Progressive Knowledge Transfer Based on Human Visual Perception Mechanism for Perceptual Quality Assessment of Point Clouds

In our proposed network, we use PointNet[46] as the backbone, which is well known for its elegance, simplicity, and excellent generalization. For effective use of key information in point clouds, we propose to extract the key clusters from the input point cloud first. Moreover, to simulate the human perception mechanism of point cloud quality, we add an attention mechanism to the network and introduce a coarse-to-fine progressive perception mechanism. In the key clusters extraction stage, we consider global geometry characteristics of the point clouds. During the deep feature extraction stage, we draw on the global and local information of the point cloud and add an attention mechanism to the last two feature extraction steps. The coarse-to-fine perception mechanism runs through the whole point cloud quality prediction network, and the overall architecture of our network is illustrated in Fig. 1

Due to its large size, it is difficult to use the point cloud object directly as the input to the no-reference network. We use key points and local clusters to represent the key clusters from the original point cloud and then feed these key clusters into the no-reference network, which solves the network process limitation without sacrificing the effective information of the original point cloud.

(1) Key Points Extraction

According to research in the field of neuroscience, the structure characteristics of objects are very important for human eye perception. For 2D image quality assessment, structural features have been widely used [47] [48] [49] [50] [51]. The full-reference point cloud quality evaluation model employing object structural features [22] has also shown promising results. For a 3D object, the general architecture can be described by key point roughly, which can create edges, contours, and skeletons, are usually found in the high spatial-frequency range. In this paper, we use a high-pass graph filtering method  [52] to extract the key points from the input point cloud.

Suppose a point cloud has $N$ points with three-dimensional coordinates and three-dimensional color attributes, we first construct a general graph of a point cloud by encoding the local geometry information. Suppose a point cloud has $N$ points with three-dimensional coordinates and three-dimensional color attributes. Then, each point corresponds to the vertex of graph, and each effective connection between two points having positive weight is referred to as edge. The edge weight is defined through an adjacency matrix $\mathbf{W}\in\mathbb{R}^{N\times N}$ as (1), where $\mathbf{W}_{\bm{\bm{\vec{x}_{i}}},\bm{\vec{x}_{j}}}$ represents the edge weight between two points $\bm{\bm{\vec{x}_{i}}}$ and $\bm{\vec{x}_{j}}$ using the geometric distance as

Here $\bm{\vec{x}_{i}^{o}},\bm{\vec{x}_{j}^{o}}$ are 3D coordinates of points $\bm{\bm{\vec{x}_{i}}},\bm{\vec{x}_{j}}$, $\sigma$ is the variance of graph nodes, and $\tau$ is a Euclidean distance threshold in clustering neighbor points into the same graph. Given this graph, the location and color information of point clouds are called $graph$ $signals$. Then, we take the graph signal as input and produce another graph signal as an output by graph filter. Let $\bm{\vec{x}_{org}}$ represent the original point cloud, we get a geometric key point $\bm{\vec{x}_{key}}$, after applying a high-pass filter $\Psi(\cdot)$,

where $L$ is the length of filter $\Psi(\cdot)$, and $\left\lfloor\cdot\right\rfloor_{\beta}$ is to intercept the first $\beta$ points as the number of key point, which is sorted from large to small by the calculation result of $\Psi(\cdot)$. Typically, the number of key points is less than the total number, this is to say that $\beta$ is less than $N$. The operation of filter $\Psi(\cdot)$ can be expressed as

where $h_{l}$ is $l$-th coefficient, and $L$ is the length of graph filter. $\mathbf{A}\in\mathbb{R}^{N\times N}$ is the most elementary nontrivial graph filter, and here we set $\mathbf{A}=\mathbf{D}^{-1}\mathbf{W}$, where $\mathbf{D}=diag(d_{1},...,d_{N})\in\mathbb{R}^{N\times N}$ with $d_{i}=\begin{matrix}\sum_{\bm{\vec{x}_{i}}}\mathbf{W}_{\bm{\vec{x}_{i}},\bm{\vec{x}_{j}}}\end{matrix}$. From a graph filtering perspective, we can also refer to $\bm{\vec{x}_{i}^{o}}$ as the input graph signal, and $\Psi(\bm{\vec{x}_{i}})$ denote the probability value of this point becoming an edge. This probability is then used as the measurement to decide whether associated point can be selected as the key points.

