 2048 resolution.
Moreover, we visualize the reconstructed results Figure 4 Compared with previous methods, our GANet is able to complete better and more detailed point clouds. Our GANet preserves the whole contour information of the input point clouds with the help of our graph- based local aggregators instead of the widely adopted PointNet-hased feature extractors.

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Table 2: Quantitative results on PCN dataset Yuan et al.
2018) on CD (x10- #Points of ground
truth is 16384.
Methods
Airplane
Cabinet
Car
Chair
Lamp
Sofa
Table
Watereraft
Avg (
NoldingNer Yang al. 2018
9.49
15.80
12.61
15.55
16.41
13.97
13.65
14.99
14.31
AtlasNet (Groueix
6.37
11.94
10.10
12.06
12.37
12.99
10.33
10.61
10.85
PCN Yuan ef al 2018
5.50
22.70
10.63
8.70
11.00
11.34
11.68
8,59
9.64
Top Tchapm Ml.
2019
7.61
13.31
12.15
CRN (Wang cl 20200
4.79
9.97
8.31
9.49
8.94
10.69
7.81
8.05
8.51
GRNe AX a.. 20206
6.45
10.37
9.45
9.41
7.96
10.51
8.44
8.04
8.83
PMPNet (Wen aral. 2021b
5.65
11.24
6.95
8.72
NSFA (Zhan el 31. 2020)
4.76
10.18
8.63
8.53
7.03
10.53
7.35
7.48
8.06
PoinTr Yu al. 2021
4.75
10.47
8.68
9.39
7.75
10.93
7.78
7,29
8.38
VE-PCN Wang c. 2021
9.85
8.32
Snowflakereet (Aiing 2a
4.29
9.16
8.08
7.89
6.07
9.23
6.55
6.40
7.21
GANet (ours)
3,98
9.21
7,86
7.43
5.53
8.91
6.35
6.14
6.92
Input
PN
PN2
MEA(Ours)
GT
Figure 5: Visualization between different designed encoders. From left to right, each column of images incomplete point clouds (Input), the results of encoders equipped with PointNet (PN) (Qi et al. 2017a), PointNet++ (PN2) (Qi et al. 2017b), and our MEA, and ground truth (GT).
4.2 RESULTS ON PCN DATASET.
Dataset. PCN Yuan et al. 2018 synthetic CAD models from ShapeNet (Chang al.) 2015) create a large-scale dataset containing numerous pairs of partial and complete point clouds. The 3D partial point clouds come from the back-projecting 2.51) depth maps. The ground truth with 16384 points is uniformly sampled from the model. This dataset includes 28974 CAD models for training and 1200 CAD models for test.
Results. We compare our GANet with recent most competitive methods on the PCN dataset Yuan al. 2018). Table Sshlws shows the quantitative results on the PCN dataset, from which we find that our proposed GANet performs best on the metric of CD.
ABLATION STUDY
In this section, conduct detailed ablation studies to evaluate designed components. The design MEA. We compare our MEA with PointNet-based encoder (Yuan et al.) 2018 and PointNet2-baseer encoder (Wen al. 2020). The quantitative results are shown
Table Comparison between different encoders on CD (x10-9) and F1-score. For the design of encoder, we have three options (PointNet (Qi
et al.) 2017a), PointNet++ (Qi et al. 2017b), and our MEA)
PN 8
PN2
MEA
CD
Fl-score (f)
5.25
0.526
5.28
0.526
4.99
0,527

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Table 4: Ablation study of our DAFormer on CD (x10-1 and Fl-score. "Skip" means skip con-
nection. "geo" is geometric neighbors, while "sem" is semantic neighbors.
Skip
Block
neighbors
CD (L)
FI-score (1)
MLP
5.55
0.508
Cross Transformer
5.10
0.524
DAFormer
5.09
0.522
DAFormer(ours)
geo
4.99
0.527
Table 3 The comparison demonstrates that our MEA achieves the best performance CD and Fi-score metrics. We visualize the results of the model with different encoders in Fig- ure [ The figure shows that the generated shape of our MEA is closer to ground truth in the whole contours compared with PointNet (PN) and PointNet++ (PN2). Both visualization and quantitative results prove that our graph-aware MEA improves the performance by exploiting the whole contour information.
