Survey on Deep Learning-Based Point Cloud Compression

Abstract

Point clouds are becoming essential in key applications with advances in capture technologies leading to large volumes of data. Compression is thus essential for storage and transmission. In this work, the state of the art for geometry and attribute compression methods with a focus on deep learning based approaches is reviewed. The challenges faced when compressing geometry and attributes are considered, with an analysis of the current approaches to address them, their limitations and the relations between deep learning and traditional ones. Current open questions in point cloud compression, existing solutions and perspectives are identified and discussed. Finally, the link between existing point cloud compression research and research problems to relevant areas of adjacent fields, such as rendering in computer graphics, mesh compression and point cloud quality assessment, is highlighted.

Full text

Survey on Deep Learning-Based
Point Cloud Compression
Maurice Quach
1
, Jiahao Pang
2
, Dong Tian
2
, Giuseppe Valenzise
1
* and Frederic Dufaux
1
1
CNRS, CentraleSupelec, Laboratoire des Signaux et Systèmes (UMR 8506), Université Paris-Saclay, Gif-sur-Yvette, France,
2
InterDigital, Princeton, NJ, United States
Point clouds are becoming essential in key applications with advances in capture
technologies leading to large volumes of data. Compression is thus essential for
storage and transmission. In this work, the state of the art for geometry and attribute
compression methods with a focus on deep learning based approaches is reviewed. The
challenges faced when compressing geometry and attributes are considered, with an
analysis of the current approaches to address them, their limitations and the relations
between deep learning and traditional ones. Current open questions in point cloud
compression, existing solutions and perspectives are identified and discussed. Finally,
the link between existing point cloud compression research and research problems to
relevant areas of adjacent fields, such as rendering in computer graphics, mesh
compression and point cloud quality assessment, is highlighted.
Keywords: point cloud, compression, deep learning, rendering, quality assessment
1 INTRODUCTION
Recent advances have increased the accuracy and availability of 3D capture technologies making
point clouds an essential data structure for transmission and storage of 3D data. 3D point clouds are
crucial to a large range of applications such as virtual reality (Bruder et al., 2014), mixed reality
(Fukuda, 2018), autonomous driving (Yue et al., 2018), construction (Wang and Kim, 2019), cultural
heritage (Tommasi et al., 2016), etc. In such applications, compression is necessary as large scale
point clouds can have large numbers of points.
Point clouds are sets of points with x, y, z coordinates and associated attributes such as colors,
normals and reflectance. Point clouds can be split into two components: the geometry, the position of
each individual point, and the attributes, additional information attached to each of these points. A
point cloud with a temporal dimension is referred to as a dynamic point cloud, and without a
temporal dimension as a static point cloud.
The Moving Picture Experts Group (MPEG) has promoted two standards (Schwarz et al., 2018):
MPEG Geometry-based Point Cloud Compression (G-PCC) and MPEG Video-based Point Cloud
Compression (V-PCC). These two standards have reached the Final Draft International Standard
stage. G-PCC makes use of native 3D data structures such as the octree to compress point clouds
while V-PCC adopts a projection-based approach based on existing video compression technologies.
In addition, the Joint Photographic Experts Group (JPEG) has issued a call for evidence (JPEG, 2020)
on PCC.
Common capturing techniques for point clouds include camera arrays (Sterzentsenko et al.,
2018), LiDAR sensing (Goyer and Watson, 1963) and RGBD cameras (Besl, 1989). It is
important to consider capturing techniques as the resulting point clouds will exhibit
specific characteristics which can be exploited for compression. Among these
characteristics, the geometry resolution and the number of points are key for point cloud
Edited by:
Yuming Fang,
Jiangxi University of Finance and
Economics, China
Reviewed by:
Miaohui Wang,
Shenzhen University, China
Ionut Schiopu,
Vrije University Brussel, Belgium
*Correspondence:
Giuseppe Valenzise
giuseppe.valenzise@
l2s.centralesupelec.fr
Specialty section:
This article was submitted to
Image Processing,
a section of the journal
Frontiers in Signal Processing
Received: 31 December 2021
Accepted: 26 January 2022
Published: 23 February 2022
Citation:
Quach M, Pang J, Tian D, Valenzise G
and Dufaux F (2022) Survey on Deep
Learning-Based
Point Cloud Compression.
Front. Sig. Proc. 2:846972.
doi: 10.3389/frsip.2022.846972
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 8469721
REVIEW
published: 23 February 2022
doi: 10.3389/frsip.2022.846972

compression algorithms. The ratio between the number of
points and the geometry resolution is the surface sampling
density of the point cloud.
For example, camera arrays tend to produce point clouds that
are dense, regularly sampled and amenable to 2D projections.
RGBD cameras produce point clouds that can be represented on a
2D image with depth and color components; the resulting point
clouds are dense, regularly sampled and susceptible to occlusions.
Spinning LiDAR sensors are commonly used for autonomous
driving, they tend to produce point clouds that can be
approximately represented on a 2D image with depth and
reflectance components. Such LiDAR point clouds are sparse
and unevenly sampled in euclidean space but more dense and
evenly sampled in spherical space which is an approximation of the
sensing mechanism. In Figure 1, we show point clouds captured
with aerial LiDAR (“Dourado Site”), camera arrays (“soldier”and
“phil”) and fused terrestrial LiDARs (“Arco Valentino”).
The target application must also be considered. In the case of
human visualization, a point cloud combined with a rendering
method is a simplified model for a plenoptic function (Landy and
Movshon, 1991) which results in six degrees of freedom.
Therefore, we aim to maximize the perceived visual quality
given a rate constraint. For autonomous driving, we instead
aim to maximize the performance of the autonomous driving
function given a rate constraint. Note that it is actually possible to
improve quality with lower bitrate in the case of point clouds. For
example, sparse samplings of surfaces are more costly to code
compared to dense samplings (watertight at a given resolution).
In addition, compared to dense samplings, sparse samplings can
result in inferior renderings and for autonomous driving, in safety
issues due to occupancy false negatives (not sampled).
This can be explained by the sampling process. The actual state of
each voxel can actually be considered as ternary instead of binary with
unseen, empty and near surface states (Curless and Levoy, 1996). As
as result, deciding the occupancy of unseen voxels is important when
performing compression as a dense surface is less costly to code than a
sparsely sampled surface. In particular, compression methods based
on surface models and deep learning tend to complete missing points
from surfaces in sparser point clouds.
Existing literature reviews provide an overview of MPEG
standardization efforts (Schwarz et al., 2018;Graziosi et al.,
2020;Cao et al., 2021), a classification taxonomy (Pereira et al.,
2020) and an analysis based on the coding dimensionality (Cao
et al., 2019). In this review, we will provide a general overview of
PCC approaches with a focus on deep learning-based methods.
Point clouds can be divided into two components: the
geometry and the attributes. The geometry is represented by
points at given positions and the attributes attach information to
each of these points. These two components can be coded
separately, although it is necessary to transfer attributes if we
code the geometry in a lossy manner as shown in Figure 2.
For geometry, one of the main difficulties is the sparsity of the
signal. Geometry can be considered as a binary signal on a regular
voxel grid. We define sparsity as the ratio between the number of
points and the number of voxels. In addition, we introduce the
concepts of global and local sparsity when evaluating point cloud
sparsity at different Level of Details (LoDs). A point cloud at its
original LoD has certain precision and coarser LoDs are obtained
by reducing this precision usually via quantization. Local sparsity
refers to sparsity localized at finer LoDs and global sparsity to
sparsity localized at coarser LoDs. Note that local and global
sparsity are not mutually exclusive. The localization of sparsity in
specific LoDs has been exploited for better entropy modeling of
octree occupancy codes at different LoDs (Jiang et al., 2012). Such
LoDs can be defined in duality with an octree representation by
assuming the voxel grid dimensions are a common power of two.
Then, quantization by a power of two and duplicate removal is
identical to octree pruning. Following this, coarser LoDs are
typically denser than finer LoDs for locally sparse point clouds
which is important as performance of compression approaches
depends on sparsity characteristics.
For attributes, the sparsity of the geometry which forms the
support for the attributes is also one of the difficulties. An
additional difficulty is the irregularity of the support: while
geometry is a sparse signal on a regular support, attributes
form a signal on an irregular support that may also be locally
sparse, globally sparse or both. Irregularity can thus be defined as
the absence of a regular support structure such as the regular grid
sampling of images. Essentially, regular supports can be defined
as the cartesian product of one or multiple regularly sampled
intervals coresponding to different dimensions (horizontal,
vertical, temporal, ...).
FIGURE 1 | Point clouds visualizations. From left to right, “Dourado Site”(Zuffo, 2018), “soldier”(d’Eon et al., 2017), “phil”(Loop et al., 2016)and“Arco Valentino”
(GTI-UPM, 2016).
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Quach et al. Deep Learning-Based Point Cloud Compression

In the case of text, audio, images and video, the attributes lie on
a regular grid, and the geometry, which represents a negligible
amount of information. In the case of point clouds, we can
consider that the information lies on a sparse subset of a
regular grid and coding this sparse subset (the point positions,
the geometry) is expensive. In addition, the information now lies
on a sparse, irregular domain with irregular neighborhoods
making attribute compression more difficult.
2 POINT CLOUD COMPRESSION
We consider geometry and attribute compression separately and
for each of them, we separate approaches tailored to LiDAR point
clouds as they tend to have very specific structures.
2.1 G-PCC and V-PCC Standards
The MPEG G-PCC standard (MPEG, 2021c) features numerous
techniques in order to handle different types of point clouds. It
separates geometry coding and attribute coding following the
scheme in Figure 2. Geometry can be coded using two modes:
octree coding and predictive geometry coding. Octree coding is a
general compression approach while predictive geometry coding
targets LiDAR point clouds. In addition, compression of LiDAR
point clouds using a sequential structure (MPEG, 2021b) and
compression of point cloud sequences with inter prediction
(MPEG, 2021a) are being investigated as exploratory
experiments.
The MPEG V-PCC standard aims to compress point cloud
sequences using video coding techniques. The point cloud is
divided into patches, they are then packed into a 2D grid and the
geometry and attributes are compressed separately with video
codecs (ITU-T, 2019). Preprocessing and postprocessing
operations such as smoothing, padding and interpolation are
applied to improve reconstruction quality.
2.2 Geometry Compression
Geometry compression can be considered as the compression of a
sparse binary occupancy signal over a regular voxel grid. One of
the main difficulties in compressing geometry is the sparsity of
the signal which can be global, local or both.
By definition, global sparsity occurs when large volumes of
space are entirely empty, e.g. when the point cloud is a scene
composed of multiple objects. It can also be a result of the
sampling process which samples only the surfaces of real
world volumes resulting in the inside of the volumes being
empty. Local sparsity can occur when the sampling density,
the number of points per unit of volume, is low compared to
the considered precision or voxel size. For example, this can
happen in fused LiDAR point clouds of monuments and
buildings as LiDAR sensors provide high precision captures
with a sampling density that can be comparatively low and/or
non uniform.
The structure of the point cloud is also primordial. Spinning
LiDAR point clouds (Li and Ibanez-Guzman, 2020) are both
globally and locally sparse in 3D space but with a model of the
sensor, such as the spherical coordinate system, it becomes more
regular, uniformly distributed and dense.
2.2.1 Regular Point Clouds
2.2.1.1 Octree
Regular point clouds are quite dense allowing compression with a
large range of operations. Among these operations, the simplest is
a hierarchical voxel grid representation with the octree data
structure. The geometry can be locally simplified by fitting a
primitive such as planes, triangles, etc. Transform coding and
dimensionality reduction are also possible by changing the voxel
grid basis to another basis, for example, with projection to 2D or
1D spaces.
The most common geometry compression algorithm is octree
coding (Schnabel and Klein, 2006). 3D space is recursively
divided into eight equal subvolumes until the desired LoD is
achieved. This is equivalent to encoding an occupancy map, i.e. a
binary signal on a voxel grid, in a multiresolution manner. When
a containing volume is empty, all its subvolumes are empty.
Therefore, only the occupancy of valid voxels, whose parents are
occupied, needs to be encoded. This explains the octree-voxel
duality as each level of an octree can be associated with a voxel
grid as shown in Figure 3.
For each octree node, coding can be done bitwise (per voxel)
but also bytewise (per octree node). When coding occupancy bits
bytewise, it is possible to reorder bits to improve compression
FIGURE 2 | Point Cloud Compression by separating geometry and attribute compression.
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Quach et al. Deep Learning-Based Point Cloud Compression

performance. Specifically, approaches using tangent planes to
guide reordering have been explored in the literature (Schnabel
and Klein, 2006;Huang et al., 2008;Jiang et al., 2012). In addition,
an octree node can have between one and eight occupied voxels.