(2) Key Clusters Formation

The capacity of the model to detect subtle features can be improved by capturing local information. This is achieved by a simple clustering algorithm, using the k-nearest neighbors (k-NN) algorithm within a variable radius centered on key points. Here we refer to it collectively as the center-neighbor-segmentation (CNS) algorithm. In the k-NN algorithm, the radius $R$ is continuously expanded by a growth factor $\sigma$ until $K$ neighbors are searched. For each local region, the same feature extraction module is for local pattern learning.

In this section, we carry out three feature extraction stages to create a higher dimensional point cloud feature representation. The first feature extraction stage is named FE, and the remaining feature extraction stages are named AFE. The FE is an ordinary convolutional structure while the AFE uses spatial and channel ’squeeze and excitation’ attention module (scSE) to implement the attention mechanism.

As shown in Fig. 1, we assume that the input of the AFE is point set $\left\{\bm{\vec{x}_{1}},\bm{\vec{x}_{2}},...,\bm{\vec{x}_{N_{1}}}\right\}$ obtained after the FE stage, and we first obtain the cluster centers $\left\{\bm{\vec{x}_{i_{1}}},\bm{\vec{x}_{i_{2}}},...,\bm{\vec{x}_{{N_{1}}^{\prime}}}\right\}$ with farthest point sampling (FPS). Given the same number of centroids, FPS provides better coverage of the complete point set than random sampling. Then we use the ball query approach to obtain the elements of each cluster for feature extraction. Then the constituents of each cluster are obtained by using the Ball Query Method (BQM). The ball query returns $K$ points within a radius of the query point. If the number of points in the radius is less than $K$, the points in the radius are repeatedly sampled until $K$ points are obtained. Here the point with the smallest index in the radius is used as the supplementary point.

The reason for using different clustering algorithms is that the KNN algorithm has the advantage of ensuring each region contains the same number of points, while the ball-query algorithm ensures that each region has the same size. In the KCE module, we need to capture as much information as possible about the original point cloud (i.e., retain more original points) so KNN algorithm is better than ball-query. However, in the DFE module, we prefer to ensure that each local region has the same perceptual field (i.e., the same region size). It is worth noting that the parameter $R$ of the ball-query algorithm is particularly important in the DFE module.

Importantly, we integrate the attention mechanism into the feature extraction module of the PointNet backbone network, termed AFE, for feature extraction of cluster2. The internal structure of the AFE is depicted in Fig. 1. To ensure that deeper features of the original point cloud are extracted, this module is repeated twice in the overall structure. According to cognitive science [22], humans selectively focus on a portion of all information while ignoring other apparent information due to bottlenecks in information processing. With limited attention resources, this is an excellent way to swiftly filter out high-value information from a vast volume of data. Neural networks incorporating attention mechanisms have made great breakthroughs in various fields, such as image classification  [53], machine translation [54] [55], and image caption [56]. Hu $et.al$ [57] proposed the Squeezeand-Excitation (SE) block as part of a convolutional neural network (CNN). This block adaptively recalibrates channel-wise feature responses by explicitly modelling interdependencies between channels, achieving excellent results on image classification tasks. Subsequently, Roy, Navab, and Wachinger renamed this SE module spatial squeeze and channel excitation (cSE) module [58], and developed a new channel squeeze and spatial excitation (sSE) module, squeezing channel-wise and exciting spatially. Importantly, they proposed a module termed scSE that merge the two features. We use the scSE module in the proposed network. The location of SE blocks in PKT-PC are shown in Fig. 2.

The scSE model consists of the cSE and sSE models, $\mathbf{U_{scSE}}=\mathbf{U_{cSE}}+\mathbf{U_{sSE}}$. The architectural flow is shown in Fig. 3. The upper part is cSE, while the lower represents sSE. We first introduced the cSE part. Consider the input feature map $\mathbf{U}=[\bm{\vec{u}_{1}},\bm{\vec{u}_{2}},...,\bm{\vec{u}_{C}}]$, where $\bm{\vec{u}_{i}}\in\mathbb{R}^{H\times W}$. Spatial squeeze first realized by a global average pooling layer, producing vector $\bm{\vec{z}}\in\mathbb{R}^{1\times 1\times C}$,

