A deep perceptual metric for 3D point clouds
Maurice Quach†, Aladine Chetouani†+, Giuseppe Valenzise†, Frederic Dufaux†;
e Paris-Saclay, CNRS, CentraleSup´
elec, Laboratoire des signaux et syst`
emes; 91190 Gif-sur-Yvette, France
+Laboratoire PRISME, Universit´
Point clouds are essential for storage and transmission of
3D content. As they can entail signiﬁcant volumes of data, point
cloud compression is crucial for practical usage. Recently, point
cloud geometry compression approaches based on deep neural
networks have been explored. In this paper, we evaluate the abil-
ity to predict perceptual quality of typical voxel-based loss func-
tions employed to train these networks. We ﬁnd that the commonly
used focal loss and weighted binary cross entropy are poorly cor-
related with human perception. We thus propose a perceptual loss
function for 3D point clouds which outperforms existing loss func-
tions on the ICIP2020 subjective dataset. In addition, we propose
a novel truncated distance ﬁeld voxel grid representation and ﬁnd
that it leads to sparser latent spaces and loss functions that are
more correlated with perceived visual quality compared to a bi-
nary representation. The source code is available at https: //
github. com/ mauriceqch/ 2021_ pc_ perceptual_ loss .
As 3D capture devices become more accurate and accessi-
ble, point clouds are a crucial data structure for storage and trans-
mission of 3D data. Naturally, this comes with signiﬁcant vol-
umes of data. Thus, Point Cloud Compression (PCC) is an essen-
tial research topic to enable practical usage. The Moving Picture
Experts Group (MPEG) is working on two PCC standards :
Geometry-based PCC (G-PCC) and Video-based PCC (V-PCC).
G-PCC uses native 3D data structures to compress point clouds,
while V-PCC employs a projection-based approach using video
coding technology . These two approaches are complementary
as V-PCC specializes on dense point clouds, while G-PCC is a
more general approach suited for sparse point clouds. Recently,
JPEG Pleno  has issued a Call for Evidence on PCC .
Deep learning approaches have been employed to compress
geometry [5, 6, 7, 8, 9, 10] and attributes [11, 12] of points clouds.
Speciﬁc approaches have also been developed for sparse LIDAR
point clouds [13, 14]. In this work, we focus on lossy point cloud
geometry compression for dense point clouds. In existing ap-
proaches, different point cloud geometry representations are con-
sidered for compression: G-PCC adopts a point representation,
V-PCC uses a projection or image-based representation and deep
learning approaches commonly employ a voxel grid representa-
tion. Point clouds can be represented in different ways in the
voxel grid. Indeed, voxel grid representations include binary and
Truncated Signed Distance Fields (TSDF) representations .
TDSFs rely on the computation of normals; however, in the case
of point clouds this computation can be noisy. We then ignore the
normal signs and reformulate TDSFs to propose a new Truncated
Distance Field (TDF) representation for point clouds
Deep learning approaches for lossy geometry compression
(a) Autoencoder model.
(b) Perceptual loss.
Figure 1. Perceptual loss based on an autoencoder. The grayed out parts
do not need to be computed for the perceptual loss.
typically jointly optimize rate and distortion. As a result, an ob-
jective quality metric, employed as a loss function, is necessary
to deﬁne the distortion objective during training. Such metrics
should be differentiable, deﬁned on the voxel grid and well corre-
lated with perceived visual quality. In this context, the Weighted
Binary Cross Entropy (WBCE) and the focal loss  are com-
monly used loss functions based on a binary voxel grid represen-
tation. They aim to alleviate the class imbalance between empty
and occupied voxels caused by point cloud sparsity. However,
they are poorly correlated with human perception as they only
compute a voxel-wise error.