The number of occupied voxels can be encoded to serve as a
context for encoding occupancies (Schnabel and Klein, 2006). For
context based entropy modeling, the estimated occupancy
probabilities can also be conditioned on the previously coded
occupancies in the current octree node (MPEG, 2021c). The
structure of an octree node requires that at least one of eight
occupancy bits is occupied (256 −1 = 255 combinations) and the
voxel grid interpretation enables the use of regular neighborhoods
as contexts.
Taking advantage of the hierarchical nature of the octree, it is
possible to use information from the parent node to code voxel
occupancies at the current LoD Garcia and de Queiroz (2018).
Such hierarchical contexts improve the compression performance
compared to using no context. Furthermore, the neighbors of the
parent node are also used as context in G-PCC neighbor-
dependent entropy context (MPEG, 2021c). Based on the
duality between each octree level and a voxel grid, a regular
neighborhood can be used to construct a voxel-based context
using both current and parent level(s).
2.2.1.2 Transforms and Dimensionality Reduction
Point clouds can be represented using 2D surfaces fitted to the
point cloud. In addition, the points can also be projected onto 2D
surfaces either using predefined surfaces (such as axis aligned
planes) or fitted surfaces. Reducing the dimensionality to a single
dimension makes the point cloud into a point sequence.
For dense point clouds, assuming that points are sampled from
surfaces is common. Therefore, local point distributions can be
modeled using surface models such as planes (Dricot and
Ascenso, 2019b), triangles (Dricot and Ascenso, 2019a), Bézier
patches (Cohen et al., 2017), etc. Surfaces can also be modeled
implicitly with Bézier volumes (Krivokuća et al., 2020) as the level
set of a volumetric function. Sim et al. (2005) also represent point
clouds as a tree of spheres.
The dimensionality of point cloud compression can also be
reduced using projection methods. For example, geometry can be
compressed with dyadic decomposition Freitas et al. (2020);
instead of an octree, a binary tree of 2D binary images is
encoded. A simplified approach based on a single projection
has also been studied (Tzamarias et al., 2021). In Kaya et al.
(2021), the point cloud is partially reconstructed from two
depthmaps and the missed points are encoded separately.
Projections can also be performed adaptively at a local level.
For example, it is possible to project points on a 2D plane and
encode a height field on this 2D plane (Ochotta and Saupe, 2004).
Similarly, the MPEG Video-based Point Cloud Compression
standard (V-PCC) projects the point cloud geometry to a 2D
grid and performs compression with video compression
technologies (ITU-T, 2019). Li et al. (2021) improve upon
V-PCC with occupancy-map-based rate distortion
optimization and partition, Xiong et al. (2021) uses occupancy
map information for fast decision of coding units and fast mode
decision. Similar to V-PCC, Zhu et al. (2021) also propose a view-
dependent video coding approach but focus on quality of
experience for streaming and show competitive results in their
subjective quality experiments. We notice that modeling point
clouds with surface models is the same as projecting the points
onto 2D surfaces with an height field that is zero everywhere i.e.
the third dimension is entirely discarded.
The dimensionality can be further reduced by considering
point clouds as sequences of points. Given a sequence of points
and a prediction method, it is interesting to ask what is the
optimal ordering for compression. However, this is difficult to
compute due to the combinatorial natural of problem. A proxy
criterion for the reordering is a formulation as the Traveling
Salesman problem which is considered in Zhu et al. (2017) with
binary tree based block partitioning.
Graph transforms have also been applied to geometry
compression. When applying the graph transform for
attribute compression, the geometry forms a support on
which a graph and a corresponding basis can be built. In
such approaches, the graph and a corresponding basis are
built from a support and a graph transform is applied to a
function lying on this support. However, the difficulty for
geometry compression is that the geometry is the support
itself or the voxel grid is the support for binary occupancy. In
the first case, the support is not available at the decoder and, in
the second case, the dimensionality is too high. This
conundrum can be resolved by encoding a lower resolution
point cloud (base layer) and upsampling it via surface
reconstruction (upsampled base layer) (de Oliveira Rente
et al., 2019). This upsampled base layer can then be used as
FIGURE 3 | Simplified 2D view of an octree construction. Octrees can be seen as hierarchical binary voxel grids. An occupied voxel has at least one point within its
volume and a valid voxel is possibly occupied while invalid voxels must be empty. Only valid voxels need to be coded at each LoD.
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a support and the original geometry becomes an attribute on
this support which resembles residual coding.
2.2.2 LiDAR Point Clouds
LiDAR point clouds are typically sparse in 3D space and can
exhibit non uniform density due to their specific structures. Due
to the scanning mechanism, spinning LiDAR point clouds are
usually denser near the sensor and sparser far from the sensor.
Such structures can be exploited for compression as these point
clouds typically lie on a lower dimensional manifold in 3D space.
Point clouds captured with LiDAR sensors can often be
represented as a sequence. LASzip (Isenburg, 2013)isa
lossless, order-preserving codec specialized for LiDAR point
clouds treating them as sequences and using metadata related
to the LiDAR scanning mechanism (ASPRS, 2019). In the special
case of spinning LiDAR sensors, Song et al. (2021) separate the
point cloud into ground, object and noise layers. Typically, most
points belong to the ground, and they form circular patterns
which can be efficiently compressed. The point cloud formed by
objects is usually globally sparse: the objects form clusters of
points sparsely located in the scene.
LiDAR point clouds can be transformed to depth images by
approximating the LiDAR sensor mechanism with quantized
spherical angular coordinates. However, this transformation is
often lossy on most LiDAR sensors albeit some new sensors make
it lossless (Pacala, 2018) by outputting a range image directly. The
distortion introduced by this transformation will be acceptable or
unacceptable depending on the application. In Ahn et al. (2015),
range images are compressed with predictive coding in hybrid
coordinate systems: spherical, cylindrical and 3D space. Using
mode selection, the range is predicted either directly, via the
elevation or using a planar estimation. In Sun et al. (2019), the
range image is segmented into ground and objects, followed by
predictive and residual coding for compression.
LiDAR point cloud packets can be directly compressed in some
cases. The point cloud in this format has a natural 2D arrangement
with the laser index and rotation. Full LiDAR point cloud frames are
produced at 10 Hz, while packets are typically produced at
frequencies greater than 1000 Hz. As a result, directly compressing
LiDAR packets is more appealing for low-latency scenarios than full
frames. Such packets can then be compressed using image
compression techniques (Tu et al., 2016). In addition, Tu et al.
(2017) propose the use of Simultaneous Localization And Mapping
(SLAM) to predict and compress dynamic LiDAR point clouds.
In three dimensions, the structure of the LiDAR sensor can
be used as a prior for octree coding. Specifically, sensor
information such as the number of lasers, the position and
angle of each laser and the angular resolution of each laser per
frame can be encoded and exploited to improve compression.
Only valid voxels, or plausible voxels according to the
acquisition model, must be encoded when the acquisition
process is known. This has been implemented as the
angular coding mode in G-PCC (MPEG, 2021c).
2.3 Attribute Compression
The geometry forms a support for the attributes. In classical
compression problems on images, videos, audios have attributes
supported on regular grids. This results in regular neighborhoods
for each sample leading to regular inputs for context modeling.
The main difference between point cloud compression and these
well studied compression problems is that the geometry, i.e. the
support of the attributes, is sparse and irregular instead of being a
regular grid. We show that the different point cloud attribute
compression approaches actually all attempt to address sparsity,
irregularity or both at once. Hence, sparsity and irregularity of
this support are key challenges for point cloud attribute
compression.
In Zhang et al. (2014), sparsity and irregularity are also
referred to as unstructured (absence of a grid structure) and
addressed with a graph transform. de Queiroz and Chou (2016)
specifically aim to address irregularity and Cohen et al. (2016)
focus on sparsity after irregularity has been addressed with a
graph transform (Zhang et al., 2014). We also note that for some
types of point clouds such as LiDAR point clouds, the point cloud
structure, e.g. acquisition structure, can be used to reduce sparsity
and irregularity.
2.3.1 Regular Point Clouds
Point cloud attributes can be compressed using a graph transform
(Zhang et al., 2014). We can construct a graph based on the point
cloud geometry to define a fourier transform on graphs. This
addresses the sparsity and irregularity issue as we are now in the
graph frequency domain instead of the spatial domain. However,
building such graphs and defining the specific transform for
compression is a complex problem. Cohen et al. (2016) focus on
sparse point clouds and propose a method to compact attributes
and generating efficient graphs for compression de Queiroz and
Chou (2017) partition the point cloud into blocks and perform
transform coding on point cloud attributes. Specifically, they
propose a Gaussian Process Transform which is a variant of the
Karhunen-Loève Transform (KLT) that assumes points are
samples of a 3D zero-mean Gaussian Process. Such
approaches resolve the irregularity by working in the spectral
domain defined by a graph transform.
The Region-Adaptive Hierarchical Transform (RAHT) (de
Queiroz and Chou, 2016) is akin to an adaptive variation of a
Haar wavelet for point cloud attribute compression. In addition,
it has been found that reordering of the RAHT coefficients
significantly improves the performance of the run-length
Golomb-Rice coding compared to other entropy coding
schemes (Sandri et al., 2018). Souto et al. (2021) improve
upon this RAHT with Set Partitioning in Hierarchical Trees
(Said and Pearlman, 1996). Chou et al. (2020) generalize the
RAHT with volumetric functions defined on a B-spline wavelet
basis. They show that the RAHT can be interpreted as a
volumetric B-Spline of first order and that higher order
volumetric B-Splines eliminate blocking artifacts. In this case,
the irregularity is resolved by considering the point cloud in an
octree structure. Indeed, the geometric structure is irregular but
the hierarchical relations are regular.
Sandri et al. (2019) propose a number of extensions to the
RAHT in order to compress plenoptic point cloud attributes. In
plenoptic point clouds, the color of a point varies with the viewing
direction. In particular, they find out that the combination of the
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RAHT and the KLT performs best: this method is referred to as
RAHT-KLT. Krivokuća and Guillemot (2020) compress
plenoptic point clouds using a combination of clustering and
separate encoding of diffuse and specular components using the
RAHT-KLT. Krivokuća et al. (2021) extend this approach to
incomplete plenoptic point clouds (6-D) where a point may not
have attributes for some viewpoints as it is not visible. This
extends the RAHT to plenoptic point clouds whose plenoptic
component is irregular. That is, for a given point, some
viewpoints may not be valid and may not have attributes
resulting in a 6-D structure.
G-PCC also proposes an attribute compression scheme based
on prediction and lifting operations (MPEG, 2021c). Multiple
LoDs are constructed and predictors are built based on the
attributes of nearest neighbors. This shows that attribute
compression schemes need not follow the same structure as
geometry compression albeit doing so may provide some
complexity advantages (single pass). Indeed, by assuming that
geometry is fully available when decoding attributes, any type of
division, segmentation can be performed using this information.
Attributes tend to be spatially correlated, hence a subset of point
attributes can form a good basis for estimating remaining
attributes. Similarly to RAHT, while the geometry is irregular,
here a regular hierarchical structure is built.
Mekuria et al. (2017) propose a complete point cloud codec for
both geometry and attribute compression. It is also known as the
“MPEG Anchor”as it was used as a comparison basis in early
stages of the MPEG standardization process for point cloud
compression. Attributes are projected to a 2D image and
compressed using the JPEG codec. Zhang et al. (2017) cluster
the point cloud with mean-shift clustering and compress the
attributes by projecting them on a 2D plane and performing a 2D
Discrete Cosine Transform (DCT). Gu et al. (2017) also explore
the use of a 1D DCT to compress point cloud attributes. First,
they group the points by blocks and order them by their Morton
codes (Morton, 1966). Then, the 1D DCT is applied and entropy
coded. In these approaches, the attributes are mapped on a 2D or
1D regular grid in a spatially contiguous manner. As a result, the
irregularity of the geometry is resolved or at least reduced.
Hou et al. (2017) make use of sparse representations via a
virtual adaptive sampling. Indeed, point cloud attributes have an
irregular structure, reducing a block of voxels (voxel grid) to the
subset of occupied voxels can be viewed as a virtual adaptive
sampling process. Gu et al. (2020) improve upon this approach
with inter-block prediction and run-length encoding. Shen et al.
(2020) also make use of this virtual adaptive sampling
formulation and propose learning a multi-scale structured
dictionary.
V-PCC (MPEG, 2020b) compresses attributes from 2D
projections and video coding. The attributes are mapped to a 2D
image, the image is then smoothed using different methods and
compressed using video compression method (ITU-T, 2019). The
smoothing aims to maximize rate-distortion performance by
completing values of empty pixels. Similarly, He et al. (2020)
propose an approach based on spherical projections to project
both geometry and attributes upon a 2D image. The attribute
image can then be compressed using image compression techniques.
In de Queiroz et al. (2021), the authors propose a model
description for volumetric point clouds that is independent of
lighting and camera viewpoint. This generalizes the concept of
plenoptic point clouds as the point cloud is no longer a simplified
model for the plenoptic function Landy and Movshon (1991).