Then, encoding the channel-wise dependencies through two fully-connected layers $\bm{\vec{w}}=\mathbf{W_{1}}(\delta(\mathbf{W_{2}}\bm{\vec{z}}))$, with weights $\mathbf{W_{1}}\in\mathbb{R}^{C\times\frac{C}{2}}$, $\mathbf{W_{2}}\in\mathbb{R}^{\frac{C}{2}\times C}$, and ReLU operator $\delta(\cdot)$. Finally, mapping $\bm{w_{i}}$ into $[0,1]$ using sigmoid layer $\sigma(\cdot)$. The result $\mathbf{U_{cSE}}$ can be expressed as

As the network learns, the channel weight $\sigma(\vec{w}_{1})$ are dynamically adjusted, turning that the less important channels are ignored and the important ones are emphasized. Unlike the cSE module, the sSE module cares more about spacial relationships. Thus, the input tensor $\mathbf{U}$ can be described as $[\bm{\vec{u}^{1,1}},\bm{\vec{u}^{1,2}},...,\bm{\vec{u}^{i,j}},...,\bm{\vec{u}^{H,W}}]$, where $\bm{\vec{u}^{i,j}}\in\mathbb{R}^{1\times 1\times C}$, and $(i,j)$ ($i\in\left\{1,2,...,H\right\}$, $j\in\left\{1,2,...,W\right\}$) represents its corresponding spatial location. The channel squeeze operation is achieved through a convolution layer, $\bm{\vec{w}}=\mathbf{U}\times\mathbf{W_{sq}}$ with $\mathbf{W_{sq}}\in\mathbb{R}^{1\times 1\times C\times 1}$. This operation generates a projection tensor $\bm{\vec{w}}\in\mathbb{R}^{H\times W}$, where $w_{i,j}$ is the linear combination of all channels in spatial location $(i,j)$. Same as cSE, $w_{i,j}$ needs to be re-scaled into $[0,1]$ with a sigmoid layer $\sigma(\cdot)$ to be a spatial weight. Finally, the spatial recalibration of input $\mathbf{U}$ is

where activation $\sigma(w_{i,j})$ indicates the relative importance of location $(i,j)$ for a given feature map, enabling more attention to some relevant spatial locations while ignoring less important space. By combining cSE and sSE, scSE provides more importance of the point which are relevent both spatially and channel-wise, that encourages the network to learn more meaningful feature maps.

Referring to the process of evaluating the quality of point clouds by human perceptual system, we can find that there exists a native hierarchical dependency. That means that humans always first determine a point cloud coarse-grained quality, i.e., excellent, fair, or bad, and then, under the branch of the quality type, give a specific quality score by relying on subtle visual cues. Fig. 4 illustrates the coarse-to-fine principle.

In the proposed network, we adopt a two-step strategy to train the PKT-PCQA model: 1) quality level classification; 2) quality score prediction. In step 2), the feature extraction part of the PKT-PCQA model is initialized with related part in step 1), then fine-tune the quality prediction network on the first quality classification basis. In the process from coarse to fine, there are two key parts, namely, the classification of quality level and the training of the network.

(1) Quality Level Classification

The classification of quality levels is based on the statistical properties of quality scores in the dataset. That is, within a certain range, the number of point clouds at each level is guaranteed to be approximately equal in each dataset. The specific classification will be discussed in the experimental settings section. In this paper, we only use three labels: excellent, fair and bad, in order to maximize the distinction of different labels.

(2) Model Training

In the classification task, the parameters $\mathbf{W_{fc}}$ of the feature extraction part and $\mathbf{W_{c}}$ of the classification part are determined by minimizing the loss function $cross-entropy$

where $\bm{\vec{x_{i}}}$ represents a specific prediction value vector for point cloud $i$, $y_{i}$ is the label value used as an index, and $c$ is the number of types of labels.

For MOS prediction network, the model parameters of the feature extraction part are initialized as $\mathbf{\hat{W}_{fc}}$, while the prediction unit is randomly initialized, represented as $\mathbf{W_{p}}$. In prediction task, we care more about how well the prediction curve fits the original score curve, rather than the difference between individual scores [59]. Therefore, the related model parameters are fine-tuned through minimizing the loss function measures the difference in fit. The parameters of the model are determined by (10) after training the k-th batch.

where $P(\bm{\vec{x_{k}}},\bm{\vec{y_{k}}})$ is pearson linear correlation coefficient (PLCC) with the range is [-1,1], and ”1” means positive correlation, ”-1” means negative correlation, ”0” means uncorrelated. In the quality prediction task, our goal is to maximize $P(\bm{\vec{x_{k}}},\bm{\vec{y_{k}}})$. Therefore, we can obtain the parameters of the quality prediction network after mining the loss function (i.e., L2).