The design of LEA. We ablate the design of LEA our DPA. We compare our LEA with MLP in T
Table 5: Comparisons between
The results demonstrate that LEA more powerful compared with vanilla MLP. We argue that the graph-based local ag- gregators help complete detailed point clouds by extracting geometric and structural features.
MLP and LEA in our DPA block.
Operation
CD())
Fi-score (1)
MLP 5.50
0.512
I.AA (ours)
4.99
0.527
The design of Former We investigate the effectiveness of our DAFormer. All results test- ing on our GANet's architecture and the MVP dataset with 2048 resolutions. We first study the influence of skip-connection, the regular methods (Yuan al., 2018 Tehapmi et al. 2019) with- out skip-connection usually use MLP to learn features. From the comparison, we find that without skip-connection, our model using MLP also achieves perfect performance, which still outperforms previous methods (Xiang et al., 202 Pan al. (021). Then, with the stip-connection, we com- pare the vanilla Cross Transformer (Chen et al. 2021) and our DAFormer. With the help of group FFN, DAFormer gains better metrics in terms of CD and F1-score. Finally, research the type neighbor in the group FFN, including geometric neighbors and semantic neighbors. The experimented results demonstrate the geometric neighbor better. We argue that the geometric neighbor constructs the feature fusion of geometric relation, which is able to generate more accurate displacements compared with the feature fusion of semantic relation.
COMPLEXITY ANALYSIS
In this section, we compare the efficiency be- tween recent methods and our GANet on the MVP dataset with the resolution of 16384 points. As shown in Table 6, our GANet is much faster and brings obviously less com- putation compared with VRCNet (Pan al.) 2021), SnowflakeNet (Xiang et al.) 2021a), and PoinTr I (Yu et al. 2021). Moreover, Table in- dicates GANet performs much better on CD and F1-score compared with these methods.
Table 6: Comparison between our GANet and the most recent methods on efficiency.
Methods VRCNet
FLOPs (G)
#Params (M)
Time (ms)
29.75
17.46
11.46
Pointr
11.14
42.55
10.12
SnowflakeNet
5.52
19.30
4.45
GANet
3.74
5.01
3.26
7 CONCLUSION
In this paper, we design a graph-aware network GANet for point cloud completion. Equipped with proposed multi-scale edge aggregator, GANet effectively learns from geometric global fea- tures from the preserved geometric structures the partial point clouds. In addition, we propose the Displacement-Aware Point Augmentation (DPA) module to upsample the coarse output from the first

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stage. With the graph-based feature extractor and Displacement-Aware Transformer (DAFormer), DPA generates accurate point displacements to upsample and refine point clouds. Extensive ex- periments on some benchmarks indicate that our GANet achieves state-of-the-an art compared with previous methods.
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ETHICS STATEMENT
In our paper, we strictly adhere to ICLR ethical research standards and laws. All datasets we use are publicly available, and all relevant publications and source codes appropriately cited.
REPRODUCIBILITY STATEMENT
We adhere to ICLR reproducibility standards and ensure the reproducibility of our work in some ways as follows:
We provide the codes of our main experiments in the supplementary material (code.zip), which includes the pretrained models and some demo samples.
Detailed framework and more experiments are presented in the Appendix.
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A EXPERIMENTS DETAILS
In this section, we present our experimental setting in terms of upsampling ratios and our detailed experiment results on the MVP dataset.
