InfoCD: A Contrastive Chamfer Distance Loss for Point Cloud Completion
Authors: Fangzhou Lin
Yun Yue
Ziming Zhang
Songlin Hou
Kazunori Yamada
Vijaya B Kolachalama
Venkatesh Saligrama
Venue: NeurIPS 2023 poster (2023)
Keywords: Contrastive learning; Point cloud completion

Abstract: A point cloud is a discrete set of data points sampled from a 3D geometric surface. Chamfer distance (CD) is a popular metric and training loss to measure the distances between point clouds, but also well known to be sensitive to outliers. To address this issue, in this paper we propose InfoCD, a novel contrastive Chamfer distance loss to learn to spread the matched points for better distribution alignments between point clouds as well as accounting for a surface similarity estimator. We show that minimizing InfoCD is equivalent to maximizing a lower bound of the mutual information between the underlying geometric surfaces represented by the point clouds, leading to a regularized CD metric which is robust and computationally efficient for deep learning. We conduct comprehensive experiments for point cloud completion using InfoCD and observe significant improvements consistently over all the popular baseline networks trained with CD-based losses, leading to new state-of-the-art results on several benchmark datasets. Demo code is available at https://github.com/Zhang-VISLab/NeurIPS2023-InfoCD.

InfoCD: A Contrastive Chamfer Distance Loss for Point Cloud Completion
Fangzhou Lin 1.+ Yun Yue!" Ziming Zhang Songlin Hou 1.3 Kazunori D Yamada
Vijaya B Kolachalama"
Venkatesh Saligrama'
Worcester Polytechnic Institute, USA TTohoku University, Japan 3 Dell Technologies, USA "Boston University, USA (flin2, yyue, zzhang15, shou @xpi edu, edp, semada@tohoku..co jP, [vkola, srv]
Abstract
A point cloud a discrete set of data points sampled from 3D geometric sur- face. Chamfer distance (CD) is popular metric and training loss measure the distances between point clouds, but also well known to sensitive to out- liers. We propose InfoCD, novel contrastive Chamfer distance loss, and learn to spread the matched points to better align the distributions of point clouds. As such InfoCD leads minimizing InfoCD equivalent to maximizing a lower bound of the mutual information between the underlying geometric surfaces represented by the point clouds, leading to a regularized CD metric which is robust and computationally efficient for deep learning. We conduct comprehensive experiments for point cloud completion using InfoCD and observe significant improvements consistently over all the popular baseline networks trained with CD-based losses, leading state-of state-of-the-art results on several benchmark datasets. Demo code is available at bttps://gitte com Waw.o//haaa---SSa///eeelee
improved surface similarity metric. We show that
/Nwer InfoCD
Introduction
Point Cloud Completion. Point clouds, one of the most important data representations that can be easily acquired, play key role in modern robotics and automation applications 1 However, raw data of point clouds captured by existing 3D sensors are usually incomplete and sparse due to occlusion, limited sensor resolution, and light reflection [4-8], which can negatively impact the performance of downstream tasks that require high-quality representation, such point cloud segmentation and detection. Point cloud completion [9] refers to the task inferring the complete shape of an object or scene from incomplete raw point clouds. Recently, many (deep) learning based approaches have been introduced to point cloud completion ranging from supervised learning, self- supervised learning to unsupervised lcarning [10H15]. Among these methods, supervised learning with general encoder-decoder structure the prevailing architectural choice for many researchers, consistently achieving oftt-oo-thhearr results mainstream benchmarks [16
[8]
Learning with Chamfer Distance (CD). CD is commonly employed metric point cloud completion, for example in studies like 19 20 It assesses the dissimilarity in shape between two sets of point clouds by calculating the average distance from each point one set its nearest neighbor in the other set. Minimizing the Euclidean distances between matched points, done in CD, is a known method that is sensitive to outliers, resulting clumping behavior that involves
"Co-first authors.
'Coresponding author.
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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Samples
Samples
16
16
12
12
Value
Value
15 15
NI
Lower Slound
-2
10
Gauss an Mean Distanoe
Gaussian Mean Distanoo
Figure 1: Illustration of comparison among CD, MI, and InfoCD with different numbers of samples.
a substantial number of many-to-one correspondences point matching, forming small clusters visually. These observations can significantly deviate from the assumption of uniform sampling from the underlying geometric surfaces, which commonly used to generate point clouds.
Learning with Mutual Information (MT). A more fundamental problem measuring point cloud similarity (or distance alternatively) is: How can we measure the similarities between the underlying geometric surfaces represented by the point clouds? To address this issue, one potential method is to compute their MI by taking each point cloud a discrete set of point samples from random variable following a certain distribution, and then plugging both point clouds into the MI formula to measure the similarity of the two random variables. However, two limitations prevent from using it directly as a loss function in learning: (1) It may be nontrivial to define the joint probability distribution between two point clouds since we do not have any prior knowledge, and (2) The requirement for extensive memory, necessary for handling a large volume of data points and deep learning models, could render the practical implementation the MI (Mutual Information) loss unfeasible.
Our Approach and Contributions. Motivated by contrastive learning, we propose a novel contrastive Chamfer distance loss, namely InfoCD, to learn to spread the matched points for better distribution alignments between point clouds as well as accounting for surface similarity estimation. Similar to InfoNCE [21]. our InfoCD minimization tends to maximize lower bound of the MI between the underlying geometric surfaces represented by the point clouds. This indeed leads to a regularized CD loss that can be minimized effectively and efficiently with similar computational complexity to CD.
We further illustrate our high level ideas in Fig. [ To plot such figures, we consider generating point clouds uniformly sampled from two ID Gaussian distributions both with unit variance but different means, one fixed at 0 and the other varying from -10 to 10 at step-size 0.1. We then compute CD, InfoCD (see Eq. [5) with distribution is computed based on the exponential of negative Euclidean distances. To better view the difference between the curves of CD and InfoCD, we also rescale the InfoCD curve by aligning its minimum and maximum values with those for CD based on linear scaling so that their value ranges the same. With different numbers of samples, we can clearly that: (1) InfoCD is more robust to outliers (i.e., the cases far away from 0 mean) than CD by penalizing larger deviations with some similar numbers (though smaller numbers of samples have more fluctuations); (2) The sharper purple curves around 0 indicate that InfoCD may lead to better convergence; (3) The lower bound based on InfoCD can approximate MI well with the maximum O, which indicates that InfoCD can be taken as good MI estimator and lead to better point distributions with fewer visual clusters.
1), the lower bound of MI (see Eq. and MI where the joint probability
To summarize, we list main contributions as follows:
We propose InfoCD by introducing contrastive learning into the CD loss, leading to a regularized
CD loss for better point distribution alignments.
We analyze the connection between InfoCD and MI as well as learning behavior with InfoCD
We achieve state-of-the-ee results on popular benchmark datasets for point cloud completion.
2
Related Work
Point Cloud Completion. As the first learning-based point cloud completion network, PCN [0]
extracts global features in similar way PointNet [22) did and generates points through folding