PKT-PCQA was implemented by using PyTorch on a computer with a 3.5 GHz CPU and GTX 1080Ti GPU.

(1) Dataset

The proposed method was evaluated on three 3D point cloud: SJTU-PCQA  [12], M-PCCD [10], and the Waterloo Point Cloud (WPC) [13] [32]. The quality level division on each dataset is shown in Fig. 5.

• •

  SJTU consists of 9 reference point clouds (redandblack, loot, longdress, hhi, soldier, ricardo, ULB Unicorn, Romanoillamp, statue, shiva) and 378 distorted versions (42 distorted items per reference item through 6 degradation types: OT: Octree-based compression, CN: Color Noise, DS: Downscaling, D+C: Downscaling and Color noise, D+G: Down-scaling and Geometry Gaussian noise, GGN: Geometry Gaussian noise and, C+G: Color noise and Geometry Gaussian noise).

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  M-PCCD consists of 8 reference point clouds (loot, longdress, soldier, Romanoillamp, amphoriskos, biplane, head, the20smaria) and 232 distorted versions (29 distorted items per reference item through 5 types of compression G-PCC with Octree coding and Lifting coding, G-PCC with Octree coding and RAHT coding, G-PCC with Triangle soup coding and Lifting coding, G-PCC with Triangle soup coding and RAHT coding, V-PCC).

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  WPC consists of 20 reference point clouds (bag, banana, biscuits, cake, cauliflower, flowerpot, glasses case, honeydew melon, house, litchi, mushroom, pen container, pineapple, ping-pong bat, puer tea, pumpkin, ship, statue, stone, tool box) and 740 distorted versions 37 distorted items per reference item through five degradation types TMC1: G-PCC with Triangle soup coding, TMC2: G-PCC with Octree coding, TMC3:V-PCC, Noise: White Gaussian noise, Downsample: Octree-Based Downsampling).

(2) Parameter Setting

The following parameter values were used

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  $\beta,L,K$ in Key Clusters Extraction
  $\beta=1024,L=4$ in key-point extraction, and $K=16$ in clustering. These values of parameters $\beta,K$ can be proved in Ablation Test, while $L$ follows the values suggested in the reference paper [22]. The parameter settings of the FE units are shown in Fig.6.

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  $R$ in Deep Feature Extraction
  DFE includes sampling, grouping and attention feature extraction twice, and the specific structure and parameters are shown in Fig.7, where scSE implements the attention function of the model. The parameter $R$ determines the size of the perceptual field. It is set to $0.4$ in the classification task and $0.35$ in the prediction task.

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  Progressive Prediction Mechanism
  The Classification and Prediction branches have a similar architecture; the only difference between them is the last layer. In the classification task, the out-channel of last layer in classification task is the number of quality level, while that of prediction task is one.

  In the classification task, the evaluation criterion is $CrossEntropy$ loss function, while in the prediction quality branch, we considered the PLCC (12) and Spearman’s rank-order correlation coefficient (SROCC) computed as

  $\displaystyle SROCC=1-\frac{6\sum_{i}d_{i}^{2}}{I\left(I^{2}-1\right)},$

  (13)

  where $I$ is the number of the tested point clouds and $d_{i}$ is the rank difference between the ground truth $MOS$ and the predicted $MOS$ of the $i$-th point cloud.

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  Parameters in Multistep Training Mechanism
  We used the Adam optimization technique with default parameters to train both the classification and prediction tasks. The batch size was set to 16 in training processing and 32 in testing processing, with a total epoch number of 200. In the classification task, the learning rate was initialized to 0.001 and subsequently reduced using $stepLR$, a strategy for adjusting the learning rate at equal intervals, with a step size of 20, and the learning rate adjustment multiplier $\gamma=0.7$. In the prediction task, the learning rate was set to 0.0001, using $stepLR$ was used as a reduction strategy with step size 30, and learning rate adjustment multiplier $\gamma=0.7$.

To fully evaluate our proposed model, we conduct the following experiments.

(1) Key Clusters Extraction
The Key Clusters Extraction (KCE) aims at simplifying the point cloud without losing critical information . Common reduction strategies include point cloud sampling and point cloud segmentation, which correspond to the global feature and local feature of a point cloud. However, in point cloud quality prediction task, neither of them is enough to represent the original point cloud. Extracting key clusters of point cloud needs to take into account global and local information. To validate this hypothesis, we evaluate point cloud extraction strategies using only global information, only local information, and both global and local information. Before making the above comparison, we need to choose a representative algorithm for each strategy.