Instead, the visual aspect of the point cloud can vary depending
on the characteristics of the scene. This is related to the
Bidirectional Scattering Distribution Function (BSDF) (Bartell
et al., 1981) which models how light is reflected or transmitted by
a given surface. In perspective, by rendering point clouds with
surfaces or volumes, it is possible to apply rendering techniques
developed for meshes such as Physically Based Rendering
Greenberg (1999) approaches. This is an important
consideration for attribute compression as it changes the
nature and structure of the attributes being compressed.
2.3.2 LiDAR Point Clouds
LASzip (Isenburg, 2013) is a specialized codec for LiDAR point
clouds. The point cloud is considered as a sequence and the
attributes are compressed using delta coding, predictive coding
and context-based entropy coding. Specifically, the LAS format
(ASPRS, 2019) contains the number of returns and the return
number for an emitted laser pulse. This information is used to
perform context-based entropy coding and improve delta coding
by selecting reference values that are more likely to be similar to
the current value.
He et al. (2020) use equirectangular projection to produce a 2D
image from a LiDAR point cloud. Then, the authors test different
image compression algorithms on color and reflectance images.
Similarly, Houshiar and Nüchter (2015) compressed color images
using the PNG format.
Yin et al. (2021) improve the predicting transform of G-PCC
by exploiting normals. Specifically, the normals of two points are
used to improve G-PCC mode selection. This demonstrates that
attributes can be conditioned on the geometry by their position
on the local characteristics of the geometry such as normals.
3 DEEP LEARNING BASED POINT CLOUD
COMPRESSION
In Figure 4, we present a taxonomy of learning-based approaches
for point cloud compression. A point cloud is composed of two
components, geometry and attributes and can include motion
(dynamic) or not (static). The components can be compressed
separately or jointly and in a lossy or lossless manner.
We also differentiate approaches based on their encoding
domain. Voxel based approaches are typically more suited to
dense point clouds and point-based approaches to sparse point
clouds. Indeed, while the complexity of voxel based approaches
depends on the dimension of the voxel grid (precision), the
complexity of point based approaches depends on the number
of points.
It is also important to consider prior information. The most
common source of structure in point clouds is usually the sensor.
Spinning LiDAR sensors can be approximately modeled using a
spherical coordinate system, point clouds from camera arrays
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have a representation as multiple 2D images, RGBD cameras
produce a point cloud that can be stored on a single 2D image etc.
Taking this prior information into account can yield significant
compression gains but requires specific processing for each type
of prior.
3.1 Geometry Compression
3.1.1 Lossy Compression
By considering point clouds as a binary signal on a voxel grid, we
can use Convolutional Neural Networks (CNNs) for point cloud
geometry compression. Specifically, CNN based autoencoder
architectures aim to transform the input into a lower
dimensional latent space and reconstruct an output identical
to the input. This can be interpreted from the point of view of
transform coding with an analysis f
a
and synthesis transform f
s
as
shown in Figure 5. The quantization part is also essential in that it
must be differentiable in order to train the neural network. It is
shown in Ballé et al. (2017) that additive uniform noise models
quantization well during training and is differentiable.
Additionally, the distribution of the latent space is modeled as
part of the network and the resulting entropy enables rate
distortion optimization of the network for specified rate
distortion tradeoffs. The probabilities predicted by the entropy
model can then be used by an arithmetic coder in order to encode
and decode the latent space.
Quach et al. (2019) introduce the use of CNNs for point cloud
geometry compression and in (Quach et al., 2020b)theproposed
approach significantly outperform MPEG G-PCC (MPEG, 2021c)as
shown in Figure 6. The decoding of a point cloud can be cast as a
binary classification problem in a voxel grid. However, point clouds
tend to be extremely sparse and this causes a class imbalance
problem; this problem is resolved with the use of the focal loss
(Lin et al., 2017). Quach et al. (2021) investigate differentiable loss
functions and their correlation with perceived visual quality. Also,
Guarda et al. (2020b) propose a neighborhood adaptive loss function
as an alternative to the focal loss.
A drawback of CNNs on voxel grids is the significant temporal
and spatial complexity. This can be alleviated by using block
partitioning (Guarda et al., 2019;Wang et al., 2019;Quach et al.,
2020b). Wang et al. (2020) go further along this path by making
use of sparse convolutions (Choy et al., 2019) which reduces the
temporal and spatial complexities even further. However, the
disadvantage is that compression performance on sparse point
clouds is degraded. Furthermore, Killea et al. (2021) propose the
use of lightweight 1D+2D separable convolutions for point cloud
geometry compression resulting in less operations and network
parameters with almost equivalent performance to their
baseline model.
FIGURE 4 | A taxonomy of Learning-based Point Cloud Compression.
FIGURE 5 | Simple autoencoder architecture for compression. f
a
is an
analysis transform, f
s
a synthesis transform, Qrefers to quantization and AC to
arithmetic coding with its associated entropy model.
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Overall, more elaborate neural network architectures are
explored in Wang et al. (2019,2020) and the impact of deeper
neural network architectures is measured in Quach et al. (2020b).
Wang et al. (2020) propose a multiscale approach using sparse
convolutions. This approach is extended in Wang et al. (2021) by
making use of both the previous LoD and the current LoD by
progressively building the current LoD. In particular, the authors
study different levels of progressivity: n-stage with a sequential
dependency chain, eight-stage which unpacks a voxel into eight
subvoxels one by one and 3-stage which unpacks a voxel
dimension-wise into two, four and finally eight voxels. The
authors also make use of the lossless-lossy compression
scheme to adapt their method to point clouds with different
levels of density.
Since the decoding can be cast as a classification problem
(Quach et al., 2019), the compression performance can be
improved significantly with adaptive thresholding approaches.
Indeed, the density of the training dataset and the test dataset may
vary. This can cause a mismatch between the distribution of
predicted occupancy probabilities and the actual occupancies.
This mismatch can be corrected with adaptive thresholding. For
example, Wang et al. (2019) encode the number of points as a
threshold so that the reconstruction has the same number of
points as the original. Quach et al. (2020b) encode a threshold
that is optimal given a specific distortion metric. Guarda et al.
(2020a) perform mode selection on models trained for different
densities in order to achieve adaptive behavior.
The key observation is that CNNs for point cloud geometry
compression tend to be biased towards a particular density
depending on the training dataset and loss function
parameters (Quach et al., 2020b). Adaptive thresholding can
correct this bias and can be based on factors such as the
number of points and the distortion metric. Using mode
selection on models targeting different densities is another way
of making a density adaptive solution. The neighborhood
adaptive loss function also removes the need to adjust focal
loss parameters.
Commonly, one neural network is trained for each Rate-
Distortion (RD) tradeoff. In that way, each network is optimized
for a RD tradeoff at the cost of additional training time. Different
approaches have been proposed to reduce the training time. Quach
et al. (2020b) propose a sequential training scheme that significantly
reduce the training time by progressively finetuning a model trained
on a first RD tradeoff to subsequent RD tradeoffs. Guarda et al.
(2020c) propose the use of implicit-explicit quantization of the latent
space which reduces the number of models to be trained. Implicit
quantization controls the RD tradeoff with a scalar RD tradeoff
parameter in the loss function when training. On the other hand,
explicit quantization controls the RD tradeoff by varying the
quantization step on the latent space. Surprisingly, the
performance of implicit-explicit quantization is higher compared
to implicit-only quantization.
In (Lazzarotto et al., 2021), CNNs are used for block
prediction. More precisely, the blocks are predicted from
already decoded neighboring blocks. Lazzarotto and Ebrahimi
(2021) perform residual coding and encode a residual between a
ground-truth block and a degraded block compressed with
G-PCC. (Akhtar et al., 2020) perform super-resolution using
CNNs which improves the reconstruction quality significantly
without any additional coding cost.
3.1.2 Lossless Compression
Lossless compression algorithms can be extended using deep
learning based entropy models. These entropy models predict
occupancy probabilities which are then fed into an entropy coder.
Different types of contexts can be used to make such predictions.
In the context of octree coding, parent node information can
be used as context. Huang et al. (2020) improve the coding of an
FIGURE 6 | Comparison between geometry compression codecs in (Quach et al., 2020b ) and MPEG G-PCC v10.0 (MPEG, 2021c). Learning-based approaches
can achieve significantly lower distortions at equivalent bitrates.
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octree by proposing a neural network based entropy model for
octree codes. Specifically, this neural network takes the location
and information from the parent node to predict occupancy
probabilities. Biswas et al. (2020) extend this to dynamic point
clouds and propose the use of continuous convolutions to
improve probability predictions using already decoded frames.
However, such a context only provides limited information.
By introducing a sequential dependency in the voxel grid, one
can use voxels at the current LoD as context. Nguyen et al. (2021)
proposes a deep CNN with masked convolutions called
VoxelDNN for lossless compression of point cloud geometry.
The neural network predicts the occupancy probability of each
voxel, and the probabilities are then fed to an arithmetic coder.
The rate-optimized octree partitioning improves performance on
sparser regions. The compression performance is further
improved with data augmentation and context extension
techniques (Nguyen et al., 2021a). The drawback of such
approaches is that the sequential dependency increases
complexity significantly. Nguyen et al. (2021b) reduce the
temporal complexity significantly with a multiscale approach.
It reduces the complexity by estimating the probabilities in
parallel with a multiscale approach which reduces the
sequential dependency when estimating occupancy probabilities.
Also, we can entirely remove the sequential dependencies by
predicting the voxel occupancy using only the parent LoD. Que
et al. (2021) propose a neural network which takes a voxel grid
context from the parent LoD to predict occupancy probabilities.
These probabilities are then used for entropy coding. In addition,
they predict an offset for each point in order to further refine
coordinates. Although such approaches have a reasonable
complexity, they do not take into account already decoded
voxels at the current LoD which limits compression performance.
Kaya and Tabus (2021) propose an approach that makes use of the
current LoD while reducing complexity. Such approaches typically
exhibit a sequential dependency in the current LoD. To alleviate this
issue, the authors propose to process the current LoD by slice. In this
way, the probabilities can be estimated slice by slice instead of voxel
per voxel. The resulting parallelization significantly reduces
complexity while preserving most of the context in the current LoD.
3.1.3 Point-Based Approaches
Point-based approaches process the point cloud as a set of points
instead of a binary occupancy signal over a voxel grid. Yan et al.
(2019) proposed the use of a PointNet-like (Charles et al., 2017)
autoencoder architecture for point cloud geometry compression.
Wen et al. (2020) proposes a similar scheme improved with
curvature-based adaptive octree partitioning and clustering. Gao
et al. (2021) propose a more elaborate neural network architecture
with a novel neural graph sampling module. Wiesmann et al. (2021)
propose a point-based neural network for LiDAR point cloud
compression. The authors propose a convolutional autoencoder
architecture based on the KPConv (Thomas et al., 2019)anda
novel deconvolution operator to compress point cloud geometry.
3.1.4 LiDAR Specific Approaches
With some sensors, the LiDAR point cloud frame is constructed
from packets. A packet is arranged as 2D data with respect to the
laser ID and emission. Tu et al. (2019a) exploit this 2D structure
to compress point cloud geometry with a convolutional Long
Short-Term Memory (LSTM) neural network (Hochreiter and
Schmidhuber, 1997;Shi et al., 2015) and residual coding; this is an
extension of Tu et al. (2017).Tu et al. (2019b) take inspiration
from video coding and divide dynamic point cloud frames into
I-frames and B-frames (ITU-T, 2019). The B-frames are
predicted with U-net (Ronneberger et al., 2015) based flow
computation and interpolation extending work in Tu et al.
(2016).
Assuming that LiDAR point clouds can be represented as a 2D
range image, Sun et al. (2020) also take inspiration from video
coding and propose the use of a convolutional LSTM neural
network to compress the range images.
3.2 Deep Learning Based Attribute
Compression
One key difficulty for point cloud attribute compression is the
irregularity of the geometry. Indeed, the geometry forms the
support of the attributes. Hence, irregular geometry results in
irregular neighborhoods which in turn make context modeling
and prediction schemes difficult. Existing works attempt to
resolve this irregularity by substituting the support.
First, it is possible to assume that the point cloud is a sampling
of a 2D manifold and that it has a 2D parameterization that allows
attributes to be projected onto a 2D image. This is similar to the
concept of UV texture maps (Catmull, 1974) in Computer
Graphics except that here we seek to recover such a
parameterization from a point cloud. In this context, Quach
et al. (2020a) propose a folding based approach for point
cloud compression illustrated in Figure 7. FoldingNet (Yang
et al., 2017) reconstructs a point cloud by folding a 2D plane using
an autoencoder neural network. Building upon this, Quach et al.
(2020a) parameterize a point cloud as a 2D manifold and project
the attributes in 2D space. The attributes can then be compressed
using any image compression method.
Alternatively, attributes can be directly mapped onto a voxel
grid. Alexiou et al. (2020) extend convolutional neural networks
used for geometry compression to attribute compression.
