A) Subjective quality assessment

The first subjective evaluation study for point clouds reported in the literature was conducted by Zhang et al. [Reference Zhang, Huang, Zhu and Hwang6], in an effort to assess the visual quality of models at different geometric resolutions, and different levels of noise introduced in both geometry and color. For the former, several down-sampling factors were selected to increase sparsity, while for the latter, uniformly distributed noise was applied to the coordinates, or the color attributes of the reference models. In these experiments, raw point clouds were displayed in a flat screen that was installed on a desktop set-up. The results showed an almost linear relationship between the down-sampling factor and the visual quality ratings, while color distortions were found to be less severe when compared to geometric degradations.

Mekuria et al. [Reference Mekuria, Blom and Cesar7] proposed a 3D tele-immersive system in which the users were able to interact with naturalistic (dynamic point cloud) and synthetic (computer generated) models in a virtual scene. The subjects were able to navigate in the virtual environment through the use of the mouse cursor in a desktop setting. The proposed encoding solution that was employed to compress the naturalistic contents of the scene was assessed in this mixed reality application, among several other aspects of quality (e.g. level of immersiveness and realism).

In [Reference Mekuria, Laserre and Tulvan8], performance results of the codec presented in [Reference Mekuria, Blom and Cesar7] are reported, from a quality assessment campaign that was conducted in the framework of the Call for Proposals [9] issued by the MPEG committee. Both static and dynamic point cloud models were evaluated under several encoding categories, settings, and bit rates. A passive subjective inspection protocol was adopted, and animated image sequences of the models captured from predefined viewpoints were generated. The point clouds were rendered using cubes as primitive elements of fixed size across a model. This study aims at providing a performance benchmark for a well-established encoding solution and evaluation framework.

Javaheri et al. [Reference Javaheri, Brites, Pereira and Ascenso10] performed a quality assessment study of position denoising algorithms. Initially, impulse noise was added to the models to simulate outlier errors. After outlier removal, different levels of Gaussian noise were introduced to mimic sensor imprecisions. Then, two denoising algorithms, namely Tikhonov and total variation regularization, were evaluated. For rendering purposes, the screened Poisson surface reconstruction [Reference Kazhdan and Hoppe51] was employed. The resulting mesh models were captured by different viewpoints from a virtual camera, forming video sequences that were visualized by human subjects.

In [Reference Javaheri, Brites, Pereira and Ascenso11], the visual quality of colored point clouds under octree- and graph-based geometry encoding was evaluated, both subjectively and objectively. The color attributes of the models remained uncompressed to assess the impact of geometry-based degradations; that is, sparser content representations are obtained from the first, while blocking artifacts are perceived from the latter. Static models representing both objects and human figures were selected and assessed at three quality levels. Cubic geometric primitives of adaptive size based on local neighborhoods were employed for rendering purposes. A spiral camera path moving around a model (i.e. from a full view to a closer look) was defined to capture images from different perspectives. Animated sequences of the distorted and the corresponding reference models were generated and passively consumed by the subjects, sequentially. This is the first study with benchmarking results on more than one compression algorithms.

Alexiou et al. [Reference Alexiou and Ebrahimi12,Reference Alexiou and Ebrahimi13] proposed interactive variants of existing evaluation methodologies in a desktop set-up to assess the quality of geometry-only point cloud models. In both studies, Gaussian noise and octree-pruning was employed to simulate position errors from sensor inaccuracies and compression artifacts, respectively, to account for degradations of different nature. The models were simultaneously rendered as raw point clouds side-by-side, while human subjects were able to interact without timing constraints before grading the visual quality of the models. These were the first attempts dedicated to evaluate the prediction power of metrics existing at the time. In [Reference Alexiou, Upenik and Ebrahimi14], the same authors extended their efforts by proposing an augmented reality (AR) evaluation scenario using a head-mounted display. In the latter framework, the observers were able to interact with the virtual assets with 6 degrees-of-freedom by physical movements in the real-world. A rigorous statistical analysis between the two experiments [Reference Alexiou and Ebrahimi13,Reference Alexiou, Upenik and Ebrahimi14] is reported in [Reference Alexiou and Ebrahimi15], revealing different rating trends under the usage of different test equipment as a function of the degradation type under assessment. Moreover, influencing factors are identified and discussed. A dataset containing the stimuli and corresponding subjective scores from the aforementioned studies, has been recently releasedFootnote ².

In [Reference Alexiou16] subjective evaluation experiments were conducted in five different test laboratories to assess the visual quality of colorless point clouds, enabling the screened Poisson surface reconstruction algorithm [Reference Kazhdan and Hoppe51] as a rendering methodology. The contents were degraded using octree-pruning, and the observers visualized the mesh models in a passive way. Although different 2D monitors were employed by the participating laboratories, the collected subjective scores were found to be strongly correlated. Moreover, statistical differences between the scores collected in this experiment and the subjective evaluation conducted in [Reference Alexiou and Ebrahimi13] indicated that different visual data representations of the same stimuli might lead to different conclusions. In [Reference Alexiou17], an identical experimental design was used, with human subjects consuming the reconstructed mesh models through various 3D display types/technologies (i.e. passive, active, and auto-stereoscopic), showing very high correlation and very similar rating trends with respect to previous efforts [Reference Alexiou16]. These results suggest that human judgments on such degraded models are not significantly affected by the display equipment.