A number of metrics have been proposed for Point Cloud
Quality Assessment (PCQA): the point-to-plane (D2) metric ,
PC-MSDM , PCQM , angular similarity , point to
distribution metric , point cloud similarity metric , im-
proved PSNR metrics  and a color based metric . These
metrics operate directly on the point cloud. However, they are
not deﬁned on the voxel grid and hence cannot be used easily as
loss functions. Recently, to improve upon existing loss functions
such as the WBCE and the focal loss, a neighborhood adaptive
loss function  was proposed. Still, these loss functions are
based on the explicit binary voxel grid representation. We show
in this paper that loss functions based on the TDF representation
are more correlated with human perception than those based on
the binary representation.
The perceptual loss has previously been proposed as an ob-
jective quality metric for images . Indeed, neural networks
learn representations of images that are well correlated with per-
ceived visual quality. This enables the deﬁnition of the perceptual
loss as a distance between latent space representations. For the
case of images, the perceptual loss provides competitive perfor-
mance or even outperforms traditional quality metrics. We hy-
pothesize that a similar phenomenon can be observed for point
0.5 0.5 0.5 0.5 0.5 0.5 0.5
-0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5
-1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 −0.8
(b) Truncated Signed Distance Field (TSDF).
0.5 0.5 0.5 0.5 0.5 0.5 0.5
0.5 0.5 0.5 0.5 0.5 0.5 0.5
(c) Truncated Distance Field (TDF).
Figure 2. Voxel grid representations of a point cloud. The upper bound distance value is 2 for the TDF and the TSDF. Normals are facing up in the TSDF.
Table 1: Objective quality metrics considered in this study.
Domain Name Signal type Block
D1 MSE Coordinates 7 7 Point-to-point MSE
D2 MSE Coordinates 7 7 Point-to-plane MSE
D1 PSNR Coordinates 7 7 Point-to-point PSNR
D2 PSNR Coordinates 7 7 Point-to-plane PSNR
Bin BCE Binary L1 7Binary cross entropy
Bin naBCE Binary L1 7Neighborhood adaptive binary cross entropy 
Bin WBCE 0.75 Binary L2 7Weighted binary cross entropy with w=0.75
Bin PL Binary L1 3Perceptual loss (explicit) on all feature maps
Bin PL F1 Binary L1 3Perceptual loss (explicit) on feature map 1
TDF MSE Distances L1 7Truncated distance ﬁeld (TDF) MSE
TDF PL Distances L1 3Perceptual loss (implicit) over all feature maps
TDF PL F9 Distances L1 3Perceptual loss (implicit) on feature map 9
Therefore, we propose a differentiable perceptual loss for
training deep neural networks aimed at compressing point cloud
geometry. We investigate how to build and train such a perceptual
loss to improve point cloud compression results. Speciﬁcally, we
build a differentiable distortion metric suitable for training neu-
ral networks to improve PCC approaches based on deep learning.
We then validate our approach experimentally on the ICIP2020
 subjective dataset. The main contributions of the paper are
• A novel perceptual loss for 3D point clouds that outperforms
existing metrics on the ICIP2020 subjective dataset
• A novel implicit TDF voxel grid representation
• An evaluation of binary (explicit) and TDF (implicit) rep-
resentations in the context of deep learning approaches for
point cloud geometry compression
Voxel grid representations
In this study, we consider different voxel grid representations
for point clouds. A commonly used voxel grid representation is
the explicit binary occupancy representation where the occupancy
of a voxel (occupied or empty) is represented with a binary value
(Figure 2a). In the binary (Bin) representation (Figure 2a), each
voxel has a binary occupancy value indicating whether it is occu-
pied or empty. When the ith voxel is occupied, then xi=1 and
Another representation is the implicit TSDF representation
which has been employed for volume compression . Instead of
an occupancy value, the value of a voxel is the distance from this
voxel to the nearest point and the sign of this value is determined
from the orientation of the normal (Figure 2b). However, this
requires reliable normals which may not be available in sparse
and/or heavily compressed point clouds.
Hence, we propose an implicit TDF representation which is
a variant of the TSDF without signs and therefore does not re-
quire normals. In the implicit TDF representation (Figure 2c), the
ith voxel value is xi=d, where dis the distance to its nearest
occupied voxel. Consequently, xi=0 when a voxel is occupied
and xi=dwith d>0 otherwise. Additionally, we truncate and
normalize the distance values into the [0,1]interval with
where uis an upper bound value.