Specifically, they propose joint compression of geometry and
attributes defined on a voxel grid.
Another approach is to design neural networks that
embrace this irregularity. This can be done with point-
based neural networks and convolutions expressed directly
on points (point convolutions). Sheng et al. (2021) propose a
point-based neural network for point cloud attribute
compression. In particular, they propose a second-order
point convolution which improves upon the general point
convolution. Biswas et al. (2020) also make use of point
convolutions for inter-frame coding of intensities for
intensity prediction in dynamic LiDAR point clouds.
Isik et al. (2021) compress point cloud attributes by
representing them with volumetric functions. This is strongly
related to Chou et al. (2020) where attributes are encoded using
volumetric functions parameterized with a B-spline basis. In Isik
et al. (2021), volumetric functions are parameterized with
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coordinate based networks instead and the latent vectors of a
hierarchy of volumetric functions are compressed with RAHT.
Overall, existing works handle the irregularity of the support,
the geometry, by mapping attributes onto a 2D plane, using
CNNs to compress attributes on a voxel grid or using point
convolutions to directly define convolutions on the points.
4 DISCUSSION AND PERSPECTIVES
4.1 Geometry Compression
In Table 1, we show an overview of geometry compression
approaches for point clouds. Methods are divided into
traditional and deep learning based. Different data structures
employed for geometry compression: octree, surface models,
sequence, graphs, voxel grids, range images etc.
For lossless octree coding, we can differentiate approaches
depending on whether they exploit the previous LoD, the current
LoD or both as a context. Using only the octree node information
of the previous LoD presents a complexity advantage in that the
information can be retrieved easily. Using the previous LoD (in a
voxel grid sense) allows for parallel probability estimations on the
current LoD that are more precise than when restrained to the
octree node in the previous LoD. When employing the current
LoD, a sequential constraint is necessary in that we can only use
already decoded occupancies as a context. This results in a more
precise entropy model at the cost of complexity. It is also possible
to combine both the previous and the current LoD. The first
advantage is that the previous LoD can provide coarse occupancy
information for areas of the current LoD that are not yet decoded.
The second advantage is that the sequential constraint can be
loosened to form a hybrid approach that balances coding
performance and complexity.
Projection and surface models transforms the data into
another space which typically has a lower dimensionality or a
different structure. Typical surface models include planes,
triangles etc... Point based deep learning approaches can be
thought of as projection based approaches in that the points
are represented by a codeword in a latent space of lower
dimensionality. The point cloud information is aggregated by
a pooling operation which can be a max-pooling, an adaptive
pooling operation or other types of pooling. Here, we refer to
adaptive pooling as a pooling which aggregates information from
points in a way that depends on the neighborhood structure. This
is typical in point based convolution operators (Thomas et al.,
2019).
Point clouds can also be compressed as a sequence of points.
This can be interesting as it allows for formulating point cloud
compression as a variant of the Traveling Salesman Problem
(TSP) (Zhu et al., 2017). In addition, for LiDAR point clouds, a
natural 1D structure exists and compression these points clouds
as a sequence preserves this natural structure (Isenburg, 2013).
Voxel-based deep learning based methods are the most
common approaches for geometry compression. Specifically,
CNN autoencoders have been used to compress point cloud
geometry as a binary signal over a regular voxel grid. We
notice that an octree level can be represented by a voxel grid
and that the two representations are interchangeable. In
particular, the octree encodes binary voxel grids at multiple
LoDs while eliminating sparsity of the binary signal and
TABLE 1 | Approaches to point cloud geometry compression divided into traditional and deep learning based methods.
Category Traditional Deep learning
Octree entropy coding
Previous LoD, octree
node
Garcia and de Queiroz (2018) Huang et al. (2020)
Previous LoD Schnabel and Klein (2006) Que et al. (2021)
Current LoD —Nguyen et al. (2021),Nguyen et al. (2021a)
Previous + current LoD MPEG (2021c) Nguyen et al. (2021b);Kaya and Tabus (2021)
Projection/Surface
models/Point based
Dricot and Ascenso (2019a,b);Cohen et al. (2017);Krivokućaetal.
(2020);Sim et al. (2005);Freitas et al. (2020);Tzamarias et al. (2021);
Kaya et al. (2021);Ochotta and Saupe (2004);MPEG (2020b)
Yan et al. (2019);Wen et al. (2020);Gao et al. (2021);Wiesmann et al.
(2021)
Sequence Zhu et al. (2017);Isenburg (2013) —
Graph de Oliveira Rente et al. (2019) —
Voxel grid
Vanilla Quach et al. (2019,2020b);Wang et al. (2019);Guarda et al. (2019);
Lazzarotto et al. (2021);Lazzarotto and Ebrahimi (2021)
+ Octree (previous LoD) —Wang et al. (2020)
+ Octree (previous +
current LoD)
MPEG (2021c) Wang et al. (2021)
LiDAR
2D range image model Ahn et al. (2015);Sun et al. (2019) Sun et al. (2020)
2D packets Tu et al. (2017) Tu et al. (2019a)
Temporal prediction Tu et al. (2016) Tu et al. (2019b)
Entropy modeling with
sensor model
MPEG (2021c) —
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reducing the redundancy between LoDs; if the parent voxel is
empty, all its children are empty and need not be encoded. In
addition, block prediction and residual coding have also been
explored using CNN architectures. In general, such networks
predict a field of probabilities. Since the decoding is a
classification problem (Quach et al., 2019), these approaches
can be employed as both lossy (thresholding) and lossless
(thresholding + residual or entropy coding) codecs.
The loss function is a crucial factor when training neural
networks for geometry compression. While for lossless
compression, the binary cross-entropy is suitable as it is
directly related to the bitrate. For lossy compression, it is
important that the loss function is suitable to the application.
For example, loss functions correlated with perceived visual
quality (Quach et al., 2021) would be relevant for applications
with human visualisation. A limitation of current approaches is
the use of simple loss functions such as the binary cross-entropy
which may not adequately model perceived visual quality. An
open question is how to best design such loss functions for the
best rate-distortion performance.
de Oliveira Rente et al. (2019) codes geometry by starting from
a low resolution point cloud, performing surface reconstruction
on this low resolution point cloud and then coding a residual
between this surface reconstruction and the original point cloud.
As Lazzarotto and Ebrahimi (2021) has explored point cloud
residual coding with neural networks, the intersection of deep
learning based residual coding and surface reconstruction can be
an interesting avenue of research.
LiDAR point clouds tend to have very specificstructures
that typically lie in one or two dimensions rather three
dimensions. As such, specialized approaches have been
developed to compress LiDAR point clouds. LiDAR point
clouds can be compressed as 2D range images, as 2D LiDAR
packets but also applying specific temporal prediction
techniques such as SLAM or flow estimation. This is
applicable both for learning-based (Tu et al., 2019b,a)and
handcrafted methods (Tu et al., 2016,2017).
4.1.1 Compression Performance
MPEG (2021d) performed a comparison in the performance of
different state of the art point cloud compression approaches.
Overall, CNN based approaches (Guarda et al., 2020a;Quach
et al., 2020b;Nguyen et al., 2021a;Kaya and Tabus, 2021;Wang
et al., 2021) outperform the G-PCC codec with the drawback of
additional computational complexity. CNN based methods seem
to perform better on denser point clouds. Indeed, a difference is
observed between 10-bit dense (watertight) point clouds
(longdress, redandblack, loot, soldier) from d’Eon et al. (2017)
and sparser 12-bit point clouds (house without roof, statue klimt)
which require downscaling the voxel grid in order to make the
point cloud denser and obtain competitive compression
performance. Also, CNN based methods using sparse
convolution (Wang et al., 2021) achieve state of the art
compression performance with lower computational
complexity compared to dense convolutions. As described in
(MPEG, 2021d), the runtime on GPU is faster to the G-PCC
runtime on CPU. However, on a CPU it is still significantly slower
(3.65 times slower for encoding and 37.1 times slower for
decoding).
4.2 Attribute Compression
Traditional approaches handle the irregularity of the geometry by
making use of the octree structure to build a multiscale
decomposition of the attributes (de Queiroz and Chou, 2016).
Also, we can build a graph and use the Graph Fourier Transforms
(GFTs) or similar transforms to compress attributes (Zhang et al.,
2014). In addition, attributes can be mapped onto a 2D grid and
then compressed using image compression methods (Mekuria
et al., 2017); and similarly, points can be ordered into a sequence
and compressed as such (Gu et al., 2017). Another type of
approach is to modelize the irregularity of the geometry with
a virtual adaptive sampling process (Hou et al., 2017). Essentially,
we modelize the attributes as a 3D field over a voxel grid and this
field is sampled at occupied voxels.
4.2.1 3D Approaches
Deep learning based methods handle the irregularity of the
geometry by using a 3D regular space (voxel grid) (Alexiou
et al., 2020), by mapping attributes onto a 2D grid (Quach
et al., 2020a) or with the use of point convolutions to define
CNNs that operate directly on the points (Sheng et al., 2021).
Note that such point convolutions can often be seen as graph
convolutions with the topology of the graph built from the point
cloud geometry and its neighborhood structure.
The essence of attribute compression is handling the
irregularity of the geometry. One approach is to map
attributes into n-dimensional regular grids where we usually
have 1 ≤n≤3. In addition to this mapping, with the virtual
adaptive sampling hypothesis, we can extrapolate attribute values
to non-occupied voxels to simplify the problem to compression of
a 3D regularly sampled field (instead of irregularly sampled).
Another approach is to embrace the irregularity of the geometry
and make use of the same octree structure that is commonly used
for compression of the geometry.
In Table 2, we can see that deep learning based point cloud
attribute compression is still relatively unexplored. Current deep
learning based approaches are not competitive with G-PCC or
V-PCC (MPEG, 2021c;2020b). One of the key difficulties is how
to handle the irregularity of the geometry and from Table 2 we
can see a few interesting points.
Alexiou et al. (2020) has explored the use of CNNs on voxel
grids for point cloud attribute compression. However, the
combination between such approaches and the virtual adaptive
sampling hypothesis explored in numerous works (Hou et al.,
2017;Gu et al., 2020;Shen et al., 2020) for learning sparse
dictionaries has not been explored. Indeed, we can interpret
point cloud attributes as a color field defined everywhere on a
voxel grid but only sampled at occupied locations. Then, these
attributes could be compressed by first extrapolating the color
field values everywhere on the voxel grid and compressing the
resulting regularly sampled color field.
Octree-based approaches, such as the RAHT (de Queiroz and
Chou, 2016), are an interesting basis for deep learning based
approaches. Specifically, sparse convolutions (Choy et al., 2019)
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may be a possible avenue to express convolutions on an octree
structure as is done for geometry compression in Wang et al.
(2020). As there is a duality between octree and voxel grids, the
same question about extrapolation applies. It is an open question
whether good convolutional transforms can be learned to
compress attributes that lie on an irregular geometry and thus
have irregular neighborhoods. In addition, inspired by RAHT,
Isik et al. (2021) propose a deep learning attribute compression
approach based on volumetric functions parameterized by
coordinate based neural networks. They adopt a hierarchical
structure of latent vectors which are compressed with RAHT.
Compressing attributes as volumetric functions is similar in
spirit to virtual adaptive sampling and extrapolation. All three of
these approaches remove the irregularity by assuming that the
attributes are samples of an attribute field defined over 3D space
(a volumetric function) which can be seen as a virtual adaptive
sampling process. In other words, this is also extrapolating
missing values from the available samples. The final result is
that the attributes are now defined over the entire 3D space
removing the sparsity and irregularity which may arise from the
geometry.
4.2.2 Dimensionality Reduction
Point cloud attribute compression is difficult due to the
irregularity and sparsity of the support. It is possible to
attenuate the irregularity with projections to lower dimensions
which makes the support denser and more regular. In addition,
techniques to remove the irregularity and sparsity in the 3D
domain are actually applicable in all dimensions. This is
interesting as point clouds are known to exhibit certain
structures. For example, LiDAR point clouds have a 1D
structure and most point clouds have a 2D manifold or
surface structure.
Numerous approaches have explored the use of 2D images for
point cloud attribute compression (Mekuria et al., 2017;Zhang
et al., 2017;MPEG, 2020b). Specifically, Quach et al. (2020a) has
explored a deep learning based approach for mapping attributes
from each point to a 2D image using a FoldingNet (Yang et al.,
2017). This presents the advantage of enabling the use of any
image processing or image compression method. However, the
complexity is high and the mapping can introduce distortion.
Similar to 3D approaches, extrapolation for empty pixels in the
image domain improves rate-distortion performance. Mekuria
et al. (2017) has proposed a simple mapping procedure that
makes use of Morton ordering and MPEG (2020b) a more
advanced procedure that segments the point cloud according
to their normals and performs bin packing to store them in a 2D
image. To the best of our knowledge, the combination of such
handcrafted mappings and deep learning based image
compression methods (Ballé et al., 2017) has not been
explored yet and may be promising.
