Pseudo-Trilateral Adversarial Training for Domain Adaptive Traversability Prediction

We consider segmentation tasks where the input space is $\mathcal{X}\subset\mathbb{R}^{H\times W\times 3}$, representing the input RGB images, and the label space is $\mathcal{Y}\subset\left\{0,1\right\}^{H\times W\times K}$, representing the ground-truth $K$-class segmentation images. The label for a single pixel at $(h,w)$ is denoted by a one-hot vector $y^{(h,w)}\in\mathbb{R}^{K}$ whose elements are by-default 0-valued except the $i^{th}$ element is labeled as $1$ if the $i^{th}$ class is specified. Domain adaptation has two domain distributions over $\mathcal{X}\times\mathcal{Y}$, named source domain $\mathcal{D}_{s}$ and target domain $\mathcal{D}_{t}$. In the setting of UDA for segmentation, we have access to $m_{s}$ i.i.d. samples with labels $\mathcal{U}_{s}=\left\{\mathbf{x}_{si},\mathbf{y}_{si}\right\}_{i=1}^{m_{s}}$ from $\mathcal{D}_{s}$ and $m_{t}$ i.i.d. samples without labels $\mathcal{U}_{t}=\left\{\mathbf{x}_{tj}\right\}_{j=1}^{m_{t}}$ from $\mathcal{D}_{t}$.

In the UDA problem, we need to reduce the prediction error on the target domain. With a slight abuse of notation, we also use $h$ to denote a hypothesis, which is a function: $\mathcal{X}\rightarrow\mathcal{Y}$. We denote the space of $h$ as $\mathcal{H}$. With the loss function $l(\cdot,\cdot)$, the expected error of $h$ on $\mathcal{D}_{s}$ is defined as

Similarly, we can define the expected error of $h$ on $\mathcal{D}_{t}$ as

Two important upper bounds related to the source and target error are given in Ben-David et al. (2010).

The first upper bound is given in the following theorem.

Theorem 1 For a hypothesis $h$,

where $d_{1}(\cdot,\cdot)$ is the $L^{1}$ divergence for two distributions, and the constant term $\lambda$ does not depend on any $h$. However, it is claimed in Ben-David et al. (2010) that the bound with $L^{1}$ divergence cannot be accurately estimated from finite samples, and using $L^{1}$ divergence can unnecessarily inflate the bound. Another divergence measure is thus introduced to replace the $L^{1}$ divergence with a new bound derived. The new measure is defined as follows,

Definition 1 Given two domain distributions $\mathcal{D}_{s}$ and $\mathcal{D}_{t}$ over $\mathcal{X}$, and a hypothesis space $\mathcal{H}$ that has finite VC dimension, the $\mathcal{H}$-divergence between $\mathcal{D}_{s}$ and $\mathcal{D}_{t}$ is defined as

where $\text{P}_{x\sim\mathcal{D}_{s}}[h(x)=1]$ represents the probability of $x$ belonging to $\mathcal{D}_{s}$. Same to $\text{P}_{x\sim\mathcal{D}_{t}}\left[h(x)=1\right]$.

The $\mathcal{H}$-divergence resolves the issues in the $L^{1}$ divergence. If we replace $d_{1}(\mathcal{D}_{s},\mathcal{D}_{t})$ in Eq. (3) with $d_{\mathcal{H}}(\mathcal{D}_{s},\mathcal{D}_{t})$, then a new upper bound for $\epsilon_{t}(h)$, named as $\mathbb{UB}_{1}$, can be written as

An approach to compute the empirical $\mathcal{H}$-divergence is also proposed in Ben-David et al. (2010), see the below Lemma 1.

Lemma 1 For a symmetric hypothesis class $\mathcal{H}$ (one where for every $h\in\mathcal{H}$, the inverse hypothesis $1-h$ is also in $\mathcal{H}$) and two sample sets

the approximated empirical $\mathcal{H}$-divergence is computed as:

where $\mathbb{I}[a]$ is an indicator function which is 1 if $a$ is true, and $0$ otherwise.

The second upper bound is based on a new hypothesis called the symmetric difference hypothesis, see the following definition.