In this study, we focus on the explicit binary and implicit
Objective quality metrics
In Table 1, we present the objective quality metrics consid-
ered in this study. Speciﬁcally, we evaluate metrics that are differ-
entiable on the voxel grid to evaluate their suitability as loss func-
tions for point cloud geometry compression. We include metrics
deﬁned on binary and TDF representations and we compare their
performance against traditional point set metrics.
Voxel grid metrics
We partition the point cloud into blocks and compute voxel
grid metrics for each block. For each metric, we aggregate metric
values over all blocks with either L1 or L2 norm. Speciﬁcally, we
select the best aggregation experimentally for each metric.
Given two point clouds A and B, we denote the ith voxel
value for each point cloud as x(A)
i. Then, we deﬁne the
WBCE as follows
where αis a balancing weight between 0 and 1. The binary cross
entropy (BCE) refers to the case α=0.5.
Different from the WBCE, the Focal Loss (FL) ampliﬁes
(γ>1) or reduces (γ<1) errors and is deﬁned as follows
where αis a balancing weight and the log arguments are clipped
between 0.001 and 0.999.
Compared to the WBCE, the FL adds two factors (1−x(B)
i)γ. However, while in the context of neural training, x(B)
is an occupancy probability, in the context of quality assessment,
iis a binary value. As a result, the FL is equivalent to the
WBCE since γhas no impact in the latter case. For this reason,
we include the WBCE with α=0.75 in our experiments as an
evaluation proxy for the FL used in .
The neighborhood adaptive BCE (naBCE)  was pro-
posed as an alternative to the BCE and FL . It is a variant
of the WBCE in which the weight αadapts to the neighborhood
of each voxel uresulting in a weight αu. Given a voxel u, its
neighboorhood is a window Wof size m×m×mcentered on
u. Then, the neighborhood resemblance ruis the sum of the in-
verse euclidean distances of neighboring voxels with the same bi-
nary occupancy value as u. Finally, the weight αuis deﬁned as
αu=max(1−ru/max(r)),0.001)where max(r)is the maximum
of all neighborhood resemblances.
The Mean Squared Error (MSE) on the TDF is expressed as
We propose a perceptual loss based on differences between
latent space representations learned by a neural network. More
precisely, we use an autoencoder as the underlying neural net-
work. The model architecture of autoencoder used and its training
procedure are presented in the following.
We adopt an autoencoder architecture based on 3D convolu-
tions and transposed convolutions. Given an input voxel grid x,
we perform an analysis transform fa(x) = yto obtain the latent
space yand a synthesis transform fs(y) = ˜xas seen in Figure 1a.
The analysis transform is composed of three convolutions with
kernel size 5, stride 2 while the synthesis transform is composed
of three transposed convolutions with same kernel size and stride.
We use ReLU  activations for all layers except for the last
layer which uses a sigmoid activation.
Using the previously deﬁned architecture, we train two neu-
ral networks: one with explicit representation (binary) and an-
other with implicit representation (TDF).
In the explicit case, we perform training of the perceptual
loss with a focal loss function as deﬁned in Eq. (3). In the implicit
case, we ﬁrst deﬁne the Kronecker delta δisuch that δi=1 when
i=0 and otherwise δi=0. Then, we deﬁne an adaptive MSE loss
function for the training of the perceptual loss as follows
where wis a balancing weight. Speciﬁcally, we choose was the
proportion of distances strictly inferior to 1 with
w=min max ∑i1−δ1−x(A)
where βis a bounding factor such that wis bounded by [β,1−β].
This formulation compensates for class imbalance while avoiding
extreme weight values.
In that way, the loss function adapts the contributions from
the voxels that are far from occupied voxels (x(A)
i=1) and voxels
that are near occupied voxels (x(A)
i<1). We train the network
with the Adam  optimizer.