Point cloud attributes can also be compressed as a sequence of
points. This is especially suitable for spinning LiDAR point clouds
which have a clear 1D structure. In Isenburg (2013), both LiDAR
point cloud geometry and attributes such as reflectance are
compressed as a sequence. Currently, while research is
considering compression with 2D structures (Tu et al., 2019a),
deep learning based approaches have not been explored for 1D
structures yet.
Dimensionality reduction for point cloud attribute
compression essentially exploits the spatial structure to
alleviate irregularity and sparsity. How to find a new geometry
(support) and a mapping from the original geometry to the new
geometry that results in the best rate-distortion performance
remains an open question. A limitation of existing approaches is
that the new geometry and its mapping are fixed and not
optimized for rate-distortion.
4.2.3 Graph Based Approaches
Graph based approaches have been used to compress point cloud
attributes with the GFT (Zhang et al., 2014;Cohen et al., 2016;de
Queiroz and Chou, 2017). Point based approaches can be
considered as a special case of graph based approaches where
the graph is defined by the point cloud geometry. In Sheng et al.
(2021), point convolutions are proposed for the compression of
attributes. Such convolutions have been shown to perform well
for tasks such as classification and segmentation but the
compression performance is currently lacking compared to
traditional approaches such as the G-PCC implementation of
RAHT (MPEG, 2021c). Point based neural networks are
interesting as the complexity of these approaches depends on
the number of points and not on the number of voxels. The
drawback is that we are not working on a regular voxel grid
anymore which makes the design of such networks more difficult.
As such, a currently open question is how to build high
performance point convolutional neural networks for attribute
compression?
4.2.4 Compression Performance
Currently, deep learning based attribute compression approaches
(Alexiou et al., 2020;Quach et al., 2020a;Isik et al., 2021;Sheng
et al., 2021) are not yet competitive with the latest G-PCC codec.
TABLE 2 | Approaches to point cloud attribute compression divided into traditional and deep learning based methods.
Category Traditional Deep learning
Graph Zhang et al. (2014);Cohen et al. (2016);de Queiroz and Chou (2017) Sheng et al. (2021)
Octree de Queiroz and Chou (2016);Sandri et al. (2018);Souto et al. (2021);Chou et al. (2020) Isik et al. (2021)
Octree (plenoptic point clouds) Sandri et al. (2019);Krivokuća and Guillemot (2020);Krivokuća et al. (2021) —
Voxel grid Hou et al. (2017);Gu et al. (2020);Shen et al. (2020) Alexiou et al. (2020)
2D grid Mekuria et al. (2017);MPEG (2020b);Zhang et al. (2017) Quach et al. (2020a)
Sequence Gu et al. (2017);Isenburg (2013) —
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However, it is shown in Isik et al. (2021) and Sheng et al. (2021)
that these approaches are actually competitive with RAHT which
is used in G-PCC but improved with additional coding tools such
as predictive RAHT, context adaptive arithmetic coding and joint
entropy coding of color as discussed in Isik et al. (2021).In
addition, Quach et al. (2020a) actually show performance close to
earlier versions of G-PCC at the cost of high complexity which is
also the case of Isik et al. (2021).
4.3 LoD Decomposition and Compression
For both geometry and attribute compression, it is interesting to
consider the point cloud decomposed into multiple LoDs.
Specifically, with LoDs based on octree decomposition, we can
consider sparsity for a given LoD as the number of occupied
voxels divided by the number of valid voxels at this LoD. Then, we
can consider point clouds whose coarse LoDs are sparse as
globally sparse: it can be the case in a point cloud composed
of multiple objects. And we can consider point clouds whose finer
LoDs are sparse as locally sparse: this typically happens in LiDAR
point clouds or when the geometry resolution is too high
compared to the number of points. This is important as
certain methods are known to work better on dense point
clouds (such as CNN based methods) than sparse ones.
In addition, decomposing the point cloud into multiple LoDs
also allows us to mix differents compression methods. A common
scheme is to perform block partitioning before applying
compression methods that are more computationally
expensive. This can be seen as compressing a set of block
coordinates, which is by definition a point cloud, and then
compressing a point cloud for each block. Such
decompositions can be performed according to LoDs which
makes it possible to code sparse LoDs separately (with
different methods) from dense LoDs. A very common
situation is that the first LoDs are dense and the last few LoDs
are sparse; this typically happens when point cloud geometry is
described with a precision that is high compared to the number of
points or when the sampling is not uniform (such as with LiDAR
point clouds).
An interesting property of such decompositions is that it is
always possible to use a lossless geometry compression approach
followed by a lossy one. For example, when using block
partitioning, the compression of block coordinates can be
performed with not only octree coding but any kind of lossless
point cloud geometry compression method. This is particularly
useful combined with the observation that point clouds can be
sparse at different LoDs and that certain compression methods
are known to work better with certain densities. Considering a
LoD-based point decomposition, it is thus interesting to consider
compression schemes that select the most suitable compression
method for each LoD based on their density. In addition, the
geometric distortion introduced by such lossless-lossy schemes is
bounded by the volume of losslessly coded voxels.
At a given LoD, the relation between compression algorithm,
point cloud characteristics at a given LoD and compression
performance remains an open question. How to best select
and combine compression algorithms to adapt to different
point cloud characteristics is also mostly unexplored. A
limitation of the current state of the art is that algorithms
tend to be specialized or manually tuned towards specific
characteristics: dense, sparse, spinning LiDAR, etc.
4.4 Joint Compression of Geometry and
Attributes in Relation With Rendering
We provide a general overview of the surrounding of point cloud
compression in Figure 8.Wedefine the notion of 3D scene in a
general manner as including real world 3D scenes, meshes, voxels
etc. A 3D scene can be modelled (or acquired, sampled...) into a
point cloud and prior to rendering, point clouds must be
interpreted as they are only sets of coordinates. Common
interpretations of a point include screen-aligned squares with
a given window-space size (“point”primitive), cubes, spheres etc.
In addition, surface reconstruction can also be performed to build
a mesh from a point cloud. Note that point clouds are only one
way to compress 3D scenes and their visualizations.
As shown in Figure 2, separating geometry and attributes
compression simplifies point cloud compression by dividing it
into two independent components. However, jointly compressing
both geometry and attributes may be important when
considering the problem more globally as illustrated in
Figure 8. Indeed, for numerous applications (visualization,
machine vision) geometry and attributes may impact
performance in an interdependent manner. In Computer
Graphics, the well-known bump mapping technique simulates
wrinkled surfaces with a simplified geometry by adding
perturbations to the attributes (Blinn, 1978). In the case of
meshes, perturbations are added to the surface normals which
results in an apparently wrinkled surface due to lighting
calculations. For point clouds, the same could be achieved by
perturbating the point colors.
As a result, an open research question is how to design
compression techniques that compress point cloud geometry
and attributes while maximizing perceived visual quality
subject to a rate constraint? This differs from existing
approaches, which take geometry and attributes into account
separately and evaluate their quality separately.
4.5 LoD Decomposition and Rendering:
Points and Voxels
We have previously treated the topic of rendering and its
importance to point cloud compression and quality
assessment. Also, we have analyzed the topic of point cloud
compression with approaches based on LoD decompositions.
Decompositions can be interpreted in two manners: point based
or volumetric.
In a point based view, the decomposition can be interpreted as
as decomposing the point coordinates. With an octree
decomposition, we decompose the coordinates in base two;
then, the octree can be interpreted as a prefix tree (Briandais,
1959) on the Morton codes (Morton, 1966) of the coordinates.
On the other hand, we can interpret this decomposition in a
volumetric manner. A voxel is occupied if it contains at least one
point within its volume; otherwise, it is empty. When the point
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 84697213
Quach et al. Deep Learning-Based Point Cloud Compression

cloud is represented at a lower LoD, the voxels become larger.
With a point based interpretation, a problem of octree based
compression is that the point cloud becomes sparser at lower
LoDs. The volumetric interpretation offers an alternative in that
the geometry becomes coarser at lower LoDs but not sparser. As a
result, octree based compression with a volumetric interpretation
does not result in sparse renderings. A possible implementation is
to render each voxel as a cube of corresponding volume.
Such coarse but dense geometry for point cloud compression
is interesting as the bounded geometric error allows preservation
of watertightness which is beneficial for rendering quality. How to
best exploit such characteristics of compression algorithms for
rendering remains an open question and is currently unexplored
in the literature.
4.6 Sparsity for Geometry Compression
One of the key problems with point cloud compression is sparsity.
Sparsity can be defined as the ratio between the number of
captured points and the number of voxels which is directly
related to the geometry precision, also defined as geometry
FIGURE 7 | Folding-based attribute compression (Quach et al., 2020a). Attributes are transferred to a 2D grid using a neural network followed by image
compression.
FIGURE 8 | 3D scenes (real world, mesh, point clouds, voxels) can be compressed with point clouds. Depending on the context, different types of distortion may be
evaluated: point cloud distortion, 3D scene distortion (e.g. mesh distortion) or visualization distortion. For visualization distortion, rendering is especially important and
may be optimized as aprt of the point cloud codec.
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 84697214
Quach et al. Deep Learning-Based Point Cloud Compression

bitdepth. The capturing process is the main driver behind
sparsity: point clouds captured with camera arrays are
typically dense because the sampling density is spatially
uniform. On the other hand, LiDAR point clouds have non-
uniform density: denser near the sensor and sparser far from the
sensor. However, they exhibit near uniform density in the
spherical coordinate system which explains non-uniformity in
the 3D space.
In such point clouds, the number of points can be low
compared to the precision of the point coordinates. To obtain
a dense point cloud, it is necessary to use a geometry precision
that is suitable to the number of captured points. This is an
important consideration as some compression methods may
perform better at some density/sparsity levels. For example,
deep learning based convolutional geometry compression
approaches tend to perform better on dense point clouds.
Decomposing point clouds into LoDs is also useful to analyze
point cloud sparsity. In particular, the location of sparse LoDs is
important to differentiate global from local sparsity. Global
sparsity is typically handled by performing block partitioning
which removes global sparsity by focusing compression
algorithms onto occupied blocks. Handling local sparsity is
currently an open problem. One approach is to remove local
sparsity by removing the sparse local LoDs resulting in a dense
point cloud which is easier to compress. Another approach is to
compress these sparse LoDs separately by first using a lossless
compression methods on the first LoDs and another compression
method suitable for sparse point clouds on the later LoDs.
Also, we have observed that on local sparse LoDs, existing
methods are not able to exceed 2 dB per bit per input point per
LoD (D1 PSNR) which is equivalent to the RD performance of a
scalar quantizer. This suggests that sparse local LoDs may not be
compressible beyond this limit in some cases. Whether these local
sparse LoDs are akin to acquisition noise and are not
compressible beyond this limit remains an open question. If
this is true, compressing dense LoDs and these sparse LoDs
separately may be essential to sparse point cloud compression.
4.7 Point Cloud Quality Assessment
Commonly used distortion measures include the point-to-point
(D1), the point-to-plane metric (D2) and other metrics based on
nearest neighbors (MPEG, 2020a). These distortion metrics may
not be suitable for all applications such as LiDAR point clouds for
autonomous driving which may require application-specific
distortion metrics. For instance, Feng et al. (2020) evaluate the
performance of their LiDAR point cloud compression method
with registration translation error, object detection accuracy and
segmentation error. Such metrics may be more relevant than
generic metrics as these are common operations on such point
clouds.
In addition, interpreting LiDAR point clouds in a volumetric
manner could potentially improve safety. Indeed, with volumetric
octree compression point clouds could be compressed with only
false positives. This could be useful for collision avoidance in the
context of autonomous driving. As a result, a distorted point
cloud with distance-bounded distortion and only false positives
could actually improve collision avoidance. However, if such a
distortion is too severe, an autonomous vehicle could fail to find a
valid route to its destination by overestimating the size of
obstacles.
Another related factor is the accuracy and the precision of the
LiDAR sensor. When considering LiDAR point clouds in a
voxelized manner, we may want to consider a certain space
around each occupied voxel as occupied to account for sensor
uncertainty. This may be interesting for collision avoidance as
marking a safety margin as occupied would also make the point
cloud denser and thus easier to compress. Overall, how to design
an objective metric that correlates best with autonomous driving
performance remains an open question.
Furthermore, deep learning based point cloud quality
assessment approaches are being explored (Chetouani et al.,
2021a,b;Liu et al., 2020). We note that it presents the same
challenges as geometry and attribute compression
simultaneously. We consider the following open question: how
to design an objective metric that correlates best with perceived
visual quality? We notice that rendering must be considered as
the point cloud cannot be viewed otherwise. Generally, it is
important to consider what is the distortion of interest: point
cloud distortion, 3D scene distortion, or distortion of the 3D
scene visualization (Figure 8)?