Definition 2 For a hypothesis space $\mathcal{H}$, the symmetric difference hypothesis space $\mathcal{H}\Delta\mathcal{H}$ is the set of hypotheses

where $\oplus$ denotes an XOR operation. Then we can define the $\mathcal{H}\Delta\mathcal{H}$-distance as

Similar to Eq. (5), if we replace $d_{1}(\mathcal{D}_{s},\mathcal{D}_{t})$ with the $\mathcal{H}\Delta\mathcal{H}$-distance $d_{\mathcal{H}\Delta\mathcal{H}}(\mathcal{D}_{s},\mathcal{D}_{t})$, the second upper bound for $\epsilon_{t}(h)$, named as $\mathbb{UB}_{2}$, can be expressed as

where $\lambda$ is the same term as in Eq. (3).

The two bounds (Eq. (5) and Eq. (10)) for the target domain error are separately given in Ben-David et al. (2010). It has been independently demonstrated that DA corresponds to optimizing over $\mathbb{UB}_{1}$ (Ganin et al., 2016), where optimization over the upper bound $\mathbb{UB}_{1}$ (Eq. (5) with the divergence Eq. (7)) is proved as equivalent to an adversarial learning with Eq. (11) and a supervised learning with the source data, and that CA corresponds to optimizing over $\mathbb{UB}_{2}$ (Saito et al., 2018), where the $d_{\mathcal{H}\Delta\mathcal{H}}$ is approximated by the discrepancy between two different classifiers.

Training DA is straightforward since we can easily define binary labels for each domain, e.g., we can use 1 as the source domain label and 0 as the target domain label. Adversarial training over the domain labels can achieve domain alignment. For CA, however, it is difficult to implement as we do not have target labels, hence the target class features are completely unknown to us, thus leading naively using adversarial training over each class impossible. The existing way well supported by theory to perform CA (Saito et al., 2018) is to indirectly align class features by devising two different classifier hypotheses. The two classifiers have to be well trained on the source domain and are able to classify different classes in the source domain with different decision boundaries. Then considering the shift between source and target domain, the trained two classifiers might have disagreements on target domain classes. Note since the two classifiers are already well trained on the source domain, the agreements of the two classifiers represent those features in the target domain that are close to the source domain, while in contrast, the features where disagreements happen indicate that there is a large shift between the source and the target. We use the disagreements to approximate the distance between the source and the target. If we are able to minimize the disagreements of the two classifiers, then features of each class between source and target will be enforced to be well aligned.

A standard way to achieve the alignment for deep models is to use the adversarial training method, which is also used in Generative Adversarial Networks (GANs) (Goodfellow et al., 2014). Therefore we explain the key concepts of adversarial training using the example of GANs.

GAN is proposed to learn the distribution $p_{r}$ of a set of given data $\left\{\mathbf{x}\right\}$ in an adversarial manner. The architecture consists of two networks - a generator $G$, and a discriminator $D$. The $G$ is responsible for generating fake data (with distribution $p_{g}$) from random noises $\mathbf{z}\sim p_{\mathbf{z}}$ to fool the discriminator $D$ that is instead to accurately distinguish between the fake data and the given data. Optimization of a GAN involves a mini-maximization over a joint loss for $G$ and $D$.

where we use $1$ as the real label and $0$ as the fake label. Training with Eq. (11) is a bilateral game where the distribution $p_{g}$ is aligned with the distribution $p_{r}$.

We start by examining the relationship between the DA and the CA from the perspective of target error bound. We propose to use this relation to improve the segmentation performance of class alignment, which is desired for dense prediction tasks. We provide the following theorem:

Theorem 2 If we assume there is a hypothesis space $\mathcal{H}$ for segmentation model $h^{\theta,\phi}$ and a hypothesis space $\mathcal{H}_{D}$ for domain classifiers $D^{\psi}$, and $\mathcal{H}\Delta\mathcal{H}\subset\mathcal{H}_{D}$, then we have

The proof of this theorem is provided in Section. 7.1.

Essentially, we limit the hypothesis space $\mathcal{H}$ and $\mathcal{H}_{D}$ in Eq. (12) into the space of deep neural networks. Directly optimizing over $\hat{\mathbb{UB}_{2}}$ might be hard to converge since $\hat{\mathbb{UB}_{2}}$ is a tighter upper bound for the prediction error on the target domain. The bounds relation in Eq. (12) shows that the $\hat{\mathbb{UB}}_{1}$ is an upper bound of $\hat{\mathbb{UB}}_{2}$. This provides us a clue to improve the training process of class alignment, i.e., the domain alignment can be a global constraint and narrow down the searching space for the class alignment. This also implies that integrating the domain alignment and class alignment might boost the training efficiency as well as the prediction performance of UDA. This inspires us to design a new model, which we describe in the subsequent sections.