As seen in Figure 1b, in order to compare two point
clouds x(A)and x(B), we compute their respective latent spaces
fa(x(A)) = y(A)and fa(x(B)) = y(B)using the previously trained
analysis transform. These latent spaces each have Ffeature maps
of size W×D×H(width, depth, height). Then, we deﬁne the
MSE between latent spaces as follows
We compute this MSE either over all Ffeature maps or on single
Table 2: Statistical analysis of objective quality metrics.
Method PCC SROCC RMSE OR
TDF PL F9 0.951 0.947 0.094 0.375
D2 MSE 0.946 0.943 0.100 0.469
TDF MSE 0.940 0.940 0.103 0.385
D1 MSE 0.938 0.933 0.109 0.479
TDF PL 0.935 0.933 0.110 0.490
Bin PL F1 0.922 0.916 0.115 0.406
D2 PSNR 0.900 0.898 0.129 0.500
Bin WBCE 0.75 0.875 0.859 0.144 0.531
Bin PL 0.863 0.867 0.151 0.552
D1 PSNR 0.850 0.867 0.158 0.448
Bin naBCE 0.740 0.719 0.201 0.573
Bin BCE 0.713 0.721 0.207 0.635
Point set metrics
Point-to-point (D1) and point-to-plane (D2)
The point-to-point distance (D1)  measures the average
error between each point in A and their nearest neighbor in B:
where bjis the nearest neighbor of aiin B.
In contrast to D1, the point-to-plane distance (D2) 
projects the error vector along the normal and is expressed as fol-
where bjis the nearest neighbor of aiin B and niis the normal
vector at ai.
The normals for original and distorted point clouds are com-
puted with local quadric ﬁttings using 9 nearest neighbors.
The D1 and D2 MSEs are the maximum of eA,Band eB,Aand
their Peak Signal-to-Noise Ratio (PSNR) is then computed with a
peak error corresponding to three times the point cloud resolution
as deﬁned in .
We evaluate the metrics deﬁned above on the ICIP2020 
subjective dataset. It contains 6 point clouds [31, 32] compressed
using G-PCC Octree, G-PCC Trisoup and V-PCC with 5 different
rates yielding a total of 96 stimuli (with 6 references) and their
associated subjective scores.
For each metric, we compute the Pearson Correlation Coef-
ﬁcient (PCC), the Spearman Rank Order Correlation Coefﬁcient
(SROCC), the Root Mean Square Error (RMSE) and the Outlier
Ratio (OR). We evaluate the statistical signiﬁcance of the differ-
ences between PCCs using the method in . These metrics are
computed after logistic ﬁttings with cross-validation splits. Each
split contains stimuli for one point cloud (i.e. reference point
cloud and its distorted versions) as a test set and stimuli of all
other point clouds as a training set. The metrics are then com-
puted after concatenating results for the test set of each split. They
are summarized in Table 1 and the values before and after logistic
ﬁtting are shown in Figure 3.
We use an upper bound value u=5 when computing the
TDF in Eq. (1) and a block size of 64 when block partitioning
point clouds. The naBCE window size is m=5 as in the original
paper. The perceptual loss is trained with a learning rate of 0.001,
β1=0.9 and β2=0.999 on the ModelNet dataset  after block
partitioning using Python 3.6.9 and TensorFlow  1.15.0.
Comparison of perceptual loss feature maps
In our experiments, we ﬁrst considered the perceptual loss
computed over all feature maps. However, we observed that some
feature maps are more perceptually relevant than others. Con-
sequently, we include the best feature maps for each voxel grid
representation in our results. This corresponds to feature map 9
(TDF PL F9) for TDF PL and 1 (Bin PL F1) for Bin PL.
Moreover, We observe that some feature maps are unused
by the neural network (constant). Therefore, they exhibit high
RMSE values (all equal to 0.812) as their perceptual loss MSE
are equal to 0. Speciﬁcally, we observe that TDF PL has 6 unused
feature maps, while Bin PL has a single unused feature map. This
suggests that the perceptual loss learns a sparser latent space rep-
resentation when using TDF compared to binary. Thus, implicit
representations may improve compression performance compared
to explicit representations as fewer feature maps may be needed.