4.8 Relation to Mesh Compression
Meshes can be constructed from point clouds using Poisson
surface reconstruction (Kazhdan et al., 2006) and point clouds
can be sampled from meshes. Surfaces can be represented
explicitly with polygons but also implicitly as Truncated
Signed Distance Functions (TSDFs). As such, meshes can
be compressed under a TSDF representation and deep
learning based convolutional compression techniques for
point clouds (Quach et al., 2019)andformeshes(Tang
et al., 2020) are strongly related. The key difference lies in
the signal representation which can be binary (point clouds)
or a distance field (point cloud or surface). Surface
reconstruction from TSDFs can be performed with
methodssuchasMarchingCubesLorensen and Cline
(1987). It remains an open question how exchange of ideas
between techniques of point cloud and mesh compression
could further progress in both fields.
5 CONCLUSION
Point clouds are increasingly common, with numerous
applications and the large amounts of data are a challenge for
transmission and storage. Compression is thus crucial but also
complex as point cloud compression lies at the intersection of
signal processing, data compression, computer graphics and even
deep learning for state of the art approaches. The signal
characteristics make point cloud compression significantly
different from traditionally compressed media such as images
and video. Indeed, the geometry can be seen as a sparse binary
signal on a voxel grid or as a set of points and the attributes then
lie on this sparse, irregular geometry posing challenges for point
cloud compression.
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 84697215
Quach et al. Deep Learning-Based Point Cloud Compression

In recent works, deep learning based approaches have
exhibited outstanding performance on geometry compression
and have become comparable to state of the art approaches on
attribute compression. However, many challenges remain and
exchange of ideas between traditional and deep learning based
methods have led to fast progress in the field. In this work, we put
a focus on deep learning approaches and highlight their relation
to traditional methods. Specifically, we highlight different
categories of geometry and attribute compression approaches
with relations between deep learning and traditional approaches.
We discuss the importance of LoD decomposition for
compression, the limitation of separating geometry and
attribute compression and the importance of rendering in the
context of compression. Then, we discuss the specific challenges
posed by sparsity for geometry compression, the importance of
point cloud quality assessment and how its challenges mirror
those of compression. Finally, we discuss how point cloud
compression relates to mesh compression and point out their
intersection.
We note that approaches for compressing point cloud
geometry have improved significantly by exploiting the duality
between octree and voxel grid and the LoD decomposition
resulting from octrees. Currently, deep learning approaches
using sparse convolutions offer state of the art performance
and competitive complexity (with GPU) compared to G-PCC
(with CPU). However, the characteristics of point cloud geometry
can vary significantly resulting in numerous parameters that need
to be tuned for a codec to work uniformly well across various
point clouds. We believe that geometry compression approaches
need to combine both hand-crafted and learning based
approaches in order to achieve compression performance,
reasonable complexity and adaptability to different point cloud
characteristics (e.g. density).
In comparison, learning based attribute compression
approaches has been the subject of less research compared to
geometry compression. Current learning based approaches
struggle to compete the state of the art and often come at high
complexity cost. We believe that research into the different
methods to construct regular or almost regular neighborhoods
for the attributes is essential for learning based attribute
compression. For example, using an octree provides a
hierarchical regular neighborhood (one parent for each octree
node) and mapping the attributes to 2D grid can provide an
almost regular neighborhood. The attributes are spatially
correlated and this can be verified visually. As such, a key
question is how can learning based approaches best exploit
this spatial correlation for compression? Using which
representation?
AUTHOR CONTRIBUTIONS
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including articles by sole authors. If an appropriate statement is
not provided on submission, a standard one will be inserted
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authors referred to by their initials and, in doing so, all
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Please see here for full authorship criteria.
FUNDING
This work was funded by the ANR ReVeRy national fund
(REVERY ANR-17-CE23-0020).
REFERENCES
Ahn, J., Lee, K., Sim, J., and Kim, C. (2015). Large-Scale 3D Point Cloud
Compression Using Adaptive Radial Distance Prediction in Hybrid
Coordinate Domains. IEEE J. Sel. Top. Signal. Process. 9, 422–434. doi:10.
1109/JSTSP.2014.2370752
Akhtar, A., Gao, W., Zhang, X., Li, L., Li, Z., and Liu, S. (2020). “Point Cloud
Geometry Prediction Across Spatial Scale Using Deep Learning,”in 2020 IEEE
International Conference on Visual Communications and Image Processing
(VCIP) (IEEE), 70–73. doi:10.1109/VCIP49819.2020.9301804
Alexiou, E., Tung, K., and Ebrahimi, T. (2020). “Towards Neural Network Approaches
for Point Cloud Compression,”in Applications of Digital Image Processing XLIII
(International Society for Optics and Photonics), 1151008. doi:10.1117/12.2569115
ASPRS (2019). LAS Specification, Version 1.4 –R15. American Society for
Photogrammetry & Remote Sensing.
Ballé, J., Laparra, V., and Simoncelli, E. P. (2017). “End-to-end Optimized Image
Compression,”in 2017 5th International Conference on Learning
Representations (ICLR) (IEEE).
Bartell, F. O., Dereniak, E. L., and Wolfe, W. L. (1981). “The Theory and Measurement
of Bidirectional Reflectance Distribution Function (Brdf) and Bidirectional
Transmittance Distribution Function (BTDF),”in Radiation Scattering in
Optical Systems (Huntsville, United States: SPIE), 154–160. doi:10.1117/12.959611
Besl, P. J. (1989). “Active Optical Range Imaging Sensors,”in Advances in Machine
Vision. Editor J. L. C. Sanz (New York, NY: Springer Series in Perception
Engineering), 1–63. doi:10.1007/978-1-4612-4532-2_1
Biswas, S., Liu, J., Wong, K., Wang, S., and Urtasun, R. (2020). MuSCLE: Multi
Sweep Compression of LiDAR Using Deep Entropy Models. Adv. Neural Inf.
Process. Syst. 33, 1.
Blinn, J. F. (1978). “Simulation of Wrinkled Surfaces,”in Proceedings of the 5th Annual
Conference on Computer Graphics and Interactive Techniques (New York, NY:
Association for Computing Machinery), 286–292. doi:10.1145/800248.507101
Briandais, R. D. L. (1959). “File Searching Using Variable Length Keys,”in IRE-
AIEE-ACM Computer Conference (San Francisco, California, United States:
ACM). doi:10.1145/1457838.1457895
Bruder, G., Steinicke, F., and Nüchter, A. (2014). “Poster: Immersive point Cloud
Virtual Environments,”in 2014 IEEE Symposium on 3D User Interfaces
(3DUI) (IEEE), 161–162. doi:10.1109/3DUI.2014.6798870
Cao, C., Preda, M., and Zaharia, T. (2019). “3D Point Cloud Compression,”in The
24th International Conference on 3D Web Technology (UCLA, CA: ACM),
1–9. doi:10.1145/3329714.3338130
Cao, C., Preda, M., Zakharchenko, V., Jang, E. S., and Zaharia, T. (2021).
Compression of Sparse and Dense Dynamic Point Clouds-Methods and
Standards. Proc. IEEE 109, 1537–1558. doi:10.1109/JPROC.2021.3085957
Catmull, E. E. (1974). A Subdivision Algorithm for Computer Display of Curved
Surfaces. Salt Lake City, United States: Ph.D. thesis, The University of Utah.
Charles, R. Q., Su, H., Kaichun, M., and Guibas, L. J. (2017). “PointNet: Deep
Learning on Point Sets for 3D Classification and Segmentation,”in 2017 IEEE
Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE),
77–85. doi:10.1109/CVPR.2017.16
Chenxi Tu, C., Takeuchi, E., Miyajima, C., and Takeda, K. (2016). “Compressing
Continuous Point Cloud Data Using Image Compression Methods,”in 2016
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 84697216
Quach et al. Deep Learning-Based Point Cloud Compression

IEEE 19th International Conference on Intelligent Transportation Systems
(ITSC) (IEEE), 1712–1719. doi:10.1109/ITSC.2016.7795789
Chetouani, A., Quach, M., Valenzise, G., and Dufaux, F. (2021a). “Convolutional
Neural Network for 3D Point Cloud Quality Assessment with Reference,”in
IEEE International Workshop on Multimedia Signal Processing (MMSP’2021)
(IEEE).
Chetouani, A., Quach, M., Valenzise, G., and Dufaux, F. (2021b). “Deep Learning-
Based Quality Assessment of 3d Point Clouds Without Reference,”in 2021
IEEE International Conference on Multimedia Expo Workshops (ICMEW)
(IEEE), 1–6. doi:10.1109/ICMEW53276.2021.9455967
Chou, P. A., Koroteev, M., and Krivokuca, M. (2020). A Volumetric Approach to
Point Cloud Compression-Part I: Attribute Compression. IEEE Trans. Image
Process. 29, 2203–2216. doi:10.1109/TIP.2019.2908095
Choy, C., Gwak, J., and Savarese, S. (2019). “4D Spatio-Temporal ConvNets:
Minkowski Convolutional Neural Networks,”in 2019 IEEE/CVF Conference
on Computer Vision and Pattern Recognition (CVPR) (Long Beach, CA: IEEE),
3070–3079. doi:10.1109/CVPR.2019.00319
Cohen, R. A., Krivokuca, M., Feng, C., Taguchi, Y., Ochimizu, H., Tian, D., et al.
(2017). “Compression of 3-D point Clouds Using Hierarchical Patch Fitting,”in
2017 IEEE International Conference on Image Processing (ICIP) (IEEE),
4033–4037. doi:10.1109/ICIP.2017.8297040
Cohen, R. A., Tian, D., and Vetro, A. (2016). “Attribute Compression for Sparse
Point Clouds Using Graph Transforms,”in 2016 IEEE International
Conference on Image Processing (ICIP) (IEEE), 1374–1378. doi:10.1109/
ICIP.2016.7532583
Curless, B., and Levoy, M. (1996). “A Volumetric Method for Building Complex
Models from Range Images,”in Proceedings of the 23rd Annual Conference on
Computer Graphics and Interactive Techniques - SIGGRAPH ’96 (New
Orleans, LA, United States: ACM Press), 303–312. doi:10.1145/237170.237269
de Oliveira Rente, P., Brites, C., Ascenso, J., and Pereira, F. (2019). Graph-Based
Static 3D Point Clouds Geometry Coding. IEEE Trans. Multimedia 21,
284–299. doi:10.1109/TMM.2018.2859591
de Queiroz, R. L., and Chou, P. A. (2016). Compression of 3D Point Clouds Using a
Region-Adaptive Hierarchical Transform. IEEE Trans. Image Process. 25,
3947–3956. doi:10.1109/TIP.2016.2575005
de Queiroz, R. L., and Chou, P. A. (2017). Transform Coding for Point Clouds
Using a Gaussian Process Model. IEEE Trans. Image Process. 26, 3507–3517.
doi:10.1109/TIP.2017.2699922
de Queiroz, R. L., Dorea, C., Freitas, D. R., Krivokuca, M., and Sandri, G. P. (2021).
Model-Centric Volumetric Point Cloud Attributes. arXiv [Preprint]. Available
at: https://arxiv.org/abs/2106.15539.
de Queiroz, R., Souto, A., Figueiredo, V., and Chou, P. (2021). Set Partitioning in
Hierarchical Trees for Point Cloud Attribute Compression. doi:10.36227/
techrxiv.15032901.v1
d’Eon, E., Harrison, B., Myers, T., and Chou, P. A. (2017). “8i Voxelized Full Bodies
- A Voxelized Point Cloud Dataset,”in ISO/IEC JTC1/SC29 Joint WG11/WG1
(MPEG/JPEG) Input Document WG11M40059/WG1M74006 (Geneva: ISO).
Dricot, A., and Ascenso, J. (2019a). “Adaptive Multi-Level Triangle Soup for
Geometry-Based Point Cloud Coding,”in 2019 IEEE 21st International
Workshop on Multimedia Signal Processing (MMSP) (IEEE), 1–6. doi:10.
1109/MMSP.2019.8901791
Dricot, A., and Ascenso, J. (2019b). “Hybrid Octree-Plane Point Cloud Geometry
Coding,”in 2019 27th European Signal Processing Conference (EUSIPCO),
1–5. doi:10.23919/EUSIPCO.2019.8902800
Feng, Y., Liu, S., and Zhu, Y. (2020). Real-Time Spatio-Temporal LiDAR Point
Cloud Compression. arXiv [Preprint]. Available at: https://arxiv.org/abs/2008.
06972.
Freitas, D. R., Peixoto, E., de Queiroz, R. L., and Medeiros, E. (2020). “Lossy Point
Cloud Geometry Compression via Dyadic Decomposition,”in 2020 IEEE
International Conference on Image Processing (ICIP) (IEEE), 2731–2735.
doi:10.1109/icip40778.2020.9190910
Fukuda, T. (2018). “Point Cloud Stream on Spatial Mixed Reality - toward
Telepresence in Architectural Field,”in Computing for a Better Tomorrow -
Proceedings of the 36th eCAADe Conference - Volume 2. Editors
A. Kepczynska-Walczak and S. Bialkowski (Lodz, Poland: Lodz University
of Technology), 727–734.