In [Reference Torlig, Alexiou, Fonseca, de Queiroz and Ebrahimi18], the visual quality of voxelized colored point clouds was assessed in subjective experiments that were performed in two intercontinental laboratories. The voxelization of the contents was performed in real-time, and orthographic projections of both the reference and the distorted models were shown side-by-side to the subjects in an interactive platform that was developed and described. Point cloud models representing both inanimate objects and human figures were encoded after combining different geometry and color degradation levels using the codec described in [Reference Mekuria, Blom and Cesar7]. The results showed that subjects rate more severely degradations on human models. Moreover, using this encoder, marginal gains are observed with color improvements at low geometric resolutions, indicating that the visual quality is rather limited at high levels of sparsity. Finally, this is the first study conducting performance evaluation of projection-based metrics on point cloud models; that is, predictors based on 2D imaging algorithms applied on projected views of the models.

In [Reference Alexiou and Ebrahimi19], identically degraded models as in [Reference Torlig, Alexiou, Fonseca, de Queiroz and Ebrahimi18] were assessed using a different rendering scheme. In particular, the point clouds were rendered using cubes as primitive geometric shapes of adaptive sizes based on local neighborhoods. The models were assessed in an interactive renderer, with the user's behavior also recorded. The logged interactivity information was analyzed and used to identify important perspectives of the models under assessment based on the aggregated time of inspection across human subjects. This information was additionally used to weight views of the contents that were acquired for the computation of objective scores. The rating trends  were found to be very similar to [Reference Torlig, Alexiou, Fonseca, de Queiroz and Ebrahimi18]. The performance of the projection-based metrics was improved by removing background color information, while further gains were reported by considering importance weights based on interactivity data.

In [Reference Cruz20], the results of a subjective evaluation campaign that was issued in the framework of the JPEG Pleno [Reference Ebrahimi, Foessel, Pereira and Schelkens52] activities are reported. Subjective experiments were conducted in three different laboratories in order to assess the visual quality of point cloud models under an octree- and a projection-based encoding scheme at three quality levels. A passive evaluation in conventional monitors was selected and different camera paths were defined to capture the models under assessment. The contents were rendered with fixed point size that was adjusted per stimulus. This is reported to be the first study aiming at defining test conditions for both small- and large-scale point clouds. The former class corresponds to objects that are normally consumed outer-wise, whereas the latter represents scenes which are typically consumed inner-wise. The results indicate that regular sparsity introduced by octree-based algorithms is preferred by human subjects with respect to missing structures that appeared in the encoded models due to occluded regions.

Zerman et al. [Reference Zerman, Gao, Ozcinar and Smolić21] conducted subjective evaluations with a volumetric video dataset that was acquired and releasedFootnote ³, using V-PCC. Two point cloud sequences were encoded at four quality levels of geometry and color, leading to a total of 32 video sequences, that were assessed in a passive way using two subjective evaluation methodologies; that is, a side-by-side assessment of the distorted model and a pair-wise comparison. The point clouds were rendered using primitive ellipsoidal elements (i.e. splats) of fixed size, determined heuristically to result in visualization of watertight models. The results showed that the visual quality was not significantly affected by geometric degradations, as long as the resolution of the represented model was sufficient to be adequately visualized. Moreover, in V-PCC, color impairments were found to be more annoying than geometric artifacts.

In [Reference Su, Duanmu, Liu, Liu and Wang22] a large scale evaluation study of 20 small-scale point cloud models was performed. The models were newly generated by the authors, and  degraded using down-sampling, Gaussian noise and compression distortions from earlier implementations of the MPEG test models. In this experiment, each content was rendered as a raw point cloud. A virtual camera path circularly rotating around the horizontal and the vertical axis at a fixed radius was defined in order to capture snapshots of the models from different perspectives and generate video sequences. The distance between the camera and the models was selected so as to avoid perception of hollow regions, while preserving details. The generated videos were shown to human subjects in a side-by-side fashion, in order to evaluate the visual quality of the degraded stimuli. Comparison results for the MPEG test models based on subjective scores reveal better performance of V-PCC at low bit rates.

1) Discussion

Several experimental methodologies have been designed and tested in the subjective evaluation studies conducted so far. It is evident that the models' characteristics, the evaluation protocols, the rendering schemes, and the types of degradation under assessment are some of the main parameters that vary between the efforts. In Table 1, a categorization of existing experimental set-ups is attempted to provide an informative outline of the current approaches.

Table 1. Experimental set-ups. Notice that single and double stand for the number of stimuli visualized to rate a model. Moreover, sim. and seq. denote simultaneous and sequential assessment, respectively. Finally, incl. zoom indicates varying camera distance to acquire views of the model.