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operations as in FoldingNet [3 In order to obtain local structures among points, Zhang et al. [2] proposed extracting multi-scale features from different layers in the feature extraction part to enhance the performance. CDN 25 uses cascaded refinement network to bridge the local details of partial input and the global shape information together. Lyu et al. (26] proposed treating point cloud completion as conditional generation problem in the framework of denoising diffusion probabilistic models (DDPM) [27]. Attention mechanisms such as Transformer (28), demonstrate their superiority in capturing rangee interaction as compared to CNNs' constrained receptive fields. For instance, to preserve more detailed geometry information for point cloud generation in the decoder, SA-Net [29 uses the kiip-attention mechanism to merge local region information from the encoder and point features of the decoder. SnowflakeNet [17] and PointTr [16] pay extra attention to the decoder part with Transformer-Hi designs. PointAttN was proposed solely based on Transformers.
Distance Metrics for Point Clouds. Distance in point clouds is a non-negative function that measures the dissimilarity between them. Since point clouds are inherently unordered, the shape-level distance typically derived from statistics of pair-wist point-level distances based on particular assignment strategy [20]. With relatively low computational cost fair design, CD and its variants are extensively
32 Earth Mover's Distance (EMD), which is another widely used metric, relies on finding the optimal mapping function from one set to the other by solving an optimization problem. In some cases, is considered to be more reliable than CD, but it suffers from high computational overhead and is only suitable for sets with exact numbers of points [33 34]. Recently, Wu et al. (20) propose Density-aware Chamfer Distance (DCD) as new metric for point cloud completion which can balance the behavior of CD and computational cost in EMD to a certain level. Lin et al. (35) proposed a HyperCD that computes CD in hyperbolic space and achieves significantly better performance than DCD.
used learning-bast basen methods for point cloud completion tasks 30 26
Contrastive Learning. Recently, learning representations from unlabeled data in contrastive way (36 37 has been one of the most competitive research fields [21 38 50]. Popular model structures like SimCLR 42) and Moco [45] apply the commonly used loss function InfoNCE [21] learn a latent representation that is beneficial to downstream tasks. Several theoretical studies show that contrastive loss optimizes data representations by aligning the same image's 's two views (positive pairs)
while pushing different images (negative pairs) away on the hypersphere (51544) 54 A good survey on contrastive learning can be found in (55). More recently, contrastive learning has found its way into point cloud applications as well. For instance, Tang et al. (56) proposed a contrastive boundary learning framework for point cloud segmentation. Yang et al. (57) proposed the mutual attention module and co-contrastive learning for point cloud object co-segmentation. Jiang et al. (58) proposed a guided point contrastive loss to enhance the feature representation and model generalization ability in cemi-supervised settings for point cloud segmentation. Du et al. [59] proposed a self-contrastive learning approach for self self-supervised point cloud representation learning. Wang et al. [60] proposed exploring whether maximizing the mutual information across shallow and deep layers is beneficial to improve representation learning on point clouds, leading to a new design of Maximizing Mutual Information (MMI) Module. Afham et al. [6] proposed CrossPoint, a simple cross-modal contrastive learning approach to learn transferable 3D point cloud representations with 2D) images. Shao et al. 62) proposed spatial consistency guided network (SCRnet) using contrastive learning for point cloud registration.
3
InfoCD Loss
3.1 Preliminaries
InfoNCE Loss. In (21), the InfoNCE loss is defined as follows:
exp { s 22; xz;0}}
LInfNCC =- -- log exp s 22 0) + E.- exp { + xx; x);
(1)
where xr, a.tttt,, xt denote the anchor, its positive and negative samples, denotes a similarity function parametrized by 0, and 2 0 is a predefined temperature that controls the sharpness.
Proposition (InfoNCE vs. MI (21)). Let et be the context at the 1-th time step, and ri be the future target. Then given a set of rundom samples, {x1.... , ,,N ) containing one positive sample from the distribution p( p(Ie+ (e)) and N - negative samples from the "proposal" distribution
3

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p(z++k), we have
T (t) 2 log(N) IIffNCE.
where I denotes the mutual information (MI) operator.
Please refer to the appendix in [21] for the proof. This proposition provides us with an alternative way to measure MI approximately and implicitly. If point clouds can fit into the setting of InfoNCE, then may better estimate the underlying surface similarities from point clouds.
Chamfer Distance Loss. In the sequel, we denote (Iz, ys) as the i-th point cloud pair, with æ; {mgg} and - (vi*) } as two sets of 3D points, and d((-,) as a certain distance metric. Then the CD loss for point clouds can be defined as follows:
( us) = (D. vi) + (CD(Ui.;)) x,) = Iyal Σ min d(raj, Ysk) +
Σ
min d( Ma),
k
where | denotes the cardinality of a set. For point cloud completion, function d usually refers to d(rij, Wik)
|
yik
as LI LI-distance as 12-distance
(4)
|aa - yik 1?
where || |||
denotes the Euclidean l norm of a vector.
3.2
Our Loss Function
Given the considerations above, we propose the following formula as our InfoCD loss:
LinfoDD v:)
EInfoC Mii + l InfoCD (3/;, x;); where
exp( min, d(æ.j, max) }
InfoCD (zs, (1),
lykl
log
Σn exp(- min, d(rij, Mek)} f
h
1
min d(ziij vax) + x Alog Σ exp - { min daaig val)
(5)
7
expl - miny d(aigj va))
log
(6)
exp( - miny d(asy, {(*)}}*
= LInoCDD(ai (zi, vi) LCD(1s (2., vi) + XR(xi, V4)
with R(xi, vi) log { exp { [miny d(raaj yin) ming d(zims ya.) as regularizer and A = = (0, as predefined constant controlling the trade-off between the loss and the regularizer. The smaller LCD(#;, (2,, y:) is, the larger (xx yi) accordingly. From this perspective, we can easily see that our InfoCD loss is equivalent to regularized CD loss.
3.3 Analysis
InfoCD vs. MI. To see the connections between InfoCD and MI, we have the following lemma:
Lemma 1. Consider two point clouds x; = (Righ. Vi = [yu representing two underlying geometric
surfaces X, Vr. Now we introduce a new random variable Zyux whose probability distribution plzyal/K X; = Vi) indicates how likely point yık can be sampled from Y, conditional X; = Y:, and "proposal" distribution p(zyaz) indicates the likelihood of generating an arbitrary Yok- With these notations, we will huve
1Z & = -.) 2 log(ly:) InfooD y:).
(8)
Proof. By following Prop. and the proof (2I, we can take Zyss X; Y: as the replacements for Zitk; Ct. Then samples from p(zy, 12C, D.) will be "positive", and ones from p(zy.e) will be