We first compared several global information extraction strategies, including random sampling, farthest point sampling, and key-point extraction. The result of using them separately to complete the prediction of point cloud quality is shown in Fig.8. Using key points to represent the global feature gives the best result. Therefore, extracting key points method is used as a proxy for global information extraction strategy to participate in the comparison with the other two feature extraction strategies.

A popular technique for representing point clouds using local information is to partition them into chunks. However, in the task of predicting the quality score of a point cloud, it is challenging to determine the score of the entire point cloud using this method because each chunk receives a score, and it is inappropriate to choose one of them to represent the whole or determine the average of all chunks. Here, we only contrast the effects of the two strategies on the outcomes that is key points and key clusters. We can see that using key clusters gives better result than just using key points.

Comparing the influence of these three reconstruction methods in point cloud prediction task, as shown in Fig.9, the proposed method that considers both global and local features is a better strategy to extract the key clusters of point cloud. The results in Fig.9 also proved that strategy can provide more efficient information to subsequent network in point cloud quality evaluation task.

To find the most suitable number of the new point cloud, we also test several combinations of keypoints and local points $\beta\times K$ (i.e. $1024\times 16,1024\times 32,2048\times 16,512\times 16$).

The network structure is shown in Fig.6 and Fig.8 with the same training strategies. The experimental results are shown in Table I. We can see that the best combination of the number of key point and local point number is $1024\times 16$. The reason is that too many key points may cause information redundancy in the original point cloud, affecting the information provided by valid points, while too few key points cannot provide enough information, so the number of key points needs to be apposite.

(2) Deep Feature Extraction

The radius $R$, which represents the perceptual field size of the depth extraction network is a critical parameter. If $R$ is too large, the tightness of neighbors and clustering centers cannot be guaranteed because the range of random sampling is too large. On the other hand, if $R$ is too small, not enough neighbor points can be collected, leading to the reduction of effective information obtained in the local area. We used $1024\times 16$ point cloud key clusters to test the network with radius 0.4, 0.35, and 0.30. The results in Table II show that $R=0.35$ provides the maximum prediction accuracy.

(3) Attention Mechanism
The impact of the attention mechanism on the model depends on the type of SE block and its location. To fully explore it, we compare the effects of the three type SE blocks at different locations in the model. As for the location, we discuss the different locations of SE in KCE and DFE modules separately.

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  Attention Mechanism for Initial Feature Map Generation Generally speaking, adding the attention mechanism can improve the performance of the proposed network. However, in our proposed network, we extract key points in KCE module, which may lead to the failure of the spatial attention mechanism in initial feature map generation. Also, since there are only six channels for each point in this step which represents their three-dimensional coordinates and color information, it is difficult to say which channel is more important. Therefore, the channel attention mechanism may not have much effect in initial feature map.
  To check this assumption, we conducted comparative experiments on a key clusters ($1024\times 16$) . SE Blocks in the DFE part are set as scSE. The result is shown in Fig.10. It is obviously that without any SE module in initial feature map generation can get better prediction result.

  $\beta\times K$	KCE	DFE	PLCC	SROCC
  1024 $\times$ 16	-	-	0.8827	0.9077
  	-	scSE	0.9122	0.9316
  	scSE	scSE	0.8869	0.9047

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  Attention Mechanism in Deep Feature Extraction
  Different with the initial feature map, the deep feature of point cloud is much more abstract, that is why attention mechanism can greatly improve the performance of the original model. The degree of improvement depends not only on the type of the attention unit, but also on its location.

  Fig.11 shows the effect of different attention mechanism types at different locations of the AFE module. In the experiments, initial feature extraction did not include an adopt SE block. The best prediction accuracy of each model presented in Table III.

  Fig. 11.11(a) shows the performance of different SE modules at the ideal position, and the black line result means that no any SE module is added, and the red, blue and green line results represent the performance of adding scSE, cSE, and sSE, respectively. We can see that the scSE module provides the best performance. We also tested the performance of different SE modules in various locations, as shown in Fig. 11.11(b) to Fig. 11.11(e). Fig. 11.11(b) allows us to evaluate whether the SE block should be before or after the ReLU layer. Fig. 11.11(c) and Fig. 11.11(d) can determine if the SE block is appropriate in only one feature extraction step of the DFE module. Besides, Fig. 11.11(e) helps to decide whether more than one SE block should be added to an AFE module. We can see that adding scSE to the last convolutional layer of each AFE module gives the best results.