B) Objective quality metrics

Objective quality assessment in point cloud representations is typically performed by full reference metrics, which can be distinguished in: (a) point-based, and (b) projection-based approaches [Reference Torlig, Alexiou, Fonseca, de Queiroz and Ebrahimi18], which is very similar to the classification of perceptual metrics for mesh contents [Reference Lavoué and Mantiuk39].

A) Content selection and preparation

A total of nine static models are used in the experiments. The selected models denote a representative set of point clouds with diverse characteristics in terms of geometry and color details, with the majority of them being considered in recent activities of the JPEG and MPEG committees. The contents depict either human figures, or objects. The former set of point clouds consists of the longdress [Reference d'Eon, Harrison, Myers and Chou55] (longdress_vox10_1300), loot [Reference d'Eon, Harrison, Myers and Chou55] (loot_vox10_1200), redandblack [Reference d'Eon, Harrison, Myers and Chou55] (redandblack_vox10_1550), soldier [Reference d'Eon, Harrison, Myers and Chou55] (soldier_vox10_0690), and the20smaria [Reference Ebner56] (HHI_The20sMaria_Frame_00600) models, which were obtained from the MPEG repositoryFootnote ⁵. The latter set is composed by amphoriskos, biplane (1x1_Biplane_Combined_000), head (Head_00039), and romanoillamp. The first model was retrieved from the online platform SketchfabFootnote ⁶, the second and the last were selected from the JPEG repositoryFootnote ⁷, while head was recruited from the MPEG database.

Such point clouds are typically acquired when objects are scanned by sensors that provide either directly or indirectly a cloud of points with information representing their 3D shapes. Typical use cases involve applications in desktop computers, hand-held devices, or head-mounted displays, where the 3D models are consumed outer-wise. Representative poses of the reference contents are shown in Fig. 1, while related information is summarized in Table 2.

Fig. 1. Reference point cloud models. The set of objects is presented in the first row, whilst the set of human figures is illustrated in the second row. (a) amphoriskos, (b) biplane, (c) head, (d) romanoillamp, (e) longdress, (f) loot, (g) redandblack, (h) soldier, (i) the20smaria.

Table 2. Summary of content retrieval information, processing, and point specifications.

The selected codecs under assessment handle solely point clouds with integer coordinates. Thus, models that have not been provided as such in the selected databases were manually voxelized after eventual pre-processing. In particular, the contents amphoriskos and romanoillamp were initially pre-processed. For amphoriskos, the resolution of the original version is rather low; hence, to increase the quality of the model representation, the screened Poisson surface reconstruction algorithm [Reference Kazhdan and Hoppe51] was applied and a point cloud was generated by sampling the resulting mesh. The CloudCompare software was used with the default configurations of the algorithm and 1 sample per node, while the normal vectors that were initially associated to the coordinates of the original model were employed. From the reconstructed mesh, a target of 1 million points was set and obtained by randomly sampling a fixed number of samples on each triangle, resulting in an irregular point cloud. Regarding romanoillamp, the original model is essentially a polygonal mesh object. A point cloud version was produced by discarding any connectivity information and maintaining the original points' coordinates and color information.

In a next step, contents with non-integer coordinates are voxelized, that is, quantization of coordinates which leads to a regular geometry down-sampling; the color is obtained after sampling among the points that fall in each voxel to avoid texture smoothing, leading to more challenging encoding conditions. For our tests design, it was considered important to eliminate influencing factors related to the sparsity of the models that would affect the visual quality of the rendered models. For instance, visual impairments naturally arise by assigning larger splats on models with lower geometric resolutions, when visualization of watertight surfaces is required. At the same time, the size of the model, directly related to the number of points, should allow high responsiveness and fast interactivity in a rendering platform. To enable a comparable number of points for high-quality reference models while not making their usage cumbersome in our renderer, voxel grids of 10-bit depth are used for the contents amphoriskos, biplane, romanoillamp, and the20smaria, whereas a 9-bit depth grid is employed for head. It should be noted that, although a voxelized version of the latter model is provided in the MPEG repository, the number of output points is too large; thus, it was decided to use a smaller bit depth.

B) Codecs

In this work, the model degradations under study were derived from the application of lossy compression. The contents were encoded using the latest versions of the state-of-the-art compression techniques for point clouds at the time of this writing, namely version 5.1 of V-PCC [Reference Mammou28] and version 6.0-rc1 of G-PCC [Reference Mammou, Chou, Flynn and Krivokuća29]. The configuration of the encoders was set according to the guidelines detailed in the MPEG Common Test Conditions document [57].

1) Video-based point cloud compression

V-PCC, also known as TMC2 (Test Model Category 2), takes advantage of already deployed 2D video codecs to compress geometry and texture information of dynamic point clouds (or Category 2). V-PCC's framework depends on a Pre-processing module which converts the point cloud data into a set of different video sequences, as shown in Fig. 2.

Fig. 2. V-PCC compression process. In (a), the original point cloud is decomposed into geometry video, texture video, and metadata. Both video contents are smoothed by Padding in (b) to allow for the best HEVC [Reference Bross, Han, Sullivan, Ohm and Wiegand58] performance. The compressed bitstreams (metadata, geometry video, and texture video) are packed into a single bitstream: the compressed point cloud.