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"negative" in the language of contrastive learning, Now we can construct 13 groups, as illustrated in Fig. 2 where each group consists of the entire point cloud Fy and point y.- We further can take
an arbitrary group as positive and the rest negatives. Finally, by parametrizing p(=yy [ oc
Plauca
exp ( + min, dzzz ( } for positives and similarly to negatives, we can complete our proof. O
Therefore, based on this lemma, minimizing InfoCD tends to better estimate the lower bound of MI that indicates the underlying surface similarities between point clouds.
X1
X1
Y
Y
ly copies
Point Spread in Learning & Testing, To better understand the behavior of different losses, first introduce another lemma as follows:
X
Lemma 2. Consider an optimization problem min E. (h((xww)) where h: X x -2-++0 g. R - I are both Lipschitz continuous functions, h also smooth over w. and 24 E X is a data point. Then based on gradient descent, i.e., Wh+1
Zyy
Figure 2: Illustration of group con- struction process for MI estimation.
We The E (g(h(z,; wi)) with a learning rate T) 2 O at the t-th iteration and a gradient operator V, holds that given new data point it
0g
0g Oh (mrw)))
h();w;) h((::)+1)
Σ The Th (19520)))
(Maaaa)""V(iiy 17: E
<(z;, ā: wr).
where wo is the initialization of w. denotes (neural) langent kernel function parametrized by wa. (-) is the matrix transpose operator, and 8g is the derivative of g over h at point (I::)).
8h (z(aas)
Proof. Using the linear approximation of h and the assumptions, easily prove this lemma. L
To connect this lemma with CD and InfoCD, let us first compute the gradients of &CD and InfoCD:
VCCD(I
Σ
Velasss War),
(10)
yi
1
expf } d Min)
Vl vi)
Vd(rw yae).
(11)
Σn expl d( vit)
where W/' = arg min, d(zij, 9aa), Vk. By viewing d as h and LCD (or InfoCD) as g. we can see the expl de
weight (CpDl 3d
Tyi but Www...e dd
y1 T' Σ, exp( ddl (1)) E R.
vd(..) To simplify the analysis and explanation, assuming that the normalized gradients, |/V can be viewed as random samples from a high dimensional (i.e., the number of network parameters that is much larger than the number of samples in mini-batches) normal distribution, then for two different random inputs (Zem' Fim), (Ian's Min). it will be expected 63 that the corresponding gradients will be close to being orthogonal to each other, i.e., Vd(zimm Vik) Vd(zin, Vik) z 0. Now by substituting this assumption into Eq. we can have
DLCD (#ik, WERT w))
(CD( ys: wi) ( Mi: w1+)))) R2 ne Σ
Vd (u)ta. 11
(12)
0d
(InooDD(a, wi))) - LInfoCD ( W1) T1t
Ol (waw, Miki w))
V VVdcaw yu))
Od
(13)
with another assumption that the matched point pairs keep unchanged over iterations. From this perspective, we can easily see that the negative weights of (ttafscc(R..)/.a with smaller distances
dd
will push the predicted points away from the matched ground-truth points, while positive weights will tend to reduce the distances in both metrics, as illustrated in Fig. 3 In this contrastive way, the predicted points will be more likely to be spread for better alignment with the ground-truth points.
5

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L1-CD
0.9
LL1-CD
L2-CD
0.8
-2-CD
DCD
DCD
EMD
0.7
EMD
Percentage
InfoCD
Percentage
0.6
InfoCD
0.5
0.4
0.4
0.3
0.2
>0
>1
>2
33
>4
>5
>6
>0
>1
>2
-3
24
>5
>6
# Matches
# Matches
(a) Prediction Ground truth
(b) Ground truth Prediction
Figure 4: Comparison on point percentage the number of matches per point using CP-Net 64 on ShapeNet-Paad 65 dataset, where the CP-Net trained with five different loss functions. Clearly. InfoCD has better point spread and thus distribution alignments.
To demonstrate the capability of our InfoCD loss to spread the matched points at test time, we illustrate some comparison results in Fig. + where we can see clearly that InfoCD can sig- nificantly reduce the numbers of many-to-one matched points, leading to better point distribu- tion alignments.
Convergence. In general, there is no guaran- tee that training networks with InfoCD using (stochastic) gradient descent will converge the matched point pairs between the predictions and ground truth are frequently changed. However, empirically we observe that such training stabilization can be efficiently reached using different net- works on different datasets as well. For instance, as illustrated in Fig. a InfoCD with L.1 -isttacee in Eq. 4 behaves similarly in terms of convergence rate to L1-CD that has convergence guarantee, but reduces the loss more significantly.
Chamfer distance
(b) InfoCD
Figure 3: Illustration of the moving directions of
matched points using (a) Chamfer distance or (b) InfoCD. Blue: ground truth; Red: predictions.
As illustrated in Fig. ()), ideally CD aims to reach the status where all the predicted points will be aligned per- fectly with ground truth with no errors by consistently minimizing the distances. Such requirement may be so strict that in learning the optimization may be much eas- ier to be stuck the suboptimal solutions, e.g., forming clusters around some points. In contrast, InfoCD aims to align the point distributions with sufficiently small errors, as illustrated in Fig. [5(c with the dotted lines indicating a Voronoi diagram the ground-truth point cloud. This is much less strict than CD, and thus will be more likely to locate better solutions. In fact, movements of predicted points in Fig. ())b provide an effective way towards learning such an alignment in Fig. 5(c) by avoiding bad suboptimal solutions.
Training Loss
1.8
1.6
1.4
50
100
150
200
Epochs
(a)
Choice of d in InfoCD, In particular, we utilize L1- distance in Eq. 4 as the choice for d in InfoCD, be- cause it is unbiased the distance, i.e., Vd(æaj, ya)) V| Ball. In practice, we observe that using d(ziy yik) = ||a Ii 1PP.P > 0.p * 1, the perfor- mance of InfoCD is very unstable for different networks
(b)
(c)
Figure 5: Illustration of (a) training loss using CP-Net on ShapeNet-Part, and ideal point alignment with (b/c) CD/InfOCD.
TThe two loss curves aligned for better view that the starting values identical.