Upsampling ratios. We set the size of coarse output to 512 x 3. In the different resolutions,
the detailed upsampling ratios of three Displacements-Awar Point Augmentor (DPA) blocks shown in following:
Resolutions
Upsampling ratios
2048
1,2,2
4096
1,2,4
8192
1,2,8
16384
1,2,16
Detailed results on the MVP dataset. We further present the detailed complete results on the MVP
dataset (16384) in terms of Fl-score. The results of every category are shown in following:
Aupiau
Nowch
Mathyols
Avg (1)
PCN
Foat 21 20015
0.0.4
0.585
0351
0253
0.302
0.22
0,001
0.546
0.775
03006
0..74
01801
Top
2019
0.680
0.879
0.730
0.696
0.569
0.797
0.677
0.808
0.44
0.742
8.000
0.797
All Porel
0.833
0.586
0.763
0.753
0.75
From the table, we can see that our GANet achieves state-of-the-an results all categories.
B THE DESIGN OF EDGE AGGREGATOR.
We ablate the design of multi-scalin (the combination of pk: fk,, fKs compared with fK, only) and multi-layer thhree-layer MLP compared with single-layer MLP in MM). The results of testing the MVP dataset with 2048 resolutions are shown following.
Scale
Layer
CD (J)
Fl-score (f)
Single
Single
5.19
0.525
Multi
Single
5.16
0.523
Single
Multi
5.08
0.524
Multi
Multi
4.99
0.527
From the comparison, multi-scale with multi-layer works the best on CD and F1-score.
C RESULTS ON THE REAL SCENE
LiDAR scans can be very sparse, with some containing fewer than 10 points. KITTI (Geiger et al., 2013) a real-world dataset that scanned point clouds using a Velodyne LiDAR. order to compare the sensitivity and performance of models for the sparse point cloud in the LiDAR scans, we test the general models trained on the PCN ShapeNetCars. The visualized completion results are shown in Figure. (6 We compare
GANet with previous competitive methods, VRCNet (Pan et al. 2021). PoinTTr (Yu et al.) 2021) and SnowflakeNet (Xiang et al.) 2021a). All the results show that methods perform better in terms of details.
D MORE VISUALIZED RESULTS
In this section, show visualized complete results the MVP dataset. From Figure 7 Figure and Figure we find that our method generate better shape with structure details compared with previous methods PCN (Yuan al. 2018), VRCNet (Pan et al. 2021). PoinTr (Yu et al. 2021)
and SnowflakeNet (Xiang et al. 2021a)
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Inputs
VRCNet
PoinTr
Snow
Ours
Figure 6: Visualized results on KITTI dataset.
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Inputs
PCN
PoinTr
Snow
VRCNet
Ours
GT
Figure 7: Visualized results on MVP dataset.
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Inputs
PCN
PoinTr
Snow
VRCNet
Ours
GT
Figure 8: Visualized results on MVP dataset.
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Inputs
PCN
VRCNet
PoinTr
Snow
Ours
GT
1
1
1
Figure 9: Visualized results on MVP dataset.
19


Reviews:
[{"review_id": "XA1ME1qUQ4", "reviewer": "Reviewer_97KL", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a model for coarse-to-fine point cloud completion. The model first extracts global features from a partial input, then produces a coarse point cloud which is fed to several blocks in a sequential manner, each increasing the number of output points and modifying them. Overall, architecture heavily relies on the use of restricted local self-attention and multi-scale feature processing.\n\nArchitecture is evaluated on PCN and MVP datasets and compared to a large list of recent related models showing performance exceeding state of the art. Additionally, the authors provide several ablation studies, evaluating the performance of various model components; and compare their model in terms of memory footprint and computational efficiency.", "summary_of_the_review": "Given overall quality of the submission including detailed introduction of the model, extensive experiments with two benchmarks and various ablation studies, and the resulting state-of-the-art performance, I think this paper is a good candidate for acceptance, even if the novelty of the approach is limited. If the authors will release their code, it will definitely be interesting to the community.", "strength_and_weaknesses": "Strength:\n* The model demonstrates state-of-the-art performance.\n* Evaluation is done for two benchmarks and the chosen baselines are recent.\n* Ablation studies are provided, showing how important different components are.\n***\nWeaknesses:\n* Although complete model is very specifically engineered, overall novelty is limited, since the proposed techniques rely on existing prior ideas.