In essence, two video sequences, one for capturing the geometry information of the point cloud data (padded geometry video) and another for capturing the texture information (padded texture video), are generated and compressed using HEVC [Reference Bross, Han, Sullivan, Ohm and Wiegand58], the state-of-the-art 2D video codec. Additional metadata (occupancy map and auxiliary patch info) needed to interpret the two video sequences are also generated and compressed separately. The total amount of information is conveyed to the decoder in order to allow for the decoding of the compressed point cloud.

2) Geometry-based point cloud compression

G-PCC, also known as TMC13 (Test Model Categories 1 and 3), is a coding technology to compress Category 1 (static) and Category 3 (dynamically acquired) point clouds. Despite the fact that our work is focused on models that belong by default to Category 1, the contents under test are encoded using all the available set-up combinations to investigate the suitability and the performance of the entire space of the available options. Thus, configurations typically recommended for Category 3 contents are also employed. It is suitable, thus, to present an overview of the entire G-PCC framework.

The basic approach consists in encoding the geometry information at first and, then, using the decoded geometry to encode the associated attributes. For Category 3 point clouds, the compressed geometry is typically represented as an octree [Reference Meagher59] (Octree Encoding module in Fig. 3) from the root all the way down to a leaf level of individual voxels. For Category 1 point clouds, the compressed geometry is typically represented by a pruned octree (i.e. an octree from the root down to a leaf level of blocks larger than voxels) plus a model that approximates the surface within each leaf of the pruned octree, provided by the TriSoup Encoding module. The approximation is built using a series of triangles (a triangle soup [Reference Schwarz4,Reference Pavez, Chou, de Queiroz and Ortega60]) and yields good results for a dense surface point cloud.

Fig. 3. Overview of G-PCC geometry encoder. After voxelization, the geometry is encoded either by Octree or by TriSoup modules, which depends on Octree.

In order to meet rate or distortion targets, the geometry encoding modules can introduce losses in the geometry information in such a way that the list of 3D reconstructed points, or refined vertices, may differ from the source 3D-point list. Therefore, a re-coloring module is needed to provide attribute information to the refined coordinates after lossy geometry compression. This step is performed by extracting color values from the original (uncompressed) point cloud. In particular, G-PCC uses neighborhood information from the original model to infer the colors for the refined vertices. The output of the re-coloring module is a list of attributes (colors) corresponding to the refined vertices list. Figure 4 presents the G-PCC's color encoder which has as input the re-colored geometry.

Fig. 4. Overview of G-PCC color attribute encoder. In the scope of this work, either RAHT or Lifting is used to encode contents under test.

There are three attribute coding methods in G-PCC: Region Adaptive Hierarchical Transform (RAHT module in Fig. 4) coding [Reference de Queiroz and Chou61], interpolation-based hierarchical nearest-neighbor prediction (Predicting Transform), and interpolation-based hierarchical nearest-neighbor prediction with an update/lifting step (Lifting module). RAHT and Lifting are typically used for Category 1 data, while Predicting is typically used for Category 3 data. Since our work is focused on Category 1 contents, every combination of the two geometry encoding modules (Octree and TriSoup) in conjunction with the two attribute coding techniques (RAHT and Lifting) is employed.

A) Experiment design

For this experiment, every model presented in Session IV.A is encoded using six degradation levels for the four combinations of the G-PCC encoders (from most degraded to least degraded: R1, R2, R3, R4, R5, R6). Moreover, five degradation levels for the V-PCC codec (from most degraded to least degraded: R1, R2, R3, R4, R5) were obtained, following the Common Test Conditions document released by the MPEG committee [57]. Using the V-PCC codec, the degradation levels were achieved by modifying the geometry and texture Quantization Parameter (QP). For both the G-PCC geometry encoders, the positionQuantizationScale parameter was configured to specify the maximum voxel depth of a compressed point cloud. To define the size of the block on which the triangular soup approximation is applied, the log2_trisoup_node_size was additionally adjusted. From now on, the first and the second parameters will be referred to as depth and level, respectively, in accordance with [Reference Schwarz4]. It is worth clarifying that, setting the level parameter to 0 reduces the TriSoup module to the Octree. For both the G-PCC color encoders, the color QP was adjusted per degradation level, accordingly. Finally, the parameters levelOfDetailCount and dist2 were set to 12 and 3, respectively, for every content, when using the Lifting module.

The subjective evaluation experiments took place in two laboratories across two different countries, namely, MMSPG at EPFL in Lausanne, Switzerland and LISA at UNB in Brasilia, Brazil. In both cases, a desktop set-up involving an Apple Cinema Display of 27-inches and $2560\times 1440$ resolution (Model A1316) calibrated with the ITU-R Recommendation BT.709-5 [62] color profile was installed. At EPFL, the experiments were conducted in a room that fulfills the ITU-R Recommendation BT.500-13 [63] for subjective evaluation of visual data representations. The room is equipped with neon lamps of 6500 K color temperature, while the color of the walls and the curtains is mid gray. The brightness of the screen was set to 120 cd/m² with a D65 white point profile, while the lighting conditions were adjusted for ambient light of 15 lux, as was measured next to the screen, according to the ITU-R Recommendation BT.2022 [64]. At UNB, the test room was isolated, with no exterior light affecting the assessment. The wall color was white, and the lighting conditions involved a single ceiling luminary with aluminum louvers containing two fluorescent lamps of 4000 K color temperature.