Comparison of objective quality metrics
In Table 2, we observe that the TDF PL F9 is the best method
overall. In particular, identifying the most perceptually relevant
feature map and computing the MSE on this feature map provides
a signiﬁcant improvement. Speciﬁcally, the difference between
the PCCs of TDF PL F9 and TDF PL is statistically signiﬁcant
with a conﬁdence of 95%.
For voxel grid metrics, we observe that TDF metrics per-
form better than binary metrics. In particular, the RMSEs of the
former are noticeably lower for point clouds compressed with G-
PCC Octree compared to the RMSE of the latter as can be seen in
Table 3. This suggests that implicit representations may be bet-
ter at dealing with density differences between point clouds in the
context of point cloud quality assessment.
We proposed a novel perceptual loss that outperforms ex-
isting objective quality metrics and is differentiable in the voxel
grid. As a result, it can be used as a loss function in deep neural
networks for point cloud compression and it is more correlated
with perceived visual quality compared to traditional loss func-
tions such as the BCE and the focal loss. Overall, metrics on the
proposed implicit TDF representation performed better than ex-
plicit binary representation metrics. Additionally, we observed
that the TDF representation yields sparser latent space represen-
tations compared to the binary representations. This suggests that
switching from binary to the TDF representation may improve
compression performance in addition to enabling the use of better
Logistic G-PCC Octree G-PCC Trisoup V-PCC Reference
0 20004000 6000 8000 0.0 0.2 0.4 0.00 0.25 0.50 0.0 0.2
Bin WBCE 0.75
Bin PL C1
0 10 20 30 0.0 0.5 1.0 0.0 2.5 5.0 7.5 10.0 0.0 0.2
TDF PL C9
Figure 3. Scatter plots between the objective quality metrics and the MOS values. The plots before and after logistic ﬁtting are shown.
Table 3: Statistical analysis of objective quality metrics by compression method.
Method G-PCC Octree G-PCC Trisoup V-PCC
PCC SROCC RMSE PCC SROCC RMSE PCC SROCC RMSE
TDF PL F9 0.975 0.859 0.078 0.936 0.910 0.101 0.897 0.850 0.106
D2 MSE 0.962 0.829 0.094 0.954 0.924 0.103 0.903 0.860 0.103
TDF MSE 0.952 0.839 0.106 0.933 0.917 0.106 0.912 0.867 0.098
D1 MSE 0.976 0.851 0.082 0.937 0.918 0.126 0.876 0.844 0.119
TDF PL 0.970 0.840 0.087 0.918 0.900 0.127 0.876 0.837 0.115
Bin PL F1 0.941 0.786 0.138 0.927 0.907 0.107 0.898 0.865 0.109
D2 PSNR 0.943 0.890 0.110 0.926 0.895 0.108 0.738 0.723 0.166
Bin WBCE 0.75 0.923 0.747 0.163 0.918 0.886 0.112 0.850 0.786 0.164
Bin PL 0.931 0.852 0.186 0.892 0.886 0.130 0.880 0.852 0.142
D1 PSNR 0.903 0.859 0.156 0.910 0.895 0.117 0.599 0.689 0.202
Bin naBCE 0.552 0.357 0.277 0.846 0.786 0.154 0.748 0.692 0.170
Bin BCE 0.946 0.841 0.188 0.776 0.800 0.177 0.574 0.500 0.250
We would like to thank the authors of  for providing their
implementation of naBCE. This work was funded by the ANR
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Maurice Quach received the Computer Science Engineer
Diploma from University of Technology of Compi`
egne in 2018.
He is currently studying for a PhD on Point Cloud Compression
and Quality Assessment under the supervision of Frederic Dufaux
and Giuseppe Valenzise at Universit ´
e Paris-Saclay, CNRS, Cen-
elec, Laboratoire des signaux et syst`