Finally, we used $1024\times 16$ key clusters of the point cloud to examine several combinations of the attention module in the KCE and DFE modules (Table IV). The attention module is set as scSE module since prior experiments have shown that this module can significantly improve model performance. We can observe that using the scSE module only in the DFE part leads to the highest score prediction accuracy.

(4) Progressive Prediction Mechanism

The proposed network predicts the quality of the tested point cloud using a coarse-to-fine progressive mechanism from quality classification to quality prediction. To verify the importance of quality classification information initialization for the quality prediction task, we compared with random initialization. To make a fair comparison, all the parameters of the prediction task were identical. The results are shown in Fig.12. It can be seen that the PLCC and SROCC of the progressive method from coarse to fine are both higher than 0.9, while those of the random initialization method used are only about 0.5. The above results fully demonstrate the effectiveness of the progressive prediction mechanism.

To test the performance of PKT-PCQA, we conducted experiments on the SJTU-PCQA, M-PCCD, and WPC datasets. We randomly selected about 80% of the point clouds for training and the remaining 20% for testing. There were no overlapping samples between the training and the testing sets. The performance results of the proposed network on different datasets are shown in Table V. We should note that the PLCC and SROCC can be positive or negative, and the closer the absolute value of these to 1, the better the performance.

The result in Table V shows that our network achieved excellent results on SJTU-PCQA and M-PCCD. Its performance was lower on WPC. One possible reason is that for WPC, the texture content of the point clouds is richer, and the content of the point clouds at each quality level is also richer, so the demand of data is also larger, and the amount of point cloud data in the WPC dataset can provide is very limited. For the proposed network, the task of predicting quality on WPC dataset is more difficult, therefore, the performance on WPC dataset degrades slightly.

We alse compared PKT-PCQA with standard and state-of-the-art FR and RR point cloud quality metrics on different datatsets. The compared metrics were chosen to cover a diversity of design philosophies, including point-based, feature-based, projection-based and deep learning-based. The FR quality metrics include $PSNR_{MSE,p2po}$, $PSNR_{HF,p2po}$, $PSNR_{Y}$, $PCQM$, $GraphSIM$, $IW-SSIM_{p}$, $PointSSIM$, and $LP-PCQM$. The RR quality metrics include $PCM\_{RR}$. More importantly, the sophisticated advanced $PQA-NET$ [42] method is selected as the compared NR point cloud quality metric to prove the effectiveness of the proposed $PKT-PCQA$ method. To map the dynamic range of the scores from objective quality assessment models into a common scale, the logistic regression recommended by VQEG is used [62]. These results are shown in Table. VI and they provide some useful insights with respect to the approaches for point cloud quality assessment. First of all, the performance of RR and NR point cloud quality metrics are generally lower than that of the FR point cloud quality metrics. Obviously, the RR and NR metrics can only use part or no original information, while, the FR metric can take advantage of all the original information. Limited by the unfair usage of the original information, the performance of RR and NR methods are reasonably worse than the FR methods. From the results,we can see that the performance of the proposed PKT-PCQA is the best in the RR and NR quality metrics and only slightly lower than the best FR methods, indicating the advantage of the proposed PKT-PCQA. In the WPC dataset, which provides the largest number of samples in the three datasets, both PLCC and SROCC of the PKT-PCQA are 0.56 which is the best in the NR point cloud quality metrics. More surprisingly, the performance of PKT-PCQA was better than the RR quality metric $PCM_{RR}$, and is only slightly lower than the best FR quality metric $IW-SSIM_{p}$. The performance of PKT-PCQA was also impressive on SJTU-PCQA and M-PCCD datasets. Similarly, PKT-PCQA performed better than the other NR point cloud quality metric and even better than the RR point cloud quality metric. The PLCC and SROCC of PKT-PCQA were even larger than 0.91 on SJTU-PCQA. On the M-PCCD dataset, the SROCC reached 0.91. The SROCC and PLCC of the best FR point quality metric were 0.95 and 0.96, which are only 0.02 and 0.05 larger than that of PKT-PCQA. It is worth indicating that the NR point cloud quality metric PKT-PCQA does not need to refer to the original point cloud information, so its application scenarios are far more than the FR point cloud quality metrics.