The stimuli were displayed using the renderer presented and described in Section III. The resolution of the canvas was specified to 1024 × 1024 pixels, and a non-distracting mid-gray color was set as the background. The camera zoom parameter was limited in a reasonable range, allowing visualization of a model in a scale from 0.2 up to 5 times the initial size. Note that the initial view allows capturing of the highest dimension of the content in its entirety. This range was specified in order to avoid distortions from corner cases of close and remote viewpoints.

When it comes to splat-based rendering of point cloud data, there is an obvious trade-off between sharpness and impression of watertight models; that is, as the splat size is increasing, the perception of missing regions in the model becomes less likely, at the expense of blurriness. Given that, in principle, the density of points varies across a model, adjusting the splat size based on local resolutions can improve the visual quality. Thus, in this study, an adaptive point size approach was selected to render the models, similarly to [Reference Javaheri, Brites, Pereira and Ascenso11,Reference Alexiou and Ebrahimi19]. The splat size for every point p is set equal to the mean distance x of its 12 nearest neighbors, multiplied by a scaling factor that is determined per content. Following [Reference Alexiou and Ebrahimi19], to avoid the magnification of sparse regions, or isolated points that deviate from surfaces (e.g. acquisition errors), we assume that x is a random variable following a Gaussian distribution $N (\mu _{x}, \sigma _{x})$, and every point p with mean outside of a specified range, is classified as an outlier. In our case, this range is defined by the global mean $\mu = \bar {\mu }_x$ and standard deviation $\sigma = \bar {\sigma }_x$. For every point p, if $x \geq \mu + 3 \cdot \sigma$, or $x \leq \mu - 3 \cdot \sigma$, then p is considered as an outlier and x is set equally to the global mean μ, multiplied by the scaling factor. The scaling factor was selected after expert viewing, ensuring a good compromise between sharpness and perception of watertight surfaces for each reference content. In particular, a value of 1.45 was chosen for amphoriskos, 1.1 for biplane, 1.3 for romanoillamp, and 1.05 for the rest of the contents. Notice that the same scaling factor is applied for each variation of the content. In Fig. 5, the reference model amphoriskos along with encoded versions at a comparable visual quality are displayed using the developed renderer, to indicatively illustrate the nature of impairments that are introduced by every codec under assessment.

Fig. 5. Illustration of artifacts occurred after encoding the content amphoriskos with the codecs under evaluation. To obtain comparable visual quality, different degradation levels are selected for V-PCC and G-PCC variants. (a) Reference. (b) V-PCC, Degradation level = R1. (c) Octree-Lifting, Degradation level = R3. (d) Octree-RAHT, Degradation level = R3. (e) TriSoup-Lifting, Degradation level = R3. (f) TriSoup-RAHT, Degradation level = R3.

In this experiment, the simultaneous Double-Stimulus Impairment Scale (DSIS) with 5-grading scale was adopted (5: Imperceptible, 4: Perceptible, 3: Slightly annoying, 2: Annoying, 1: Very annoying). The reference and the distorted stimuli were clearly annotated and visualized side-by-side by the subjects. A division element with radio buttons was placed below the rendering canvases, enlisting the definitions of the selected grading scale among which the subjects had to choose. For the assessment of the visual quality of the models, an interactive evaluation protocol was adopted to simulate realistic consumption, allowing the participants to modify their viewpoint (i.e. rotation, translation, and zoom) at their preference. Notice that the interaction commands given by a subject were simultaneously applied on both stimuli (i.e. reference and distorted); thus, the same camera settings were always used in both models. A training session preceded the test, where the subjects got familiarized with the task, the evaluation protocol, and the grading scale by showing references of representative distortions using the redandblack content; thus, this model was excluded from the actual test. Identical instructions were given in both laboratories. At the beginning of each evaluation, a randomly selected view was presented to each subject at a fixed distance, ensuring entire model visualization. Following the ITU-R Recommendation BT.500-13 [63], the order of the stimuli was randomized and the same content was never displayed consecutively throughout the test, in order to avoid temporal references. In Fig. 6, an example of the evaluation platform is presented.

Fig. 6. Illustration of the evaluation platform. Both reference and distorted models are presented side-by-side while being clearly remarked. Users' judgments can be submitted through the rating panel. The green bar at the bottom indicates the progress in the current batch.

In each session, eight contents and 29 degradations were assessed with a hidden reference and a dummy content for sanity check, leading to a total of 244 stimuli. Each session was equally divided in four batches. Each participant was asked to complete two batches of 61 contents, with a 10-min enforced break in between to avoid fatigue. A total of 40 subjects participated in the experiments at EPFL, involving 16 females and 24 males with an average of 23.4 years of age. Another 40 subjects were recruited at UNB, comprising of 14 females and 26 males, with an average of 24.3 years of age. Thus, 20 ratings per stimulus were obtained in each laboratory, for a total of 40 scores.