Following our proposed PTGS and the identified relation in Eq. (12), we design the structure of our CALI model as shown in stage I of Fig. 4. Four networks are involved, a shared feature extractor $G^{\phi}$, a domain discriminator $D^{\psi}$ and two classifiers $C_{1}^{\theta}$ and $C_{2}^{\theta}$. Furthermore, as defined in Eq. (9), $h$ and $h^{{}^{\prime}}$ are two different hypotheses, thus we have to ensure the classifiers $C_{1}^{\theta}$ and $C_{2}^{\theta}$ are different. Note that the supervision signal from the source domain ($\mathbf{y}_{s}$ in Fig. 4) is used to train $C_{1}^{\theta}$ and $C_{2}^{\theta}$ because both classifiers are expected to generate correct decision boundaries on the source domain. No label from the target domain is used during training.

We also show steps involved in our ICALI model in Fig. 4-stages II & III. Stage II shows how a pair of a mixed image and the corresponding mixed label is generated. First, the prediction of the source image $\mathbf{o}_{1s}$ is used to compute the performance (indicated by the mean Intersection over Union (mIoU)) for all classes. Note that $\mathbf{o}_{1s}$ is the prediction of $C_{1}^{\theta}$ in stage I. The classes are then divided into a group of well-performing classes and a group of under-performing classes. The ratio for the division is a hyperparameter. Then a selection mask for source data $\mathbf{M}_{s}$ is generated by extracting the regions of under-performing classes in the source ground-truth label. We can easily obtain the mask for target data: $\mathbf{M}_{t}=\mathbf{1}-\mathbf{M}_{s}$. Next, the mixed data can be generated by:

where $\mathbf{o}_{1t}$ is the prediction of $C_{1}^{\theta}$ in stage I.

In stage III, the newly generated data $\left\{\mathbf{x}_{m},\mathbf{y}_{m}\right\}$ are used to train the model $G^{\psi}$ and $C_{1}^{\theta}$. Note that the model $C_{2}^{\theta}$ is not included in the training of stage III such that the difference between the two models can be well maintained.

We denote raw images from the source or target domain as $\mathbf{x}$, and the label from the source domain as $\mathbf{y}$. We use semantic labels in the source domain to train all of the nets, but the domain discriminator, in a supervised way (see the solid red one-way arrow in Fig. 4). We need to minimize the supervised segmentation loss since Eq. (12) and other related Eqs suggest that the source prediction error is also part of the upper bound of the target error. In this section, we omit superscripts for all model notations. The supervised segmentation loss for training CALI is defined as

where $\odot$ represents the element-wise multiplication between two tensors.

To perform domain alignment, we need to define the joint loss function for $G$ and $D$

where no segmentation labels but domain labels are used, and we use the standard cross-entropy to compute the domain classification loss for both source ($\mathcal{CE}_{s}(\mathbf{x})$) and target data ($\mathcal{CE}_{t}(\mathbf{x})$). We have

and

Note we include $G$ in Eq. (16) since both the source data and target data are passed through the feature extractor. This is different than standard GAN, where the real data is directly fed to $D$, without passing through the generator.

To perform class alignment, we need to define the joint loss function for $G$, $C_{1}$, and $C_{2}$

where $d(\cdot,\cdot)$ is the distance measure between two distributions from the two classifiers. In this paper, we use the same $L_{1}$ distance in Saito et al. (2018) as the measure, thus $d(p,q)=\frac{1}{K}|p-q|_{1}$, where $p$ and $q$ are two distributions and $K$ is the number of label classes.

To prevent $C_{1}$ and $C_{2}$ from converging to the same network throughout the training, we use the cosine similarity as a weight regularization to maximize the difference of the weights from $C_{1}$ and $C_{2}$, i.e.,

where $\mathbf{w}_{1}$ and $\mathbf{w}_{2}$ are the weight vectors of $C_{1}$ and $C_{2}$, respectively.

