esa-sceva/satcom-chunk-collection huggingface dataset:
###### Abstract  
Timely detection and treatment of moisture anomalous regions in grain storage facilities is crucial for preventing mold growth, germination, and pest infestation. To locate these regions, this paper presents a novel anomalous moisture region localization algorithm based on the delay-multiply-and-sum (DMAS) beamforming techniques, including the design of an effective spatial arrangement of electromagnetic wave transmitters and receivers, along with comprehensive testing of detectable regions and experimental validation of anomaly localization across varying moisture levels and positions within grain piles. Following initial localization using the proposed algorithm, the study introduces a reliability assessment method for unknown samples based on the signal-to-mean ratio (SMR) value and compares the region of maximum response intensity with that of maximum connected domain volume. The system demonstrated successful localization of a 7 cm \(\times\) 7 cm \(\times\) 7 cm region with 15.4% moisture content within a cubic experimental bin containing 10.5% moisture content long-grained rice, achieving an average recall accuracy exceeding 50%. The proposed method presents rapid detection capabilities and precise localization, showing potential for moisture content evaluation of anomalous regions and practical applications in grain storage monitoring systems.  
Keywords:moisture detection; grain; electromagnetic wave; anomaly localization; delay multiply and sum algorithms +
Footnote †: journal: Applied sciences
# World Ocean Thermocline Weakening and Isothermal Layer Warming
## 4 Results and Discussions
### Trends of (\(H_{\it TTL}\), \(G\)) for Global and Regional Oceans  
The 13 time series pairs [\(<\)\(H_{\it TTL}\)(\(\tau_{i}\))\(>\), \(<\)G(\(\tau_{i}\))\(>\)] show the overall temporal (yearly) variability for the global and individual regional ocean. The significant level to estimate the trend of the time series is set as \(\alpha\) = 0.05. The trends of \(G\) are all negative (i.e., \(\partial G/\partial\tau<0\)) in the global ocean [(\(-2.11\pm 0.31\)) \(\times\) 10\({}^{-3}\)\({}^{\circ}\)C/(m \(\times\) yr)] (Figure 4) as well as in all the 12 regions (Figures 5 and 6). For regional oceans, the maximum weakening rate is [(\(-3.51\pm 0.63\)) \(\times\) 10\({}^{-3}\)\({}^{\circ}\)C/(m \(\times\) yr)], occurring in the equatorial Pacific (10\({}^{\circ}\) S-10\({}^{\circ}\) N). The minimum weakening rate is [(\(-0.378\pm 0.3\)) \(\times\) 10\({}^{-3}\)\({}^{\circ}\)C/(m \(\times\) yr)], appearing in the central South Pacific (10\({}^{\circ}\) S-60\({}^{\circ}\) S, 170\({}^{\circ}\) W-120\({}^{\circ}\) W). The trends of \(H_{\it TTL}\) are positive (i.e., \(\partial H_{\it TTL}\)/\(\partial\tau>0\)) in the global ocean [0.142 \(\pm\) 0.014 W/m\({}^{2}\)] (Figure 4) as well as in the 12 regions (Figures 5 and 6) except the Southern Ocean. The maximum warm rate is (0.160 \(\pm\) 0.028 W/m\({}^{2}\)), occurring in the Indian Ocean. The warm rate in the Equatorial Pacific (10\({}^{\circ}\) S-10\({}^{\circ}\) N) is also high (0.156 \(\pm\) 0.066 W/m\({}^{2}\)).  
Figure 4: Yearly evolutions (1970–2017) of total number of observations (upper panel), relative heat content (unit: 10\({}^{8}\) J/m\({}^{2}\)) (middle panel), and thermocline gradient (unit: \({}^{\circ}\)C/m) (lower panel) for the world oceans excluding the Arctic Ocean. Note that the positive real number in the parentheses mean the half size of the confidence interval with the confidence level \(\alpha\) = 0.05.  
The robust weakening trend of the thermocline gradient (\(\partial G\)/\(\partial\tau\) \(<\) 0) and the warming trend of the isothermal layer (\(\partial H_{HTL}\)/\(\partial\tau\) \(>\) 0) are found in global and regional oceans except the Southern Ocean, where slightly decreasing in the relative heat content (\(-\)0.0272 W m\({}^{-2}\)). The data are very sparse in the Southern Ocean with a total number of observations of 7942 (Figures 3 and 5f, and Table 4) and make the trends in the Southern Ocean not robust. The highest warming rate (0.160 \(\pm\) 0.028 W m\({}^{-2}\)) of \(H_{HTL}\) in the Indian Ocean (Table 4) is coherent with the recent results on the fastest rate of warming in the tropical Indian Ocean among tropical oceans [27].  