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across different datasets. This is understandable: in the extreme cases where || - yik - 0, p 1 would make the predicted point unchanged. while 0 < p < would make the move of the predicted point very far away. Such updates will violate the goal of InfoCD as shown in Fig. [(c).. Other distance metrics will be investigated in our future work.
4
Experiments
Datasets. We conducted experiments for point cloud completion on the following datasets:
This is subset of ShapeNet [66] with shapes from 8 categories. The incomplete point clouds are generated by back-projecting 2.5D depth images from 8 viewpoints in order to simulate real-world sensor data. For each shape, 16,384 points uniformly sampled from the mesh surfaces as complete ground truth, and 2,048 points are sampled as partial input [00]]
PCN [00]:
Multi-view partial point cloud (MVP) 167/: This dataset covers 16 categories with 62,400 and 41, 11,600 pairs for training and testing, respectively. It renders the partial 3D shapes from 26 uniformly distributed camera poses for each 3D CAD model selected from ShapeNet [68] and the ground -round-truth point cloud is sampled via Poisson Disk Sampling (PDS).
ShapeNer- -55-3//44 !6 ShapeNet-55 contains 55 categories ShapeNet with 41,952 shapes for training and 10,518 shapes for testing. ShapeNet-34 uses a subset of 34 categories for training and leaves 21 unseen categories for testing where 46,765 object shapes are used for training. 3,400 for testing on seen categories and 2,305 for testing on novel (unseen) categories. In both datasets, 2,048 points are sampled as input and 8,192 points as ground truth. Following the same evaluation strategy with [16]. 8 fixed viewpoints are selected and the number of points in the partial point cloud is set to 2,048, 4,096 or 6, 144 (25%, 50% or 75% of a complete point cloud) which corresponds to three difficulty levels of simple, moderate and hard in the test stage.
ShapeNet- [65/: This is a subset of ShapeNetCore (66) 3D meshes, containing 17,775 different 3D meshes with 16 categories. The ground-truth point clouds were created by sampling 2,048 points uniformly on each mesh. The partial point clouds were generated by randomly selecting a viewpoint as center among multiple viewpoints and removing points within certain radius from the complete data. The number of points we remove from each point cloud is 512.
Implementation. We con- sidered three state-of-the- art networks, CP-Net [64], PointAutN and Seed-
Table I: Comparison on PCN in terms of per-point LI-CD x 1000..
Methods
Plane Cabinet
Car
Chair Lamp Couch Table Boat Avg.
TopNet
69
7.61
13.31
10.90
13.82
14.44
14.78
11.22
11.12
Former 8 as our back-
AtlasNet 70
6.37
11.94
10.10
12.06
12.37
12.99
10.33
10.61
10.85
bone networks for compar-
GRNet 7
6.45
10.37
9.45
9.41
7.96
10.51
8.44
8.04
8.83
CRN 25
4.79
9.97
8.31
9.49
8.94
10.69
7.81
8.05
8,51
ison and analysis. We also
NSFA 24
4.76
10.18
8663
8.53
7.03
10.53
7.35
7.48
8.06
applied InfoCD to almost all the popular completion networks, i.e., PCN [10)
FBNett 72
3,99
9.05
7.90
7.38
5.82
8.85
6.35
6.18
6.94
PCN 10
5.50
22.70
10.63
8.70
11.00
11.34
11.68
8.59
11.27
ClyperCD 355
+ PCN
5,95
11.62
9.33
12.45
12.58
13.10
9.82
9.85
10.59
Foldingget (23) TopNet
InfoCD PCN
5.07
22.27
10.18
8.26
10.57
10.98
11.23
8.15
10.83
669
MSN 33 Cascaded
FoldingNet
23
9.49
15.80
12.61
15.55
16.41
15.97
13.65
14.99114331
14.31
HyperCD + Folding Net
7,89
12,90
10.67
14.55
13.87
14.09
11.86
10.89
12.09
155
VRC (67. PMP-
InloCD+Foldingeet
7,90
12.68
10.83
14.04
14.05
14,56
11.61
11.45
12.14
Net
73
PoinTr [16].
PMP-Net (73
5.65
11.24
9.64
9.51
6.95
10.83
8.72
7.25
8.73
SnowflakeNet [17]. to ver-
HyperCD + PMP-Net
5,06
10.67
9.30
9.11
6.83
11.01
8.18
7.03
8.40
ify its performance by re- placing the original CD loss wherever it occurs. We performed the same replacement for all the other comparative losses in our experiments. We trained all these networks from scratch using Py- Torch, optimized by either Adam [74 or Adam W
InfoCD+PMP-Ner
4.67
10.09
8.87
8.59
6.38
10.48
7.51
6.75
7.92
PoinTr 16]
4.75
10.47
8.68
9.39
7.75
10.93
7.78
7.29
8.38
HyyperCD PoinTr
4.42
9.77
8. 8.22
8.22
6.62
9.62
6.97
6.67
7.56
InfoCD + PoinIr
4.06
9.42
8.11
7.81
6.21
9.38
6.57
6.40
7.24
SnowflakeNet [17
4.29
9.16
8.08
7.89
6.07
9.23
6.55
6.40
7.21
HyperCD SnowflakeNet
3.95
9,01
7.88
7.37
5.75
8.94
6.19
6.17
6.91
InfoCD + SnowflakeNet
4.01
8.81
7.62
5.51
5,80
8.91
6.21
5.05
6,86
PointAut i
3.87
9.00
7.63
7.43
5,90
8.68
6.32
6.09
6.86
HyperCD + PointAmt
3.76
8.93
7.49
7.06
5.61
8.48
6.25
5.92
6.68
Info PointAttN
3.72
8.87
7.46
7.02
5.60
8.45
6.23
5.92
6.65
SeedFormer g
3.85
9.05
8.06
7.06
5.21
8.85
6.05
5.85
6.74
HyperCD SeedFormer
3.72
8.71
7.79
6.83
5,11
8.61
5.82
5.76
6.54
75). Hyperparameters
InfoCD + SeedFormer
3.69
8.72
7.68
6.84
5.08
8.61
5.83
5.75
6.52
such as learning rates, batch sizes and balance factors in the original losses for training baseline
7

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Figure 6: Visual result comparison on PCN. Row-1: Inputs of incomplete point clouds. Row-2:
Outputs of Seedformer with CD. Row-3: Outputs of Seedformer with InfoCD. Row-4: Ground truth.
Table 2: Completion results on MVP in terms of L2-CD x10 and EMD x10?
Waterendff
bookshelf
motorbike
skateboard
airplane
cabinet
Car
chair
hppp
sofa
tabel
bed
heach
bus
guitar
pistol
Methods
Avg.
PCN [1]
4.50
8.83
6.41
13.01
21.33
9.90
12.86
9.46
20.00
10.26
14.63
4.94
1.73
6.17
5.84
5.76
9.78
InfoCD+PCN
3.95
8.82
6.38
12,03
9.63
12.41
8.69
18.92
13.40
5.02
1.84
6.06
5.81
4.37
9.41
TopNet 69
9.12
7.44
13.26
18.64
10.77
12.95
8.98
19.99
9.21
16.06
5.47
2.36
7.06
7.04
4.68
10.30
InfoCD+Top..
9.81 7.42
13.24
17.87
10.52
12.45
8.93
19.69
8.52
5.42 14.62
2.35
7.05
6.52
4.11
10.01
MSN 33
2.73 8.92 6.50
10.75
13.37
9.26
10.17
7.70
17.27
6.64
12.10
1.37
4,59
4.62
3.38
7.99
CD
InfoCD+ MSN
7.28 8.51 6.03
10.18
12.91
8.87
9.72
7.24
16.82
6.21
11.67
4.79
0.91
4.15
4.17
2.97
7.56
Cascaded 25
2.54 8.62 5.93
8.76
11.22
8.46
9.20
6.61
14.63
6.09
10.17
4.95
1.55
4,34
4.23
3.19
7.25
Cascade
2.43 8.05 5.73
8.77
10.47
8.24
9.18
6.41
14.37
6.02
10.45
4.70
1.45
4.23
4.16
2.99
7.12
VRC [7]
2.20 7.92 5.60
7.49
7.45
7.52
5.20
11.90
4,88
7.39
4.53
1.15
3.90
3.44 3.22
6.09
InfoCD+VRC
2.03 7.88 5.41
7.31
7.92
7.22
7.30
5.01
11.67
4.65
7.14
4.30
0.97
4.68
3.19
3.04
5.87
PCN
4,70 7.99 5.75
6.90
11.99
5.32
6.60
5.40
9.84
4.85
7.87
5.24
16.56
4.93
4.86
5
6.80
InfoCD+PCN
3.75 5.59 3.97
5.23
10.11
4.42
5.45
4.67
7.29
4.21
5.55
3.53
6.12
4.02
4.70
3.84
5.17
TopNet
4.07
4.68
8.09
6.27
6.80
3.50
4,26
6.02
3.49
6.18
InfoCD+TopNet
4.47 6.02 3.81
6.82
10.21
6.05
7.12
4.37
7.87
5.87
6.02
3.31
4.06
4.11
5.82
3.15
5.72
MSN
4.02 3.47
4.44
3.74
4.46
3.82
5.27
3.34
4.28
2.92
2.07
3.30
3.62
2.21
3.94
EMD
InfoCD+MSN
2.18 2.97
3.96
5.77
3,21
3.92
3.24
4.75
2.86
3.79
2.41
1.50
2.81
3.09
2.64
3,38
Cascaded
3.03 6.82 5.44
5.16
7.55
5.57
4.73
4.88
6.85
3.51
5.71
5.81
5.30
4,30
4.42
3.44
5.18
InfoCD+Cascade
2.87
5,39
5.06
7.10
5,45
4.57
4.79
6.42
3.49
5.15
5.72
3.58
4.19
4.27
2.91
5.01
VRC
3.03 7.57 6.14
5.49
6.15
5.80
4.65
4.97
6.58
3.45
5.28
6.59
3.08
4.45
4.56
3.20
5.27
InfoCD+VRC
2.68 7.26 5.83
5.15
5.82
5.49
4.36
4.68
6.22
3.13
4.97
6.26
2.77
4.13
4.15
2.89
4.97
networks were kept consistent with the baseline settings for fair comparisons. Hyperparameter InfoCD was tuned based on grid search, while À was set to 10-7 for all the experiments. We conducted experiments Quadro RTX 6000 24G GPUs due to the large model sizes of some baseline networks.
server with NVIDIA A100 80G GPUs and one with 10 NVIDIA
Evaluation. We evaluated the best performance of all the methods using CD (lower is better). We also used F1-Score@ 1 % 776 (higher is better) to evaluate the performance. Note that for the PCN method, we report the results based on the Py PyTcchh implementation from PMP-Net When using the original TensorFlow implementation, it achieves an average result of 10.28 on PCN with the default hyperparameters. However, when trained with our infoCD, it can achieve lower value of 9.86.
4.1 State-of-the-art Comparison
PCN. Following the literature, we report CD with I.I-distance Table | As we can see, InfoCD able to improve the performance of all the baselines consistently and significantly, achieving new