The extra supervised training in ICALI only involves a simple loss:

We integrate the training processes of domain alignment and class alignment to systematically train our CALI model. To be consistent with Eq. (12), we adopt an iterative mechanism that alternates between domain alignment and class alignment. We present the pseudo-code for the training process of CALI and ICALI in Algorithm 4.1.

Note the adversarial training order of $\mathcal{V}_{1}$ in Algorithm 4.1 is $\max_{\psi_{D}}\min_{\phi_{G}}$, instead of the $\min_{\phi_{G}}\max_{\psi_{D}}$, meaning in each training iteration we first train the feature extractor and then the discriminator. The reason for this order is because we empirically find that the feature from $G$ is relatively easy for $D$ to discriminate, hence if we train $D$ first, then the $D$ might become an accurate discriminator in the early stage of training and there will be no adversarial signals for training $G$, thus making the whole training fail. The same order applies to training of the pair of $G$ and $Cs$ with $\mathcal{V}_{2}$.

We design a visual receding horizon planner to achieve feasible visual navigation by combining the learned image segmentation. Specifically, first we compute a library of motion primitives (Howard and Kelly, 2007; Howard et al., 2008) $\mathcal{M}=\left\{\mathbf{p}_{1},\mathbf{p}_{2},\cdots,\mathbf{p}_{n}\right\}$ where each $\mathbf{p}_{*}=\left\{\mathbf{x}_{1},\mathbf{x}_{2},\cdots,\mathbf{x}_{m}\right\}$ is a single primitive. We use $\mathbf{x}_{*}=\begin{bmatrix}x&y&\psi\end{bmatrix}^{T}$ to denote a robot pose. Then we project the motion primitives to the image plane and compute the navigation cost function for each primitive based on the evaluation of collision risk in image space and target progress. Finally, we select the primitive with minimal cost to execute. The trajectory selection problem can be defined as:

where $C_{c}(\mathbf{p})=\sum_{j}^{m}c_{c}^{j}$ and $C_{t}(\mathbf{p})=\sum_{j}^{m}c_{t}^{j}$ are the collision cost and target cost of one primitive $\mathbf{p}$, and $w_{1}$, $w_{2}$ are corresponding weights, respectively.

We evaluate CALI together with several baseline methods on a few challenging domain adaptation scenarios, where several public datasets, e.g., GTA5 (Richter et al., 2016), Cityscapes (Cordts et al., 2016), RUGD (Wigness et al., 2019), RELLIS (Jiang et al., 2020), as well as a small self-collected dataset, named MESH (see the first column of Fig. 9), are investigated. The GTA5 dataset contains 24966 synthesized high-resolution images in the urban environments from a video game and pixel-wise semantic annotations of 33 classes. The Cityscapes dataset consists of 5000 finely annotated images whose label is given for 19 commonly seen categories in urban environments, e.g., road, sidewalk, tree, person, car, etc. The RUGD and RELLIS are two datasets that aim to evaluate segmentation performance in off-road environments. The RUGD and the RELLIS contain 24 and 20 classes with 8000 and 6000 images, respectively. RUGD and RELLIS cover various scenes like trails, creeks, parks, villages, and puddle terrains. Our dataset, MESH, includes features like grass, trees (particularly challenging in winter due to foliage loss and monochromatic colors), mulch, etc. It helps us to further validate the performance of our proposed model for traversability prediction in challenging scenes, particularly the off-road environments.

To be consistent with our theoretical analysis, the implementation of CALI only adopts the necessary indications by Eq. (12). First, Eq. (12) requires that the input of the two upper bounds (one for DA and the other one for CA) should be the same. Second, nothing else but only domain classification and hypotheses discrepancy are involved in Eq. (12) and other related analyses (Eq. (3) - Eq. (10)). Accordingly, we strictly follow the guidance of our theoretical analyses. First, CALI performs DA in the intermediate-feature level ($f$ in Fig. 4), instead of the output-feature level used in Vu et al. (2019). Second, we exclude the multiple additional tricks, e.g., entropy-based and multi-level features based alignment, and class-ratio priors in Vu et al. (2019) and multi-steps training for feature extractor in Saito et al. (2018). We also implement baseline methods without those techniques for a fair comparison. To avoid possible degraded performance brought by a class imbalance in the used datasets, we regroup those rare classes into classes with a higher pixel ratio. For example, we treat the building, wall, and fence as the same class; the person and rider as the same class in the adaptation of GTA5$\rightarrow$Cityscapes. In the adaptation of RUGD$\rightarrow$RELLIS, we treat the tree, bush, and log as the same class, and the rock and rockbed as the same class. Details about remapping can be seen in Fig. 15 and Fig. 16 in Section. 7.2.