B) Data processing

1) Subjective quality evaluation

As a first step, the outlier detection algorithm described in the ITU-R Recommendation BT.500-13 [63] was issued separately for each laboratory, in order to exclude subjects whose ratings deviated drastically from the rest of the scores. As a result, no outliers were identified, thus, leading to 20 ratings per stimulus at each lab. Then, the Mean Opinion Score (MOS) was computed based on equation (1)

(1)\begin{equation}{\rm MOS}_{j}^{k}=\frac{\sum_{i=1}^N m_{ij}}{N} \tag{1}\end{equation}

where N=20 represents the number of ratings at each laboratory k, with $k \in \{A, B\}$), while $m_{ij}$ is the score of the stimulus j from a subject i. Moreover, for every stimulus, the $95\%$ confidence interval (CI) of the estimated mean was computed assuming a Student's t-distribution, based on equation (2)

(2)\begin{equation}{\rm CI}_{j}^{k} = t(1-\alpha/2, N-1) \cdot \frac{\sigma_j}{\sqrt{N}} \tag{2}\end{equation}

where $t(1-\alpha /2, N-1)$ is the t-value corresponding to a two-tailed Student's t-distribution with N−1 degrees of freedom and a significance level $\alpha = 0.05$, and $\sigma _j$ is the standard deviation of the scores for stimulus j.

2) Inter-laboratory correlation

Based on the Recommendation ITU-T P.1401 [65], no fitting, linear, and cubic fitting functions were applied to the $\mbox {MOS}$ values obtained from the two sets collected from the participating laboratories. For this purpose, when the scores from set A are considered as the ground truth, the regression model is applied to the scores of set B before computing the performance indexes. In particular, let us assume the scores from set A as the ground truth, with the $\mbox {MOS}$ of the stimulus i being denoted as $\mbox {MOS}_{i}^{A}$. $\mbox {MOS}_{i}^{B}$ is used to indicate the $\mbox {MOS}$ of the same stimulus as computed from set B. A predicted $\mbox {MOS}$ for stimulus i, indicated as $\mbox {P(MOS}_{i}^{B})$, is estimated after issuing a regression model to each pair $[\mbox {MOS}_{j}^{A}, \mbox {MOS}_{j}^{B}]$, $\forall \ j \in \lbrace 1, 2, \ldots, N \rbrace$. Then, the Pearson linear correlation coefficient (PLCC), the Spearman rank order correlation coefficient (SROCC), the root-mean-square error (RMSE), and the outlier ratio based on standard error (OR) were computed between $\mbox {MOS}_{i}^{A}$ and $\mbox {P(MOS}_{i}^{B})$, for linearity, monotonicity, accuracy, and consistency of the results, respectively. To calculate the OR, an outlier is defined based on the standard error.

To decide whether statistically distinguishable scores are obtained for the stimuli under assessment from the two test populations, the correct estimation (CE), under-estimation (UE), and over-estimation (OE) percentages are calculated, after a multiple comparison test at a $5\%$ significance level. Let us assume that the scores in set A are the ground truth. For every stimulus, the true difference $\mbox {MOS}_{i}^{B}$–$\mbox {MOS}_{i}^{A}$ between the average ratings from every set is estimated with a $95\%$ CI. If the CI contains 0, correct estimation is observed, indicating that the visual quality of stimulus i is rated statistically equivalently from both populations. If 0 is above, or below the CI, we conclude that the scores in set B under-estimate, or over-estimate the visual quality of model i, respectively. The same computations are repeated for every stimulus. After dividing the aggregated results with the total number of stimuli, the correct estimation, under-estimation, and over-estimation percentages are obtained.

Finally, to better understand whether the results from the two tests conducted in EPFL and UNB could be pooled together, the Standard deviation of Opinion Score (SOS) coefficient was computed for both tests [Reference Hoßfeld, Schatz and Egger66]. The SOS coefficient a parametrizes the relationship between MOS and the standard deviation associated with it through a square function, given in equation (3).

(3)\begin{equation} {\rm SOS}(x)^2 = a \cdot (-x^2 + 6x - 5) \tag{3}\end{equation}

Close values of a denote similarity among the distribution of the scores, and can be used to determine whether pooling is advisable.

3) Objective quality evaluation

The visual quality of every stimulus is additionally evaluated using state-of-the-art objective quality metrics. For the computation of the point-to-point (p2point) and point-to-plane (p2plane) metrics, the software version 0.13.4 that is presented in [Reference Tian, Ochimizu, Feng, Cohen and Vetro67] is employed. The MSE and the Hausdorff distance are used to produce a single degradation value from the individual pairs of points. The geometric PSNR is also computed using the default factor of 3 in the numerator of the ratio, as implemented in the software. For the plane-to-plane (pl2plane) metric, the version 1.0 of the software released in [Reference Alexiou and Ebrahimi15] is employed. The RMS and MSE are used to compute a total angular similarity value. For the point-based metrics that assess color-only information, the original RGB values are converted to the YCbCr color space following the ITU-R Recommendation BT.709-6 [68]. The luma and the color channels are weighted based on equation (4), following [Reference Ohm, Sullivan, Schwarz, Tan and Wiegand69], before computing the color PSNR scores. Note that the same formulation is used to compute the color MSE scores.