---

state-of-the-ane results. As discussed earlier, numerical metrics such as CD may not faithfully reflect the visual quality, we also provide qualitative evaluation results in Fig. 6 compared with results generated from Seedformer trained with the CD loss. As we can see, both models can reconstruct point clouds in general outlines to some extent, but the completion results with CD are more likely to suffer from distortion in several areas with high noise levels on the surface. In contrast, InfoCD can help the baseline network demonstrably better reconstruct point clouds in general outlines while maintaining the realistic details of the original ground truth with significant noise reduction.
MVP. We evaluate the universality of InfoCD on this dataset with several popular networks for tasks with higher diversities and different designs of architectures. Following the literature, we report CD with L2-distance and EMD in Table 2 Similar to Table the introduction of InfoCD can consistently and significantly improve the performance of all different baselines in both two metrics,
ShapeNet-55/34. We eval-
Table 3: Results on ShapeNet-55 using L.2- x2-CDx10000 and Fl score.
uate the adaptability of In-
foCD on both datasets for
Methods
[Table Chair Plane Car Sofa CD-S
CD-M CD-H Avg. F1
the tasks with higher diver-
PFNet 777
3.95
4.24
1.81
2.53
3.34
3.83
3.87
7.97
5.22
0.339
sities. Table B lists the L2- CD on three difficulty lev-
TopNet [69]
2.21
2.53
1.14
2.18
2.36
2.26
2.16
4.3
2.91
0.126
PCN [0]
2.13
2.29
1.02
1.85
2.06
1.94
1.96
4.08
2.66 0.133
GRNel 71
1.63
1.88
1.02
1.64
1.72
1.35
1.71
2.85
1.97
0.238
els well the average.
FoldingNet 23
2.53
2.81
1.43
1.98
2.48
2.67
2.66
4.05
3.12/0.082
Following the literature, we
InfoCD + FoldinggNet
2.14
2.37
1.03
1.55
2.04
2.17
2.50
3.46
2.71 00137
show the results in 5 cate- gories (Table, Chair, Plane, Car, and Sofa) whose num- bers of training samples are more than 2,500. We also provide the results using the Fl metric. Again InfoCD has significantly improved the baseline models, especially when networks are simpler such as FoldingNet. Please refer to our supplementary for more qualitative evaluations.
PoinTr I6
0.81
0.95
0.44
0.91
0.79
0,58
0.88
1.79
1.09)04464
InfoCD + PoinTr
0.69
0.83
0.33
0.80
0.67
0.47
0.73
1.50
0.90
0.524
SeedFormer X
0.72 0.81
0..0
0.89 0.71
0.50
0.77
1.49
0.422
HyperCD + SeedFFomerr
0.66
0.74
0.35
0.83
0.64
0.47
0.72
1.40
86 0.482
InfoCD SeedFormer
0,65 0.72
0.31 0.81 0.62 0.43
0.71
1.38
0.84
0.490
On ShapeNet-34, we eval- uate performances within 34 seen categories (same as training) as well as 21 unseen categories (not used in training) and list our results in Table We can observe that, again, InfoCD can improve the
Table 4: Results on ShapeNet-34 using L2-CD 1000 and F1 score.
34 seen categories
21 unseen categories
Methods
CD-S CD-M CD-II Avg.
F1
CD-S
CD-M CD-II Avg.
F1
PFNet 77
3.16
3.19
7.71
4.68
0.347
5.29
5.87
13.33
8.16
0.322
TopNet 66
1.77
1.61
3.54
2.31
0.171
2.62
2.43
5.44
3.50
0.121
PCN [0
1.87
1.81
2.97
2.22
0.154
3.17
3.08
5.29
3.85 0.101
GRNel 71
1.26
1.39
2.57
1.74
0.251
1.85
2.25
4.87
2.99
0.216
FoldingNet 23
1.86
1.81
3.38
2.35
0.139
2.76
2.74
5.36
3.62 0.095
InfoCD + FoldingNet
1.54
1.60
3.10
2.08
0.177
2.42
2.49
5.01
3.31 0.157
performance of baseline models, indicating that In- foCD is highly generaliz- able for point cloud com- pletion.
PoinTr [6] InfoCD Poin'Tr
0.76
1.05
1.88
1.23
0.421
1.04
1.67
3.44
2.05 0.384
0.47
0.69
1.35
0.84
0.529
0.61
1.06
2.55
1.41 0.493
SoodFormer H
0.48
0.70
1.30
0.83
0.452
0.61
1.08
2.37
1.35 0.402
HyperCDD SeedFormer
0.46
0.67
1.24
0.79
0.459
0.58
1.03
2.24
1.31 0.428
InfoCD + SeedFormer
0.43
0.63
1.21
0.75
0.581
0.54
1.01
2.18
1.24 0.449
ShapeNet-Part. Previous results in Figs. 4 5 a) show the perfor- mance of CP-Net on this dataset. Below we summarize more results: Table our comparison results of CP-Net trained with some pop- ular losses in the forms of mean and standard deviation (std). From the perspective of the mean, it is clear that InfoCD outperforms the others. Moreover, from the perspective of the std, training with InfoCD much more stable than the others. Fig. ssoows the ablation study for learning rate (Ir) and T in Eq. 5 in terms of L2-CD. Overall, training with InfoCD not sensitive to such hyperparameters.
Table 5: CP-Net Avg. re- sults on ShapeNet-Part.
Loss
L2-CD+10*
LI-CD
4.16++0.028
L2-CD
4.82+0.117
DCD 20)
5.7440.009
HyperCD
4.03 +0.007
InfoCD
4.01
5 Conclusion
In this paper, we propose new loss for point cloud completion, namely InfoCD, contrastive Chamfer distance loss. We show that by regularizing the CD loss with contrastive learning, InfoCD can better align the point distributions between prediction and ground truth, achieving the goal of