We use the PyTorch (Paszke et al., 2019) framework for implementation. Training images from source and target domains are cropped to be half of their original image dimensions. The batch size is set to 1 and the weights of all batch normalization layers are fixed. We use the ResNet-101 (He et al., 2016) pretrained on ImageNet (Deng et al., 2009) as the model $G$ for extracting features. We use the ASPP module in DeepLab-V2 (Chen et al., 2017a) as the structure for $C_{1}$ and $C_{2}$. We use the similar structure in Radford et al. (2015) as the discriminator $D$, which consists of 5 convolution layers with kernel $4\times 4$ and with channel size $\left\{64,128,256,512,1\right\}$ and stride of 2. Each convolution layer is followed by a Leaky-ReLU (Maas et al., 2013) parameterized by 0.2, but only the last convolution layer is follwed by a Sigmoid function. During the training, we use SGD (Bottou, 2010) as the optimizer for $G,C_{1}$ and $C_{2}$ with a momentum of 0.9, and use Adam (Kingma and Ba, 2014) to optimize $D$ with $\beta_{1}=0.9,\beta_{2}=0.99$. We set all SGD optimizers a weight decay of $5\text{e-}4$. The initial learning rates of all SGDs for performing domain alignment are set to $2.5\text{e-}4$ and the one of Adam is set as $1\text{e-}4$. For class alignment, the initial learning rate of SGDs is set to $1\text{e-}3$. All of the learning rates are decayed by a poly learning rate policy, where the initial learning rate is multiplied by $(1-\frac{iter}{max\_iters})^{power}$ with $power=0.9$. All experiments are conducted on a single Nvidia Geforce RTX 2080 Super GPU.

We present comparative experimental results of our proposed model, CALI, compared to different baseline methods – Source-Only (SO) method, Domain-Alignment (DA) (Vu et al., 2019) method, and Class-Alignment
(Saito et al., 2018) method. Specifically, we first perform evaluations on a sim2real UDA in city-like environments, where the source domain is represented by GTA5 while the target domain is the Cityscapes. Then we consider a transfer of real2real in forest environments, where the source domain and target domain are set as RUGD and RELLIS, respectively. All models are trained with full access to the images and labels in the source domain and with only access to the images in the target domain. The labels in target datasets are only used for evaluation purposes. Finally, we further validate our model performance for adapting from RUGD to our self-collected dataset MESH.

To ensure a fair comparison, all the methods use the same feature extractor $G$; both DA and CALI have the same domain discriminator $D$; both CA and CALI have the same two classifiers $C_{1}$ and $C_{2}$. We also use the same optimizers and optimization-related hyperparameters if any is used for models under comparison.

We use the mIoU as the metric to evaluate each class and overall segmentation performance on testing images. IoU is computed as $\frac{n_{tp}}{n_{tp}+n_{fp}+n_{fn}}$, where $n_{tp},n_{tn},n_{fp}$ and $n_{fn}$ are true positive, true negative, false positive and false negative, respectively.

In this section, we aim to discuss our model (CALI) behaviors in more details. Specifically, first we will explain the advantages of CALI over CA from the perspective of training process. Second, we will show the vital influence of mistakenly using the wrong order of adversarial training.

The most important part in CA is the discrepancy between the two classifiers, which is the only training force for the functionality of CA. It has been empirically studied in Saito et al. (2018) that the target prediction accuracy will increase as the target discrepancy is decreasing, hence the discrepancy is also an indicator showing if the training is on the right track. We compare the target discrepancy changes of CALI and our baseline CA in Fig. 10, where the curves for the three UDA scenarios are presented from (a) to (c) and we only show the data before iteration 30k. It can be seen that before around iteration 2k, the target discrepancy of both CALI and CA are drastically decreasing, but thereafter, the discrepancy of CA starts to increase. On the other hand, if we impose a DA constraint over the same CA (iteratively), leading to our proposed CALI, then the target discrepancy will be decreasing as expected. This validates that integrating DA and CA will make the training process of CA more stable, thus improving the target prediction accuracy.