(4)\begin{equation} \mbox{PSNR}_{\rm YCbCr} = \left( 6 \cdot \mbox{PSNR}_{\rm Y} + \mbox{PSNR}_{\rm Cb} + \mbox{PSNR}_{\rm Cr} \right) / 8 \tag{4}\end{equation}

For each aforementioned metric, the symmetric error is used. When available, normal vectors that are associated with a content were employed to compute metrics that require such information; that is, the models that belong to the MPEG repository excluding head, which was voxelized for our needs as indicated in Table 2. For the rest of the contents, normal estimation based on a plane-fitting regression algorithm was used [Reference Hoppe, DeRose, Duchamp, McDonald and Stuetzle70] with 12 nearest neighbors, as implemented in Point Cloud Library (PCL) [Reference Rusu and Cousins71].

For the projection-based approaches, captured views of the 3D models are generated using the proposed rendering technology on bitmaps of $1024\times 1024$ resolution. Note that the same canvas resolution was used to display the models during the subjective evaluations. The stimuli are captured from uniformly distributed positions that are lying on the surface of a surrounding view sphere. A small number of viewpoints might lead to omitting informative views of the model with high importance [Reference Alexiou and Ebrahimi19]. Thus, besides the default selection of $K = 6$ [Reference Torlig, Alexiou, Fonseca, de Queiroz and Ebrahimi18], it was decided to form a second set of a higher number of views (K = 42) in order to eliminate the impact of different orientations that exhibit across the models and capture sufficient perspectives. The K = 6 points were defined by the positions of vertices of a surrounding octahedron, and the K = 42 points were defined by the coordinates of vertices after subdivision of a regular icosahedron, as proposed in [Reference Lavoué, Larabi and Vás̆a48]. In both cases, the points are lying on a view sphere of radius equal to the camera distance used to display the initial view to the subjects, with the default camera zoom value. Finally, the camera direction vector points towards the origin of the model, in the middle of the scene.

The projection-based objective scores are computed on images obtained from a reference and a corresponding distorted stimulus, acquired from the same camera position. The parts of the images that correspond to the background of the scene can be optionally excluded from the calculations. In this study, four different approaches were tested for the definition of the sets of pixels over which the 2D metrics are computed: (a) the whole captured image without removing any background information; a mid-gray color was set and used during subjective inspection, (b) the foreground of the projected reference, (c) the union, and (d) the intersection of the foregrounds of the projected reference and distorted models.

The PSNR, SSIM, MS-SSIM [Reference Wang, Simoncelli and Bovik72], and VIFp [Reference Sheikh and Bovik73] (i.e. in pixel domain) algorithms are applied on the captured views, as implemented by open-source MATLAB scriptsFootnote ⁸, which were modified accordingly for background information removal. Finally, a set of pooling algorithms (i.e. $l_{p}$-norm, with $p \in \lbrace 1, 2, \infty \rbrace$) was tested on the individual scores per view, to obtain a global distortion value.

4) Benchmarking of objective quality metrics

To evaluate how well an objective metric is able to predict the perceived quality of a model, subjective MOS are commonly set as the ground truth and compared to predicted $\mbox {MOS}$ values that correspond to objective scores obtained from this particular metric. Let us assume that the execution of an objective metric results in a Point cloud Quality Rating (PQR). In this study, a predicted $\mbox {MOS}$, denoted as $\mbox {P(MOS)}$, was estimated after regression analysis on each [PQR, MOS] pair. Based on the Recommendation ITU-T J.149 [74], a set of fitting functions was applied, namely, linear, monotonic polynomial of third order, and logistic, given by equations (5), (6), and (7), respectively.

(5)\begin{align} P(x) &= a \cdot x + b \tag{5}\end{align}

(6)\begin{align} P(x) &= a \cdot x^3 + b \cdot x^2 + c \cdot x + d \tag{6}\end{align}

(7)\begin{align} P(x) &= a + \frac{b}{1 + \exp^{-c \cdot (x-d)}} \tag{7}\end{align}

where a, b, c, and d were determined using a least squares method, separately for each regression model. Then, following the Recommendation ITU-T P.1401 [65], the PLCC, the SROCC, the RMSE, and OR indexes were computed between $\mbox {MOS}$ and $\mbox {P(MOS)}$, to assess the performance of each objective quality metric.