Figure 5: Same as Figure 4 except for the (**a**) North Atlantic Ocean (10\({}^{\circ}\) N–60\({}^{\circ}\) N), (**b**) equatorial Atlantic Ocean (10\({}^{\circ}\) S–10\({}^{\circ}\) N), (**c**) South Atlantic (10\({}^{\circ}\) S–60\({}^{\circ}\) S), (**d**) Indian Ocean (north of 60\({}^{\circ}\) S), (**e**) Equatorial Pacific (10\({}^{\circ}\) S–10\({}^{\circ}\) N), and (**f**) Southern Ocean (south of 60\({}^{\circ}\) S).
# Nematic Liquid Crystal Composite Materials for DC and RF Switching
## 8 Conclusions  
According to the reported works in this article, a small percent of NP doping changes the LC composite's intrinsic conductivity significantly. In addition to that, 2-4 orders of magnitude of electric field-induced conductivity switching is demonstrated by several groups. We reviewed the field-induced electrical switching behavior and related issues for LC-NP composites (focusing on LC-CNT composites) which are important in device perspectives. By comparing several technological aspects, we found that the 5 CB/CNT system could be a good choice in terms of DC and RF switching application. This composite shows more than three orders of magnitude switching near room temperature (both in the nematic and isotropic phase). The synthesis and processing of LC materials is well-established and, thus, makes it an attractive option for switching applications. In addition, optoelectronic devices and switches made from LC materials consume less power than comparable opto-mechanical technologies. Also, our simulations and analyses suggest that RF switching with an acceptable performance is possible. Based on this, LC switching appears to be an excellent, low-cost option for DC, as well as RF switching applications.  
[PERSON] conducted the literature search and simulations and wrote the first manuscript draft. [PERSON] reviewed and edited the manuscript, obtained the permissions for the published data/figures, and drew the schematic diagrams. [PERSON] proposed and refined the original idea and reviewed the manuscript.  
This research received no external funding.  
We would like to thank [PERSON], [PERSON], and [PERSON] for reviewing the final manuscript.  
The authors declare no conflict of interest.
# Stable Analysis of Compressive Principal Component Pursuit
## 4 Proof of Theorem 1  
In this section, we will provide the proof of Theorem 1. Our main proof is based on two elementary and important properties of \(\hat{x}\), which is the solution of Problem (2). First, note that \(x_{0}\) is also a feasible solution to Problem (2) and \(\hat{x}\) is the optimum solution; therefore, we can obtain \(\|\hat{x}\|_{\diamond}\leq\|x_{0}\|_{\diamond}\). Second, according to triangle inequality, we can obtain  
\[\|\hat{x}-x_{0}\|_{2} = \|\hat{x}-M-(x_{0}-M)\|_{2} \tag{6}\] \[\leq \|\hat{x}-M\|_{2}+\|x_{0}-M\|_{2}\] \[\leq 2\delta\,.\]  
Let \(\hat{x}=x_{0}+h\), where \(h=[H_{i}]\). According to the definition of subspace of \(\gamma\), we denote \(h^{\gamma}:=\mathcal{P}_{\gamma}(h)\), \(h^{\gamma^{\perp}}:=\mathcal{P}_{\gamma^{\perp}}(h)\) for short. Our main aim is to bound \(\|h\|_{2}=\|\hat{x}-x_{0}\|_{2}\), which can be rewritten as  
\[\|h\|_{2}^{2} = \|h^{\gamma}\|_{2}^{2}+\|h^{\gamma^{\perp}}\|_{2}^{2}\] \[= \|h^{\gamma}\|_{2}^{2}+\|\mathcal{P}_{T_{1}}\times\cdots\times \mathcal{P}_{T_{\tau}}h^{\gamma^{\perp}}\|_{2}^{2}\] \[+\|\mathcal{P}_{T_{1}^{\perp}}\times\cdots\times\mathcal{P}_{T_{ \tau}^{\perp}}h^{\gamma^{\perp}}\|_{2}^{2}\,.\]  
Combining with (4), we have  
\[\|h^{\gamma}\|_{2}^{2}=\sum_{i}\|\frac{\sum_{j=1}^{\tau}H_{j}}{\tau}\|_{2}^{2 }\leq\frac{4\delta^{2}}{\tau}\]  
Therefore, it is necessary to bound the other two terms on the right-hand-side of (5). We will bound the second and third terms, respectively.  