---

measuring the underlying geometric surfaces of the point clouds using mutual information (MI) estimation. In particular, we discuss and analyze the relations between InfoCD and MI. the moves of predicted points in learning, training convergence, loss landscapes, and the choice of distance metric in InfoCD. Comprehensive experiments have been conducted to demonstrate its effectiveness and efficiency using 7 networks on 5 datasets, leading to new state-of-the-an results.
Limitations. Due the introduction of new hyper- parameter r in InfoCD, tuning hyperparameter hased on grid search may need more effort, as illustrated in Fig. 7 Also due to the higher nonconvexity of In- foCD than CD, may take more time (or epochs) to train complicated networks (e.g, with large numbers of parameters, or architectures) with InfoCD
200
175
425
1.25
1:00
0.50
410
Acknowledgement
025
0.00
Fangzhou Lin was supported in part by the Support for Pioneering Research Initiated by the Next Gen- eration (SPRING) from the Japan Science and Tech-
Figure 7: Ablation study on Ir vs.
nology Agency. Yun Yue and Ziming Zhang were supported partially by NSF CCF-2006738. Dr. Kazunori D Yamada was supported in part by the Top Global University Project from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT). Vijaya B Kolachalama was supported by the National Institutes of Health (R0I-HL159620, R21-CA253499 2498, R43-DK134273, RF1-AG062109, and P30-AG0T3 300034433,,,) the American Heart Association (20FFRN35460031) and the Karen Toffler Charitable Trust. Venkatesh Saligrama was supported by the Army Research Office Grant W91 10246, AFRLGrant 1A8650--2-C1033 the National Science Foundation grants CCF2007350 and CCF- 1955919. Computations were partially performed on the NIG supercomputer ROIS National Institute of Genetics.
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14