As mentioned in Algorithm 1, we have to use adversarial training order of $\max_{\psi_{D}}\min_{\phi_{G}}$, instead of using $\min_{\phi_{G}}\max_{\psi_{D}}$. The reason for this is related to our designed net structure. Following the guidance of Eq. (12), we use the same input to the two classifiers and the domain discriminator, hence the discriminator has to receive the intermediate-level feature as the input. If we use the order of $\min_{\phi_{G}}\max_{\psi_{D}}$ in CALI, then the outputs of the discriminator will be like Fig. 11, where the domain discriminator of CALI will quickly converge to the optimal state and it can accurately discriminate if the feature is from source or target domain. In this case, the adversarial loss for updating the feature extractor will be near 0, hence the whole training fails, which is validated by changes of the target discrepancy curve, as shown in Fig. 11, where the discrepancy value is decreasing in a small amount in the first few iterations and then quickly increase to a high level that shows the training is divergent and the model is collapsed. This is also verified by the prediction results at (and after) around iteration 1k, as shown in Fig. 12, where the first row is the source images while the second row is the target images.

To further show the effectiveness of our proposed CALI model for real deployments, we build a navigation system by combining the proposed CALI (trained with RUGD $\rightarrow$ MESH set-up) segmentation model with our visual planner. We test behaviors of our navigation system in two different forest environments (MESH$\#1$ in Fig. 13 and MESH$\#2$ in Fig. 14), where our navigation system shows high reliability. In navigation tasks, the image resolution is $[400,300]$, and the inference time for pure segmentation inference is around $33$ frame per second (FPS). However, since a complete perception system requires several post-processing steps, such as navigability definition, noise filtering, Scaled Euclidean Distance Field computation, motion primitive evaluation and so on, the response time for the whole perception pipeline (in python) is around $8$ FPS without any engineering optimization. The inference of segmentation for navigation is performed on an Nvidia Tesla T4 GPU. We set the linear velocity as $0.3m/s$ and control the angular velocity to track the selected motion primitive. The path length is $32.26m$ in Fig. 13 and $28.63m$ in Fig. 14. Although the motion speed is slow in navigation tasks, as a proof of concept and with a very basic motion planner, the system behavior is as expected, and we have validated that the proposed CALI model is able to accomplish the navigation tasks in unstructured environments.

For a hypothesis $h$,

where $\lambda=\epsilon_{s}(h^{*})+\epsilon_{t}(h^{*})$ and $h^{*}$ is the ideal joint hypothesis (see the Definition 2 in Section 4.2 of Ben-David et al. (2010)).

We have the $4^{th}$, and the $8^{th}$ line because of the Lemma 3 (Ben-David et al., 2010); the $5^{th}$ line because of the Theorem 2 (Ben-David et al., 2010); the last second line because of the Lemma 2 (Ben-David et al., 2010). We have the $11^{th}$ line because $\sup|f_{1}-f_{2}|=\sup f_{1}-\inf f_{2}\leq\sup|f_{1}|-\inf f_{2}.~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\blacksquare$

We regroup the original label classes according to the semantic similarities among classes. In GTA5 and City-scapes, we cluster the building, wall and fence as the same category; traffic light, traffic sign and pole as the same group; car, train. bicycle, motorcycle, bus and truck as the same class; and treat the person and rider as the same one. See Fig. 15. Similarly, we also have regroupings for classes in RUGD and RELLIS, as can be seen in Fig. 16.

We acknowledge the supports of NSF with grant number 2006886 as well as ARL with grant number W911NF-20-2-0099. We are also grateful for the computational resources provided by the Amazon AWS Machine Learning Research Award.

Zheng Chen contributed to the algorithm design and the theoretical analysis. The experiment validation was performed by Zheng Chen and Durgakant Pushp. Jason Gregory provided fruitful discussions on the design of ICALI. The manuscript was written by Zheng Chen and all authors commented and revised the manuscript. Lantao Liu contributed to the top design and general guidance of this work. All authors read and approved the final manuscript.

The authors have no relevant financial or non-financial interests to disclose.

This paper does not involve human or animal subjects. No ethical approval is required.

This paper does not involve human subjects to participate in the study.

The paper does not contain any data/figures collected from human participants. No consent is required to publish the manuscript