A) Experiment design

Five contents were selected out of the eight tested in the first experiment, to reduce the length and cost of the subjective assessment, while maintaining a wide range of variety. In particular, two models representing objects (amphoriskos and biplane) and three models representing human figures (longdress, loot, and the20smaria) were chosen for the test. For each content, two target bit rates were selected after expert viewing, to model high and low levels of quality degradations. At every bit rate point, four geometry configurations of the G-PCC codec were evaluated. In particular, the highest depth value d that matched the targeted bit rate without employing surface approximation was selected (TriSoup level value l set to 0). This would represent the pure Octree encoding module, labeled with G0. Subsequently, combinations of d and l were selected such that the final encoded point cloud would meet the bit rate requirements, for $l = \{1, 2, 3\}$. For l = 1 (configuration G1), that meant decreasing the value of d with respect to configuration G0, as the TriSoup configuration is expected to generate a higher number of points for level 1 with respect to the Octree. This is due to the fact that TriSoup creates a surface approximation of the occupied blocks, constrained to intersect each edge of the block at most once. For l = 1 (which signifies a block size of $2\times 2\times 2$ voxels), this results in an increase in the amount of points for the decoded point cloud. For $l = 2, 3$, the number of points is decreasing by the progressively larger block sizes; thus, increasing values of d were chosen to match the bit rate (configurations G2 and G3). This procedure was followed for both high and low target bit rates,  leading to 8 configurations per content, for a total of 40 stimuli. For all configurations, the Lifting color module was used, as a slightly better performance was shown in the previous test with respect to RAHT. The color QP was always set to 4 to ensure no color degradations, which could have an effect on the rating. A summary of the encoding parameters and achieved bit rate for each content can be found in Table 6.

Table 6. Selected encoding parameters of G-PCC for experiment 2, for high and low target bit rates. The depth parameter indicates the resolution of the Octree structure, whereas the level parameter indicates the TriSoup approximation.

ITU-T Recommendations advise employing a pair comparison approach when stimuli are nearly equal in quality [75]. In order to avoid forced choices in case of imperceptible differences among the two stimuli, a ternary voting system was adopted. Each subject was presented a pair of point cloud stimuli, displayed in a side-by-side manner, and was asked to declare which of the two models they preferred, with the option of no preference. The comparisons were only performed between the same content and within the same target bit rate, for a total of 60 pairs to be assessed. Particular care was given to avoid displaying the same content consecutively, while the order of the stimuli was randomized per subject.

The test was performed in UNB. The same room, and identical configurations for the rendering software and model visualization, as described in Section V.A, were used for this experiment. One training example was shown to the subjects to help them familiarize with the testbed and the task at hand; two identical stimuli with high quality that were not part of the test were used for the purpose. Additionally, one dummy content was added at the beginning of the test to ease participants into the task, and the associated scores were discarded. A total number of 25 subjects participated, involving 13 males and 12 females, with an average of 25 years of age.

B) Data processing

Outlier detection was performed on the data according to [Reference Lee, Goldmann and Ebrahimi76]. One outlier was found, and the scores associated with it were subsequently discarded.

For each pair under assessment, the winning frequency $w_{ij}$ of stimulus i against stimulus j was computed, along with the ties $t_{ij}$. In order to obtain the preference probabilities, the winning and tie frequencies were divided by the total number of subjects after outlier detection.

The normalized MOS scores on a 0–100 scale were obtained from the winning frequencies by applying the Bradley–Terry–Luce model, according to the Recommendation ITU-T J.149 [74].

A) Experiment design

The same contents that were selected for the second experiment were also used in this test. For each content, two target bit rates were chosen based on the results of experiment 1, to model medium-high and medium-low levels of quality degradation in terms of both geometry and color. The Octree geometry in combination with the Lifting color encoding modules were adopted as the individually preferred alternatives from the previous experimentation. For contents amphoriskos and biplane, bit rate R3 was selected for the low target bit rate and R4 was selected for the high target bit rate, whereas for contents longdress, loot and the20smaria bit rates R4 and R5 were selected as low and high target bit rate, respectively. Those encoded contents would form configuration B0. For every rate, the geometry and color quantization parameters were modified such that the same target bit rate would be achieved. This is performed by either decreasing the parameter depth, which would allow allocation of more bits to the texture encoder (configuration B1), or by increasing the depth in the geometry encoder, which would lead in quality reduction of the texture encoder to match the target bit rate (configuration B2). This way, the configuration of preference can be obtained in a rate allocation problem.

A summary of the encoding parameters and achieved bit rates per content is reported in Table 7. We remind the readers that higher levels of QP correspond to a coarser color encoding, whereas lower levels of depth represent a decrease in geometry precision.

Table 7. Selected encoding parameters of G-PCC for experiment 3, for high and low target bit rates. The depth parameter indicates the resolution of the Octree structure, whereas the QP parameter indicates the quantization parameter for the Lifting encoding module.

The same methodology described in Section VI was employed in this experiment. This test was performed at EPFL, and the same room and rendering conditions described in Section VI.A were used for the experiment. One training example was shown to the subjects to help them familiarize with the testbed and the task at hand; two identical contents with high quality that were excluded from the test were used for the purpose. Additionally, one dummy content was added at the beginning of the test to ease participants into the task, and the associated scores were discarded. The same guidelines were followed for the order and presentation of the stimuli under assessment. A total number of 25 subjects participated, involving 17 males and eight females, with an average of 29.13 years of age.

B) Data processing

Outlier detection was performed on the data according to [Reference Lee, Goldmann and Ebrahimi76]. No outlier was detected among the subjects. The same data processing as described in Section VI.B was adopted to obtain the preference and tie probabilities.