Reviews:
[{"review_id": "Yix0lSRxHC", "reviewer": "Reviewer_Lt2U", "summary": "The paper proposes a contrastive Chamfer distance to tackle the point cloud completion problem. The proposed CD loss maximizes the lower bound of the mutual information between two point cloud-based geometric surfaces, which leads to a more robust measurement of the similarities between two point clouds. On the other hand, the proposed CD loss is equivalent to adding a regularizer to the scaled CD, enabling a relaxed point alignment. Experiments of replacing CD with the proposed InfoCD in many state-of-the-art point completion models on MVP and some ShapeNet-based datasets show the good performance of the method. ", "questions": "Please see the detailed comments above. My main concerns are some unclear arguments and experiment settings. ", "limitations": "The authors have mentioned some limitations in the conclusion section. However, a more detailed discussion is expected. Please see the detailed comments above.\n", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The introduction of the paper is concise and convincing. The authors have identified existing problems in the current research, and propose a solution based on these findings.\n\n- The authors have conducted extensive experiments for the point cloud completion task on various datasets and have used the proposed loss function in different state-of-the-art methods.\n\n- Although the analysis of the proposed CD loss is limited to point cloud completion tasks, the potential usage of the proposed loss function might be broader in various point cloud tasks.\n", "weaknesses": "- The authors claimed that the CD tends to have a hard constraint that points in the source point cloud should exactly lie on the points in the target point cloud. In contrast, InfoCD does not have this hard constraint. However, since usually the number of points in complete and partial point clouds is imbalanced, CD may not have this hard constraint. I wondered if a simple truncated CD would already solve this problem.\n\n- In Line 179, “with another assumption that the matched point pairs keep unchanged over iterations”, which may not always be true. Any intuitions or experimental validations?\n\n- Ablation study on $\\tau$, lr is incomplete and confusing. The limitation is discussed but lacks some quantitative results for the efficiency analysis. The authors are encouraged to discuss the efficiency of the proposed method compared to the original CD loss.\n\n- Table 1, 2, 3, 4 have inconsistent method comparisons. Could the authors provide more explanations?\n\n- The application of the proposed CD loss is limited to point cloud completion. However, a broader discussion of other point cloud tasks could be discussed.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the valuable comments. Below are our responses to the questions arising in the review:\n\n**1.1 A hard constraint on matching for CD and InfoCD:** We think that the reviewer may misunderstand this part. Firstly, we do not claim that InfoCD does not have such a constraint. In fact, due to the nature of nearest neighbor matching, InfoCD does have the hard matching constraint, i.e., one point in the source point cloud has a single match in the target point cloud. This is the same as CD. Secondly, both CD and InfoCD are applied to the reconstructed point cloud (NOT the input PARTIAL point cloud, as the review thought) and the complete point cloud, as distance metrics. \n\n**1.2 CD vs. Truncated CD vs. InfoCD:** Given the limited time, we implemented Truncated CD (T-CD) as T-CD = $\\min(CD, thd)$ where $thd\\in\\{0.2, 0.4, 0.6, 0.8\\}$ denotes a threshold, and tested T-CD on the ShapeNet-Part dataset used in the paper. This method achieves 4.72, 4.78, 4.88, and 4.75 in terms of L2-CD$\\times10^3$, which can be slightly better than CD (4.82) but significantly worse than InfoCD (4.01).\n\n**2. Experimental evidence for the assumption in L179:** In the **newly uploaded PDF file** (please check the attachment), as a demonstration we plot some point correspondences during training over epochs (10,70,130), as shown in Fig. 1 where the blue points are ground truth and the red ones are predictions. InfoCD is able to help stabilize (i.e., keep unchanged) the (correct) correspondences much faster in training.\n\n**3. Training time and GPU memory footprint for computational efficiency:** InfoCD has only a few more operations than CD and thus in theory both computational efficiency should be similar. Numerically, for training CP-Net with CD and InfoCD per iteration it takes 0.4239$\\pm$0.0019 and **0.4498$\\pm$0.0030** second with 1052.627$\\pm$0.0374 and **1053.692$\\pm$0.0425** MB in GPU memory, respectively.\n\n**4. Inconsistancy in comparable methods in Table 1, 2, 3, 4:** We follow the literature, and aim to compare methods with public code as many as possible. Table 1 provides the results on PCN which is the most popular benchmark in the task of point cloud completion. Table 2 focuses on the diversity of models on MVP. For fair comparisons, we use the code public with the dataset to implement all the networks used for MVP. Tables 3 and 4 focus on Shapenet 55/34 that are recently proposed as benchmarks and smaller than the other datasets. We follow the previous works and choose a few representative networks to compare. On all the datasets with all the networks, our InfoCD consistently improves the performance.\n\n**5. A new point cloud task --- Single View Reconstruction (SVR):** Given the limited time, we add a new task of SVR that aims to reconstruct a point cloud from an image of the underlying object. Following 3DAttriFlow (*Wen et. al. \"3D shape reconstruction from 2D images with disentangled attribute flow\". In CVPR, 2022.*) and SnowflakeNet (*Xiang et. al. \"Snowflake Point Deconvolution for Point Cloud Completion and Generation with Skip-Transformer\". TPAMI, 2022.*), we sample 30k points from the watertight mesh in ShapeNet as the ground truth, and output 2048 points for evaluation based on per-point L1-CD$\\times10^2$. We replace CD in SnowflakeNet with InfoCD for training, and list average comparison results below, demonstrating that InfoCD can generalize well for different tasks. \n\n-----------------------------\nMethod                | Ave.\n\n-----------------------------\n\n3DAttriFlow           | 3.02\n\nSnowflakeNet          | 2.86\n\n**InfoCD + SnowflakeNet | 2.73**\n\n-----------------------------\n\n"}, {"review_id": "xLHRWQpKk9", "reviewer": "Reviewer_mFMW", "summary": "The paper introduces a novel loss function called InfoCD for point cloud completion tasks. InfoCD maximizes a lower bound of the mutual information, aiming to improve the quality of the completed point clouds. The experimental results presented in the paper demonstrate promising outcomes, indicating the effectiveness of the proposed approach.", "questions": "See above", "limitations": "Limitations are discussed in the paper", "rating": 5, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Exploring the improved CD loss as a research direction for point cloud reconstruction shows promise and holds significant potential.\n- The paper is well-written and effectively communicates its ideas, making it easy to comprehend and follow.\n- The experimental setup and execution in the paper are adequate, resulting in promising outcomes and supporting the proposed approach.\n- The visual results presented in the paper demonstrate good quality, further reinforcing the effectiveness of the proposed method.", "weaknesses": "1.\n\nI observed a discrepancy between the equation presented in the paper and the implementation found in the provided demo code. This discrepancy, potentially caused by missing brackets and misrepresentation of the intended InfoCD, leads to a mismatch between the experimental results and the proposed idea. Consequently, concerns arise regarding the accuracy of the reported findings and the overall effectiveness of the proposed approach.\n\nI have reviewed the provided code in 'loss_utils.py' and compared it to the equation mentioned in Section 3.2. I have identified a discrepancy in lines 197 and 198.\n\nIn the code, the calculation for l_infoCD(x_i, y_i) is implemented as \"- torch.log(torch.exp(-0.2 * d1) + 1e-7 / torch.sum(torch.exp(-0.2 * d1) + 1e-7,dim=-1).unsqueeze(-1))\". However, it appears that there are missing brackets in the expression. The correct calculation in Python should be \"- torch.log((torch.exp(-0.2 * d1) + 1e-7) / torch.sum(torch.exp(-0.2 * d1) + 1e-7,dim=-1).unsqueeze(-1))\" when the value of \\tau is equal to 5.\n\nTherefore, the issue lies in the missing brackets in the code implementation, which deviates from the equation provided in Section 3.2.\n\n2.\n\nBased on last question, I have concerns regarding the fairness of the comparison. Specifically, I would like to inquire whether both the baseline and the baseline + InfoCD models were trained and tested using identical settings, including training hyperparameters and the number of training epochs. My worry stems from the possibility that the observed improvement may be attributed to factors such as updates to the codebase, variations in training hyperparameters, or even longer training durations. This concern is amplified by the existence of a bug affecting the loss function in the provided code.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for valuable comments. Below we respond to reviewer concerns. \n\n**1. uploaded loss_utils.py code is incorrect:** Nice catch. Indeed this was not what was implemented. We maintained several versions and we apologize for accidentally uploading the incorrect version.\n**The implemented loss is exactly the regularized loss as in Eq. 6** used in all our experiments. \\\n*The correct loss_utils.py* version has in lines 197 (as well as line 235), 198:\n>distances1 = 0.2 * d1 + 1e-7 * torch.log( torch.sum( torch.exp( -0.2 * d1 ), dim=-1 ).unsqueeze(-1) )\\\n>distances2 = 0.2 * d2 + 1e-7 * torch.log( torch.sum( torch.exp( -0.2 * d2 ), dim=-1 ).unsqueeze(-1) ) \\\n>where d1 and d2 denote two distance metrics in the original CD, and 1e-7 is a trade-off constant for the regularizer, which is universal across different datasets and networks.\n\nWe emphasize that this is exactly Eq. 6 (modulo penalty parameter):\n$\\mathcal{L_{\\text{InfoCD}}}(x_i,y_i)=\\frac{1}{\\tau} \\mathcal{L}_{\\mbox{\\small CD}}(x_i,y_i) + \\lambda \\mathcal{R}(x_i,y_i) $\n\n>where we have set $\\lambda=1e-7$ in all our experiments. Notice that the first term on the right, $\\frac{1}{\\tau} \\mathcal{L}_{\\mbox{\\small CD}}(x_i,y_i)$  corresponds to python code \"0.2*d1\" or equivalently \"-torch.log(torch.exp(-0.2 * d1), dim=-1 ).unsqueeze(-1)\" (This equivalent term bears similarity to the incorrect version and we believe is the source of our mistake.). The second term $\\mathcal{R}(x_i,y_i)$ corresponds to python code \"torch.log( torch.sum( torch.exp( -0.2 * d1 ), dim=-1 ).unsqueeze(-1) )\".\n\n\n*Intuitive issue with uploaded version*:\n>Evidently, the misplaced brackets reviewer identified and our incorrectly uploaded version may not work. This is because \"- torch.log(torch.exp(-0.2 * d1) + 1e-7 / torch.sum(torch.exp(-0.2 * d1) + 1e-7,dim=-1).unsqueeze(-1))\" suppresses contribution from the additional term rendering the loss to behave similarly to vanilla CD loss (Note that the distances are normalized to the unit interval).