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "Q18Y9besoD", "reviewer": "Reviewer_CpHT", "summary": "", "questions": "", "limitations": "", "rating": 10, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The authors propose a graph aware deep neural network for point cloud completion. The design a novel displacement aware augmenter layer to effectively up sample and refine coarse point clouds. The authors demonstrate state of the art performance of their proposed method on PCN and MVP datasets.", "summary_of_the_review": "The paper is well written. The proposed method demonstrates state of the art performance. The ideas are well explained and enough experiments and ablation studies have been conducted. I recommend the paper to be accepted.  ", "strength_and_weaknesses": "The paper is very well written. The proposed method is very interesting and shows very good performance both quantitatively and qualitatively. The authors describe well all their design choices. The paper is well evaluated and also includes ablation studies to support the design choices of the proposed method. The authors provide their code to allow reproducibility of their results. The method shows a consistent improvement over competing method. Overall, I think this paper is a solid submission and I recommend the paper to be accepted.   ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "JcmPRoZ8km", "reviewer": "Reviewer_NrG5", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a Graph-Aware Network (GANet) for point cloud completion. The network consists of 1) a graph-based Multi-scale Edge Aggregator (MEA) to extract global features from the input partial point clouds, and 2) a Displacements-aware Point Augmentor (DPA) to upsample and refine the point clouds. GANet achieves state-of-the-art performance on PCN and MVP datasets.", "summary_of_the_review": "The problem this paper aims to address is not clear, and core component in the proposed method is not novel. Besides, the overall presentation can be significantly improved, especially in Section 3, due to the confusing organization and symbols.", "strength_and_weaknesses": "Strength:\n1) GANet achieves the state-of-the-art performance on PCN and MVP datasets.\n\nWeakness:\n1) Lack of clarity: \n\n1.1) In Section 3.1, the input to Local Edge Aggregator (LEA) is defined as P’ (Nx3) and F’ (NxD). While in Figure 2-left, the input becomes P (NxC) and F is missing. The symbols used in Figure-2 left and right are also inconsistent. \n\n1.2) In Section 3.1 Para. 1, “we use a different definition of edge”, what is this definition?\n\n1.3) In Section 3.1, “we define K1, K2, K3 as 10, 20, N respectively”, what is N?\n\n1.4) In Section 3.2, “the input of DPA is the point cloud Pi (Mx3)”, then what are the input point features? \n\n1.5) Connection between Section 3.1 and 3.2 is missing. It is difficult for readers to understand the complete pipeline of the proposed method.\n\n1.6) Symbols are also inconsistent between Section 3.1 and 3.2. \n\n\n2) Lack of clear motivation:\n\n2.1) The paper claims “Prior PointNet-based methods can hardly learn geometric information as they learn the global and local features from individual points” (Section 3.1) and “They (prior methods) usually employ MLPs-based feature extractor to learn the features of input, which may fail to exploit the geometric and structural features of the input” (Section 3.2) as the motivations of the proposed GANet. More in-depth analysis about the drawback of MLP-based feature extractor and the advantage of GANet is expected. Otherwise, the proposed method is not convincing. A simple quantitative comparison in Table 3 seems not enough.\n\n2.2) It’s hard to find the relation between GANet and “graph-aware”. In its core graph-based Local Edge Aggregator (LEA), the operations shown in Equations (1) & (2) seem no difference from MLP-based paradigm.\n\n\n3) Originality:\nThe core graph-based Local Edge Aggregator (LEA) is not novel. The paper does not clarify the definition of “edge” in this part, but:\n--> If the “edge” is defined in Euclidean space of raw points, there is no difference from PointConv [1].\n--> If the “edge” is defined in feature space, there is no difference from RandLA-Net [2].\n\n[1] W. Wu et al, “PointConv: Deep Convolutional Networks on 3D Point Clouds”, CVPR 2019.\n[2] Q. Hu et al, “RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds”, CVPR 2020.\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "Not applicable"}, "extra_text": {}}]

Author rebuttal:

Decision: Reject