Gao, L., Fan, T., Wan, J., Xu, Y., Sun, J., and Ma, Z. (2021). “Point Cloud Geometry
Compression via Neural Graph Sampling,”in 2021 IEEE International
Conference on Image Processing (ICIP) (IEEE), 3373–3377. doi:10.1109/
ICIP42928.2021.9506631
Garcia, D. C., and de Queiroz, R. L. (2018). “Intra-Frame Context-Based Octree
Coding for Point-Cloud Geometry,”in 2018 25th IEEE International
Conference on Image Processing (ICIP) (IEEE), 1807–1811. doi:10.1109/
ICIP.2018.8451802
Goyer, G. G., and Watson, R. (1963). The Laser and its Application to Meteorology.
Bull. Am. Meteorol. Soc. 44, 564–570. doi:10.1175/1520-0477-44.9.564
Graziosi, D., Nakagami, O., Kuma, S., Zaghetto, A., Suzuki, T., and Tabatabai, A.
(2020). An Overview of Ongoing point Cloud Compression Standardization
Activities: Video-Based (V-PCC) and Geometry-Based (G-PCC). Sip 9, 1.
doi:10.1017/ATSIP.2020.12
Greenberg, D. P. (1999). A Framework for Realistic Image Synthesis. Commun.
ACM 42, 44–53. doi:10.1145/310930.310970
GTI-UPM (2016). JPEG Pleno Database: GTI-UPM Point-cloud Data Set.
Available at: http://plenodb.jpeg.org/pc/upm.
Gu, S., Hou, J., Zeng, H., Chen, J., Zhu, J., and Ma, K.-K. (2017). “Compression of
3D point Clouds Using 1D Discrete Cosine Transform,”in 2017 International
Symposium on Intelligent Signal Processing and Communication Systems
(ISPACS) (IEEE), 196–200. doi:10.1109/ISPACS.2017.8266472
Gu, S., Hou, J., Zeng, H., Yuan, H., and Ma, K.-K. (2020). 3D Point Cloud Attribute
Compression Using Geometry-Guided Sparse Representation. IEEE Trans.
Image Process. 29, 796–808. doi:10.1109/TIP.2019.2936738
Guarda, A. F. R., Rodrigues, N. M. M., and Pereira, F. (2021a). Adaptive Deep
Learning-Based Point Cloud Geometry Coding. IEEE J. Sel. Top. Signal. Process.
15, 415–430. doi:10.1109/JSTSP.2020.3047520
Guarda, A. F. R., Rodrigues, N. M. M., and Pereira, F. (2020c). “Deep Learning-
Based Point Cloud Geometry Coding: RD Control through Implicit and
Explicit Quantization,”in 2020 IEEE International Conference on
Multimedia Expo Workshops (ICMEW) (IEEE), 1–6. doi:10.1109/
ICMEW46912.2020.9106022
Guarda, A. F. R., Rodrigues, N. M. M., and Pereira, F. (2021b). Neighborhood
Adaptive Loss Function for Deep Learning-Based Point Cloud Coding with
Implicit and Explicit Quantization. IEEE MultiMedia 28, 107–116. doi:10.1109/
MMUL.2020.3046691
Guarda, A. F. R., Rodrigues, N. M. M., and Pereira, F. (2019). “Point Cloud Coding:
Adopting a Deep Learning-Based Approach,”in 2019 Picture Coding
Symposium (PCS) (IEEE), 1–5. doi:10.1109/PCS48520.2019.8954537
He, Y., Li, G., Shao, Y., Wang, J., Chen, Y., and Liu, S. (2020). “A point Cloud
Compression Framework via Spherical Projection,”in 2020 IEEE International
Conference on Visual Communications and Image Processing (VCIP) (IEEE),
62–65. doi:10.1109/VCIP49819.2020.9301809
Hochreiter, S., and Schmidhuber, J. (1997). Long Short-Term Memory. Neural
Comput. 9, 1735–1780. doi:10.1162/neco.1997.9.8.1735
Hou, J., Chau, L.-P., He, Y., and Chou, P. A. (2017). “Sparse Representation for
Colors of 3D point Cloud via Virtual Adaptive Sampling,”in 2017 IEEE
International Conference on Acoustics, Speech and Signal Processing
(ICASSP) (IEEE), 2926–2930. doi:10.1109/ICASSP.2017.7952692
Houshiar, H., and Nüchter, A. (2015). “3D point Cloud Compression Using
Conventional Image Compression for Efficient Data Transmission,”in 2015
XXV International Conference on Information, Communication and
Automation Technologies (ICAT) (IEEE), 1–8. doi:10.1109/ICAT.2015.
7340499
Huang, L., Wang, S., Wong, K., Liu, J., and Urtasun, R. (2020). “OctSqueeze:
Octree-Structured Entropy Model for LiDAR Compression,”in 2020 IEEE/
CVF Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE),
1310–1320. doi:10.1109/CVPR42600.2020.00139
Isenburg, M. (2013). LASzip. Photogramm Eng. Remote Sensing 79, 209–217.
doi:10.14358/pers.79.2.209
Isik, B., Chou, P. A., Hwang, S. J., Johnston, N., and Toderici, G. (2021). LVAC:
Learned Volumetric Attribute Compression for Point Clouds Using Coordinate
Based Networks. arXiv [Preprint]. Available at: https://arxiv.org/abs/2111.
08988.
ITU-T (2019). ITU-T Recommendation H.265. High efficiency video coding
(HEVC).
Jae-Young Sim, J.-Y., Chang-Su Kim, C.-S., and Sang-Uk Lee, S.-U. (2005). Lossless
Compression of 3-D point Data in QSplat Representation. IEEE Trans.
Multimedia 7, 1191–1195. doi:10.1109/TMM.2005.858410
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 84697217
Quach et al. Deep Learning-Based Point Cloud Compression

Jiang, W., Tian, J., Cai, K., Zhang, F., and Luo, T. (2012). “Tangent-plane-
continuity Maximization Based 3D point Compression,”in 2012 19th IEEE
International Conference on Image Processing (IEEE), 1277–1280. doi:10.1109/
ICIP.2012.6467100
JPEG (2020). “Final Call for Evidence on JPEG Pleno Point Cloud Coding,”in ISO/
IEC JTC1/SC29/WG1 JPEG Output Document N88014 (ISO).
Kaya, E. C., Schwarz, S., and Tabus, I. (2021). Refining the Bounding Volumes for
Lossless Compression of Voxelized point Clouds Geometry. arXiv [Preprint].
Available at: https://arxiv.org/abs/2106.00828.
Kaya, E. C., and Tabus, I. (2021). Neural Network Modeling of Probabilities for
Coding the Octree Representation of Point Clouds. arXiv [Preprint]. Available
at: https://arxiv.org/abs/2106.06482.
Kazhdan, M., Bolitho, M., and Hoppe, H. (2006). “Poisson Surface
Reconstruction,”in Proceedings of the Fourth Eurographics Symposium on
Geometry Processing (Goslar, Germany: Eurographics Association), 61–70.
Killea, R., Li, Y., Bastani, S., and McLachlan, P. (2021). DeepCompress: Efficient
Point Cloud Geometry Compression. arXiv [Preprint]. Available at: https://
arxiv.org/abs/2106.01504.
Krivokuca, M., Chou, P. A., and Koroteev, M. (2020). A Volumetric Approach to
Point Cloud Compression-Part II: Geometry Compression. IEEE Trans. Image
Process. 29, 2217–2229. doi:10.1109/TIP.2019.2957853
Krivokuća, M., and Guillemot, C. (2020). “Colour Compression of Plenoptic point
Clouds Using Raht-Klt with Prior Colour Clustering and Specular/diffuse
Component Separation,”in IEEE International Conference on Acoustics,
Speech, and Signal Processing (IEEE). doi:10.1109/icassp40776.2020.9053862
Krivokuca, M., Miandji, E., Guillemot, C., and Chou, P. (2021). Compression of
Plenoptic Point Cloud Attributes Using 6-D Point Clouds and 6-D Transforms.
IEEE Trans. Multimedia 1, 1. doi:10.1109/TMM.2021.3129341
Landy, M., and Movshon, J. A. (1991). “The Plenoptic Function and the Elements
of Early Vision,”in Computational Models of Visual Processing (MIT
Press), 3–20.
Lazzarotto, D., Alexiou, E., and Ebrahimi, T. (2021). “On Block Prediction for
Learning-Based Point Cloud Compression,”in 2021 IEEE International
Conference on Image Processing (ICIP) (IEEE), 3378–3382. doi:10.1109/
ICIP42928.2021.9506429
Lazzarotto, D., and Ebrahimi, T. (2021). “Learning Residual Coding for point
Clouds,”in Applications of Digital Image Processing XLIV (San Diego,
California, United States: International Society for Optics and Photonics),
118420S. doi:10.1117/12.2597814
Li, L., Li, Z., Liu, S., and Li, H. (2021). Occupancy-Map-Based Rate Distortion
Optimization and Partition for Video-Based Point Cloud Compression. IEEE
Trans. Circuits Syst. Video Technol. 31, 326–338. doi:10.1109/TCSVT.2020.
2966118
Li, Y., and Ibanez-Guzman, J. (2020). Lidar for Autonomous Driving: The
Principles, Challenges, and Trends for Automotive Lidar and Perception
Systems. IEEE Signal. Process. Mag. 37, 50–61. doi:10.1109/MSP.2020.2973615
Lin, T.-Y., Goyal, P., Girshick, R., He, K., and Dollár, P. (2017). “Focal Loss for
Dense Object Detection,”in 2017 IEEE International Conference on Computer
Vision (ICCV) (IEEE), 2999–3007. doi:10.1109/ICCV.2017.324
Liu, Y., Yang, Q., Xu, Y., and Yang, L. (2020). Point Cloud Quality Assessment:
Large-Scale Dataset Construction and Learning-Based No-Reference
Approach. arXiv [Preprint]. Available at: https://arxiv.org/abs/2012.11895.
Loop, C., Cai, Q., Escolano, S. O., and Chou, P. A. (2016). “Microsoft Voxelized
Upper Bodies - A Voxelized point Cloud Dataset,”in ISO/IEC JTC1/SC29 Joint
WG11/WG1 (MPEG/JPEG) Input Document m38673/M72012 (Geneva,
Switzerland: ISO).
Lorensen, W. E., and Cline, H. E. (1987). Marching Cubes: A High Resolution 3D
Surface Construction Algorithm. SIGGRAPH Comput. Graph. 21, 163–169.
doi:10.1145/37402.37422
Mekuria, R., Blom, K., and Cesar, P. (2017). Design, Implementation, and
Evaluation of a Point Cloud Codec for Tele-Immersive Video. IEEE Trans.
Circuits Syst. Video Technol. 27, 828–842. doi:10.1109/tcsvt.2016.2543039
Morton, G. M. (1966). A Computer Oriented Geodetic Data Base and a New
Technique in File Sequencing. Springer.
MPEG (2020a). “Common Test Conditions for PCC,”in ISO/IEC JTC1/SC29/
WG11 MPEG Output Document N19324 (Alpbach, Austria: ISO).
MPEG (2021a). “Description of Exploration Experiment 13.2 on Inter Prediction,”
in ISO/IEC JTC 1/SC 29/WG 7 MPEG Output Document N0155 (ISO).
MPEG (2021b). “EE 13.53 Low Latency Low Complexity LIDAR Codec (LL-LC
2
),”
in ISO/IEC JTC 1/SC 29/WG 7 MPEG Output Document N0165 (ISO).
MPEG (2021c). “G-PCC Codec Description V12,”in ISO/IEC JTC 1/SC 29/WG 7
MPEG Output Document N00151 (ISO).
MPEG (2021d). “Performance Analysis of Currently AI-Based Available Solutions
for PCC,”in ISO/IEC JTC 1/SC 29/WG 7 MPEG Output Document
N00233 (ISO).
MPEG (2020b). “V-PCC Codec Description,”in ISO/IEC JTC 1/SC 29/WG 7
MPEG Output Document N00100 (ISO).
Nguyen, D. T., Quach, M., Valenzise, G., and Duhamel, P. (2021). "Learning-based
Lossless Compression of 3D point Cloud Geometry," in ICASSP 2021 - 2021
IEEE International Conference on Acoustics, Speech and Signal Processing
(ICASSP), Toronto, Ontario, Canada, 4220–4224. doi:10.1109/ICASSP39728.
2021.9414763
Nguyen, D. T., Quach, M., Valenzise, G., and Duhamel, P. (2021a). Lossless Coding
of Point Cloud Geometry Using a Deep Generative Model. ICASSP IEEE Int.
Conf. Acoust. Speech Signal Process. 31 (12), 4617–4629. doi:10.1109/TCSVT.