\n\nWe encourage the reviewer to verify our implementation by running the demo code by replacing the indicated lines. \n\n**2. Validation of our experimental results:** We ran our experiments with InfoCD based on the **default** hyperparameters such as learning rate and the maximum number of epochs in the public code, but only replacing the CD loss with our InfoCD loss. This has been clearly stated in the paper in L264-266: **\"Hyperparameters such as learning rates, batch sizes and balance factors in the original losses for training baseline networks  are kept consistent with the baseline settings for fair comparisons.\"**."}, {"review_id": "hQfnnmYPqw", "reviewer": "Reviewer_eAft", "summary": "This paper proposed a novel metric to measure the similarity between two point sets, which is based on the basic formula of InfoNCE loss and the Chamfer distances. The key idea is to implicitly estimate the MI between the two point sets, and the way to achieve such target is to treat the distance of between points as a measurement of positive and negative samples.", "questions": "Please see weakness.", "limitations": "The author has fully addressed the limitations in the draft.", "rating": 9, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. The reviewer is highly in favor of this paper, as this draft addresses a very fundamental problem in the deep learning of point cloud data, which is the similarity measurement between two point sets.  \n2. The geometric based CD/EMD metric have been used for years in point cloud completion/reconstruction area, and the proposed InfoCD loss takes one step further to incorporate the idea of mutual information. The formulation of InfoCD, which is the combination of InfoNCE and Chamfer distance, technically makes sense and is very easy to follow.\n3. The experiments are great, which covers most of the recent work and almost all popular benchmark in point cloud completion. The improvement achieved by InfoCD is non-trivial, and the generalization ability and the performance gain is also impressive.\n4. Potential performance gain on a lot of related tasks such as 2D-3D reconstruction, unsupervised learning, shape generation can benefit from this work. The potential application of InfoCD may not be limited in point cloud completion task.\n", "weaknesses": "1. The convergence analysis is relatively weak, as only the experimental proves is provided instead of a more mathematical proof. This does not trouble the reviewer a lot, because the experimental result compared with CD loss looks very good and convincing.\n2. It is a little bit pity that only the point cloud completion task is discussed. Maybe one or two applications on other tasks could provide more evidence on the generalization ability and the effectiveness of the InfoCD loss. For example, 2D-3D reconstruction.\n\nIn all, the reviewer does not see much weakness in this draft. It is a high-quality paper in terms of the point cloud completion research.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the valuable comments. Below are our responses to the questions arising in the review:\n\n**1. Convergence:** We thank the reviewer for understanding. We will try to develop a convergence theory in our future work.\n\n**2. Generalization ability on new tasks:** Given the limited time, we add a new task of Single-View Reconstruction (SVR) that aims to reconstruct a point cloud from an image of the underlying object. Following 3DAttriFlow (*Wen et. al. \"3D shape reconstruction from 2D images with disentangled attribute flow\". In CVPR, 2022.*) and SnowflakeNet (*Xiang et. al. \"Snowflake Point Deconvolution for Point Cloud Completion and Generation with Skip-Transformer\". TPAMI, 2022.*), we sample 30k points from the watertight mesh in ShapeNet as the ground truth, and output 2048 points for evaluation based on per-point L1-CD$\\times10^2$. We replace CD in SnowflakeNet with InfoCD for training, and list average comparison results below, demonstrating that InfoCD can generalize well for different tasks. \n\n-----------------------------\nMethod                | Ave.\n\n-----------------------------\n\n3DAttriFlow           | 3.02\n\nSnowflakeNet          | 2.86\n\n**InfoCD + SnowflakeNet | 2.73**\n\n-----------------------------"}, {"review_id": "ELD9jiSIqH", "reviewer": "Reviewer_SCvJ", "summary": "This paper proposes a contrastive Chamfer distance loss, which introduces contrastive learning into the CD loss. Experiments are conducted on PCN, MVP, ShapeNet-55/34 and ShapeNet-Part datasets, and state-of-the-art results are achieved on these datasets.", "questions": "When you compare with the original methods, have you retrained these learning-based models on the same datasets?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The idea seems reasonable and the overall performance is good.\n2. The paper is overall well written and easy to follow.\n", "weaknesses": "1. Since the proposed loss is a supervised learning loss, I am a bit worried about the generalization ability of the proposed method in different datasets.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the valuable comments. Below are our responses to the questions arising in the review:\n\n**Generalization ability on different datasets:** To answer this question within limited time, we test our method on **KITTI**, a real-world dataset. Following GRNet (*Xie et. al. \"Grnet: Gridding residual network for dense point cloud completion\". In ECCV, 2020.*), we take a sequence of Lidar scans from KITTI. We then (1) extract points per frame within the object bounding boxes labeled as cars, (2) transform these incomplete point clouds to the box's coordinates, (3) complete them with a model pre-trained on cars from ShapeNet, and (4) finally transform the outputs back to the world coordinates. The table below lists our results where, again, InfoCD can improve the baselines consistently (\"Fidelity\" and \"MMD\" are two distance metrics, the smaller, the better. Please refer to GRNet for more details), demonstrating that InfoCD can generalize well for different datasets (together with the other 4 datasets in the paper). Note that here we still use the default hyperparameters in the original code for fair comparisons.\n\n--------------------\n\nMethod | Fidelity$\\downarrow$ | MMD$\\downarrow$\n\n--------------------\n\nFoldingNet | 7.467 | 0.537\n\n**InfoCD+FoldingNet** | **1.944** | **0.333**\n\n---------------------\n\nPoinTr | 0.000 | 0.526 \n\n**InfoCD+PoinTr** | 0.000 | **0.502**\n\n--------------------"}, {"review_id": "OcSvHwwR2o", "reviewer": "Reviewer_hcgP", "summary": "The paper proposes a contrastive chamfer distance (InfoCD) for point cloud completion. More specifically, the paper shows that minimizing InfoCD is equivalent to maximizing a lower bound of the mutual information between the underlying geometric surfaces, which plays a crucial role in generating and reconstructing detailed object shapes . To verify the effectiveness of the method, extensive experiments are conducted and promising results are obtained.", "questions": "None.", "limitations": "Yes, the authors adequately addressed the limitations.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The idea is interesting and the paper is well-organized.\n2. Extensive experiments are conducted and performances are promising.", "weaknesses": "1. Since the real-world scenario is a critical application in point cloud completion, how about the results on the real-world dataset such as KITTI shown in existing works? \n2. The evaluation metric in Tab.1 should be L2-CD as well according to the PCN paper, since a square root is calculated in the evaluation code.\n3. It is worth comparing the time and memory efficiency among different methods, especially when they are applied to real-world applications or mobile devices.\n4. Inconsistency citation names for [25].", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the valuable comments. Below are our responses to the questions arising in the review:\n\n**1. Results on KITTI:** Following GRNet (*Xie et. al. \"Grnet: Gridding residual network for dense point cloud completion\". In ECCV, 2020.*), we take a sequence of Lidar scans from KITTI. We then (1) extract points per frame within the object bounding boxes labeled as cars, (2) transform these incomplete point clouds to the box's coordinates, (3) complete them with a model pre-trained on cars from ShapeNet, and (4) finally transform the outputs back to the world coordinates. The table below lists our results where, again, InfoCD can improve the baselines consistently (\"Fidelity\" and \"MMD\" are two distance metrics, the smaller, the better. Please refer to GRNet for more details), demonstrating that InfoCD can generalize well for different datasets (together with the other 4 datasets in the paper). Note that here we still use the default hyperparameters in the original code for fair comparisons.\n\n--------------------\n\nMethod | Fidelity$\\downarrow$ | MMD$\\downarrow$\n\n--------------------\n\nFoldingNet | 7.467 | 0.537\n\n**InfoCD+FoldingNet** | **1.944** | **0.333**\n\n---------------------\n\nPoinTr | 0.000 | 0.526 \n\n**InfoCD+PoinTr** | 0.000 | **0.502**\n\n--------------------\n\n**2. Evaluation metric in Table 1:** We follow the paper *Yu et. al. \"PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers\". In ICCV, 2021.*, and use their evaluation code where L1-CD is used. This is different from the PCN paper.\n\n**3. Training time and GPU memory footprint for computational efficiency:** InfoCD has only a few more operations than CD and thus in theory both computational efficiency should be similar. Numerically, for training CP-Net with CD and InfoCD per iteration it takes 0.4239$\\pm$0.0019 and **0.4498$\\pm$0.0030** second with 1052.627$\\pm$0.0374 and **1053.692$\\pm$0.0425** MB in GPU memory, respectively.\n\n**4. We will check the references to make everything consistent.**"}]

Author rebuttal:
We sincerely thank all the reviewers for their valuable comments. In summary,

1. We have responded to all the reviewer comments and uploaded a PDF file to show the point correspondences in training over epochs; this is based on the comment by Reviewer Lt2U. 

2. We have added results from two new experiments: (1) a task of single-view reconstruction (SVR) for Reviewers Lt2U and eAft, and (2) KITTI results for Reviewers SCvJ and hcgP. 

3. We have clarified a mistake in our demo code, as pointed out by Reviewer mFMW. **We will release our code for reproducing our experimental results upon acceptance.**

Meta-review: The paper initially got mixed reviews. The authors submitted a solid rebuttal that helped in clarifying several issues. Unfortunately, the authors uploaded a wrong version of the source code, and caused confusion -- the reviewers accepted this as an unfortunate mistake and ignored the uploaded code. In the end, one champion for the paper and the rest of the reviewers supported this decision. 

AC believes this could be a significant paper as it proposed a new metric that overcomes some of the shortcomings of the popular CD measure used in point cloud processing. Given the importance of the topic and the potential impact, the AC agrees with the reviewers and recommends this to be accepted.
Decision: Accept (poster)