2021.3100279
Nguyen, D. T., Quach, M., Valenzise, G., and Duhamel, P. (2021b). Multiscale
Deep Context Modeling for Lossless point Cloud Geometry Compression. IEEE
Int. Conf. Multimed. Expo Workshops 2021, 1–6. doi:10.1109/ICMEW53276.
2021.9455990
Ochotta, T., and Saupe, D. (2004). Compression of Point-Based 3D Models by
Shape-Adaptive Wavelet Coding of Multi-Height Fields. Zurich, Switzerland:
The Eurographics Association. doi:10.2312/SPBG/SPBG04/103-112
Pacala, A. (2018). Lidar as a Camera - Digital Lidar’s Implications for Computer
Vision. Available at: https://ouster.com/blog/the-camera-is-in-the-lidar.
Pereira, F., Dricot, A., Ascenso, J., and Brites, C. (2020). Point Cloud Coding: A
Privileged View Driven by a Classification Taxonomy. Signal. Processing: Image
Commun. 85, 115862. doi:10.1016/j.image.2020.115862
Quach, M., Chetouani, A., Valenzise, G., and Dufaux, F. (2021). A Deep Perceptual
Metric for 3D point Clouds. Electron. Imaging 2021 (9), 257-1.
Quach, M., Valenzise, G., and Dufaux, F. (2020a). “Folding-Based Compression of
Point Cloud Attributes,”in 2020 IEEE International Conference on Image
Processing (ICIP) (IEEE), 3309–3313. doi:10.1109/ICIP40778.2020.9191180
Quach, M., Valenzise, G., and Dufaux, F. (2020b). “Improved Deep Point Cloud
Geometry Compression,”in 2020 IEEE 22nd International Workshop on
Multimedia Signal Processing (MMSP) (IEEE), 1–6. doi:10.1109/
MMSP48831.2020.9287077
Quach, M., Valenzise, G., and Dufaux, F. (2019). “Learning Convolutional
Transforms for Lossy Point Cloud Geometry Compression,”in 2019 IEEE
International Conference on Image Processing (ICCIP) (IEEE), 4320–4324.
doi:10.1109/ICIP.2019.8803413
Que, Z., Lu, G., and Xu, D. (2021). VoxelContext-Net: An Octree Based Framework
for Point Cloud Compression. arXiv [Preprint]. Available at: https://arxiv.org/
abs/2105.02158.
Ronneberger, O., Fischer, P., and Brox, T. (2015). U-net: Convolutional Networks
for Biomedical Image Segmentation. arXiv [Preprint]. Available at: https://
arxiv.org/abs/1505.04597.
Said, A., and Pearlman, W. A. (1996). A New, Fast, and Efficient Image Codec
Based on Set Partitioning in Hierarchical Trees. IEEE Trans. Circuits Syst. Video
Technol. 6, 243–250. doi:10.1109/76.499834
Sandri, G., de Queiroz, R. L., and Chou, P. A. (2018). Comments on ”Compression
of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform”. arXiv
[Preprint]. Available at: https://arxiv.org/abs/1805.09146.
Sandri, G., de Queiroz, R. L., and Chou, P. A. (2019). Compression of Plenoptic
Point Clouds. IEEE Trans. Image Process. 28, 1419–1427. doi:10.1109/TIP.2018.
2877486
Schnabel, R., and Klein, R. (2006). “Octree-based Point-cloud Compression,”in
Proceedings of the 3rd Eurographics / IEEE VGTC Conference on Point-Based
Graphics (Aire-la-Ville, Switzerland: Eurographics Association), 111–121.
doi:10.2312/SPBG/SPBG06/111-120
Schwarz, S., Preda, M., Baroncini, V., Budagavi, M., Cesar, P., Chou, P. A., et al.
(2019). Emerging MPEG Standards for Point Cloud Compression. IEEE
J. Emerg. Sel. Top. Circuits Syst. 9, 133–148. doi:10.1109/JETCAS.2018.2885981
Shen, Y., Dai, W., Li, C., Zou, J., and Xiong, H. (2020). Multi-Scale Structured
Dictionary Learning for 3-D Point Cloud Attribute Compression. IEEE Trans.
Circuits Syst. Video Tech. 1, 1. doi:10.1109/TCSVT.2020.3026046
Frontiers in Signal Processing | www.frontiersin.org February 2022 | Volume 2 | Article 84697218
Quach et al. Deep Learning-Based Point Cloud Compression

Sheng, X., Li, L., Liu, D., Xiong, Z., Li, Z., and Wu, F. (2021). Deep-PCAC: An End-
To-End Deep Lossy Compression Framework for Point Cloud Attributes. IEEE
Trans. Multimedia 1, 1. doi:10.1109/TMM.2021.3086711
Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-k., and Woo, W.-c. (2015).
Convolutional LSTM Network: A Machine Learning Approach for
Precipitation Nowcasting. arXiv [Preprint]. Available at: https://arxiv.org/
abs/1506.04214.
Song, Z., Zhao, L., Zhou, J., Wang, H., and Li, T. (2021). Learning Hybrid Semantic
Affinity for Point Cloud Segmentation. IEEE Trans. Circuits Syst. Video
Technol. 1, 1. doi:10.1109/tcsvt.2021.3132047
Sterzentsenko, V., Karakottas, A., Papachristou, A., Zioulis, N., Doumanoglou, A.,
Zarpalas, D., et al. (2018). “A Low-Cost, Flexible and Portable Volumetric
Capturing System,”in 2018 14th International Conference on Signal-Image
Technology & Internet-Based Systems (SITIS) (IEEE), 200–207. doi:10.1109/
SITIS.2018.00038
Sun, X., Ma, H., Sun, Y., and Liu, M. (2019). A Novel Point Cloud Compression
Algorithm Based on Clustering. IEEE Robot. Autom. Lett. 4, 2132–2139. doi:10.
1109/LRA.2019.2900747
Sun, X., Wang, S., Wang, M., Wang, Z., and Liu, M. (2020). A Novel Coding
Architecture for LiDAR Point Cloud Sequence. IEEE Robot. Autom. Lett. 5,
5637–5644. doi:10.1109/LRA.2020.3010207
Tang, D., Singh, S., Chou, P. A., Häne, C., Dou, M., Fanello, S., et al. (2020). “Deep
Implicit Volume Compression,”in 2020 IEEE/CVF Conference on Computer
Vision and Pattern Recognition (CVPR) (IEEE), 1290–1300. doi:10.1109/
cvpr42600.2020.00137
Thomas, H., Qi, C. R., Deschaud, J.-E., Marcotegui, B., Goulette, F., and Guibas, L.
J. (2019). “KPConv: Flexible and Deformable Convolution for Point Clouds,”in
In Proceedings of the IEEE/CVF International Conference on Computer
Vision, Seoul, Korea, 6411–6420.
Tommasi,C.,Achille,C.,andFassi,F.(2016).“From Point Cloud to Bim: A
Modelling Challenge in the Cultural Heritage Field,”in ISPRS -
International Archives of the Photogrammetry, Remote Sensing and
Spatial Information Sciences XLI-B5 (IEEE), 429–436. doi:10.5194/
isprsarchives-XLI-B5-429-2016
Tu, C., Takeuchi, E., Carballo, A., and Takeda, K. (2019a). “Point Cloud
Compression for 3D LiDAR Sensor Using Recurrent Neural Network
with Residual Blocks,”in 2019 International Conference on Robotics and
Automation (ICRA) (IEEE), 3274–3280. doi:10.1109/ICRA.2019.
8794264
Tu, C., Takeuchi, E., Carballo, A., and Takeda, K. (2019b). Real-Time Streaming
Point Cloud Compression for 3D LiDAR Sensor Using U-Net. IEEE Access 7,
113616–113625. doi:10.1109/ACCESS.2019.2935253
Tu, C., Takeuchi, E., Miyajima, C., and Takeda, K. (2017). “Continuous Point
Cloud Data Compression Using SLAM Based Prediction,”in 2017 IEEE
Intelligent Vehicles Symposium (IV) (IEEE), 1744–1751. doi:10.1109/IVS.
2017.7995959
Tzamarias, D. E. O., Chow, K., Blanes, I., and Serra-Sagristà, J. (2021).
“Compression of point Cloud Geometry through a Single Projection,”in
2021 Data Compression Conference (DCC) (IEEE), 63–72. doi:10.1109/
DCC50243.2021.00014
Wang, J., Ding, D., Li, Z., Feng, X., Cao, C., and Ma, Z. (2021). Sparse Tensor-Based
Multiscale Representation for Point Cloud Geometry Compression. arXiv
[Preprint]. Available at: https://arxiv.org/abs/2111.10633.
Wang, J., Ding, D., Li, Z., and Ma, Z. (2020). Multiscale Point Cloud Geometry
Compression. arXiv [Preprint]. Available at: https://arxiv.org/abs/2011.03799.
Wang, J., Zhu, H., Ma, Z., Chen, T., Liu, H., and Shen, Q. (2019). Learned Point
Cloud Geometry Compression. arXiv [Preprint]. Available at: https://arxiv.org/
abs/1909.12037.
Wang, Q., and Kim, M.-K. (2019). Applications of 3D point Cloud Data in the
Construction Industry: A Fifteen-Year Review from 2004 to 2018. Adv. Eng.
Inform. 39, 306–319. doi:10.1016/j.aei.2019.02.007
Wen, X., Wang, X., Hou, J., Ma, L., Zhou, Y., and Jiang, J. (2020). “Lossy Geometry
Compression of 3d Point Cloud Data via an Adaptive Octree-Guided Network, ”
in 2020 IEEE International Conference on Multimedia and Expo (ICME)
(IEEE), 1–6. doi:10.1109/ICME46284.2020.9102866
Wiesmann, L., Milioto, A., Chen, X., Stachniss, C., and Behley, J. (2021). Deep
Compression for Dense Point Cloud Maps. IEEE Robot. Autom. Lett. 6,
2060–2067. doi:10.1109/LRA.2021.3059633
Xiong, J., Gao, H., Wang, M., Li, H., and Lin, W. (2021). Occupancy Map Guided
Fast Video-Based Dynamic Point Cloud Coding. IEEE Trans. Circuits Syst.
Video Technol. 1, 1. doi:10.1109/TCSVT.2021.3063501
Yan Huang, Y., Jingliang Peng, J., Kuo, C.-C. J., and Gopi, M. (2008). A Generic
Scheme for Progressive Point Cloud Coding. IEEE Trans. Vis. Comput.
Graphics 14, 440–453. doi:10.1109/TVCG.2007.70441
Yan, W., Shao, Y., Liu, S., Li, T. H., Li, Z., and Li, G. (2019). Deep AutoEncoder-
Based Lossy Geometry Compression for Point Clouds. arXiv [Preprint].
Available at: https://arxiv.org/abs/1905.03691.
Yang, Y., Feng, C., Shen, Y., and Tian, D. (2017). “FoldingNet: Point Cloud Auto-
Encoder via Deep Grid Deformation,”in 2018 IEEE Conference on Computer
Vision and Pattern Recognition (CVPR) (IEEE).
Yin, Q., Ren, Q., Zhao, L., Wang, W., and Chen, J. (2021). Lossless Point Cloud
Attribute Compression with Normal-based Intra Prediction. arXiv [Preprint].
Available at: https://arxiv.org/abs/2106.12236.
Yue, X., Wu, B., Seshia, S. A., Keutzer, K., and Sangiovanni-Vincentelli, A. L.
(2018). “A LiDAR Point Cloud Generator,”in Proceedings of the 2018 ACM on
International Conference on Multimedia Retrieval (New York, NY: Association
for Computing Machinery), 458–464. doi:10.1145/3206025.3206080
Zhang, C., Florêncio, D., and Loop, C. (2014). “Point Cloud Attribute Compression
with Graph Transform,”in 2014 IEEE International Conference on Image
Processing (ICIP) (IEEE), 2066–2070. doi:10.1109/ICIP.2014.7025414
Zhang, X., Wan, W., and An, X. (2017). Clustering and DCT Based Color Point Cloud
Compression. J. Sign Process. Syst. 86, 41–49. doi:10.1007/s11265-015-1095-0
Zhu, W., Ma, Z., Xu, Y., Li, L., and Li, Z. (2021). View-Dependent Dynamic Point
Cloud Compression. IEEE Trans. Circuits Syst. Video Technol. 31, 765–781.
doi:10.1109/TCSVT.2020.2985911
Zhu, W., Xu, Y., Li, L., and Li, Z. (2017). “Lossless point Cloud Geometry
Compression via Binary Tree Partition and Intra Prediction,”in 2017 IEEE
19th International Workshop on Multimedia Signal Processing (MMSP)
(IEEE), 1–6. doi:10.1109/mmsp.2017.8122226
Zuffo, M. (2018). EmergIMG —Downloads - USPAULOPC. Available at: http://
uspaulopc.di.ubi.pt/.
Conflict of Interest: Authors JP and DT were employed by the company
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