Norm equivalence theorem tells us that _every two norms on a finite dimensional normed space are equivalent_, which implies that there exists two constants \(C(n,\tau)\geq c(n,\tau)>0\) satisfying  
\[c(n,\tau)\|x\|_{2}\leq\|x\|_{\diamond}\leq C(n,\tau)\|x\|_{2}\,. \tag{8}\]
# Optical Channel Selection Avoiding DIPP in DSB-RFoF Fronthaul Interface
## 6 Conclusions and Future Work  
The proposed new analog interface, with the acronym Option 10, could apply to next-generation wireless systems. The condition for introducing this solution is the development of optical Xhaul networks working in the flexible grid DWDM format. Optical nodal devices must be transparent due to the possibility of carrying RFoF signals. The A-RoF technique is more spectrally effective than D-RoF solutions and allows the use of simple AAU/RRH devices. However, the transmission of analog signals over optical fibers causes many problems. The attenuation of silica fibers is very low, but they have dispersion that must be taken into account. The paper presents a method of using the optical path to transport the DSB-RFoF radio signal in which no chromatic dispersion compensation is used. However, it is indisputable that static or dynamic compensation of chromatic dispersion is an unrivaled but costly solution. Chromatic dispersion pre-compensation can improve the total dispersion balance, which will allow the transport of RFoF signals with a higher radio carrier frequency, also exceeding 84 GHz. This may be particularly important when the fiber-optic access path lengths are long in relation to the links between the Xhaul nodes. The access fibers are usually of the G.652D or G.657A standard, which in the DWDM system operating band, introduces a high chromatic dispersion coefficient (examples of variants are given in Table 3 and Figure 5). SSB transmission can also be used, which, however, is associated with the need to use tunable filters or dedicated single-sideband modulation systems. The proposed method of selection of an optical channel based on the flexible DWDM grid for transporting RF radio signals between the DU and RU/RRH, over a dispersive optical fiber, may be a good complement to the existing techniques. This can be especially useful when we need to mass-produce transceivers for optical fronthaul communications.  
The calculations and simulations were carried out on the assumption that only one modulated RF signal is transported in the selected optical channel. In practice, in an optical Xhaul link working in the flexible DWDM format, there may be more optical channels located close to each other. There may be a high power density in the core of the optical fiber. In such a case, one should take into account the possibility of the above-mentioned non-linear distortions causing the interaction of signals located in adjacent optical channels. This is one of the issues that will be discussed in further research. In the case of multi-channel, also we need to pay attention to the guard spacing between channels. This will entail the need to disable OFDM subcarriers as required by the system requirements of the 3 GPP recommendation. In this paper, this element was omitted in order to simplify the structure of the CP-OFDM signal.  
This research received no external funding.  
Not applicable.  
All data are included within manuscript.  
The author declares no conflict of interest.
## 3 Structural Monitoring via Global Navigation Satellite System: The Case of High Wind Turbines
### The Role of Accuracy of Measurement  
As regards the accuracy of the data provided by the GNNS system, sensitivity analyses were also performed for values from 1 to 20 mm (the maximum value among those for devices in Table 2) of accuracy (that is \(a\) = 1, 5, 10, 15, 20 mm). This analysis was carried out by simulating the various measurement accuracies in MATLAB. This was done by requiring that the input displacement values for the control algorithm were rounded to the nearest multiple of \(a\). With the same approach as was used for the two previous sensitivity analyses, a value of frequency equal to 1000 Hz and a null latency (best case) have been assumed for the above simulations. It has been found that the structural response is not strongly influenced by the accuracy of the data provided by the GNNS system for all wind cases considered (no percentage change exceeds 1%). However, such a result may depend on the specific control logic, case-study turbine and type of wind load. Therefore, this aspect could deserve further study with different boundary conditions.
# An Accurate Direction Finding Scheme Using Virtual Antenna Array via Smartphones
## 5 Performance Evaluation
### Indoor Environments with Single High Frequency Acoustic Waves  
First, we deploy only one acoustic source in the indoor environment. Then, we obtain the anchor point's direction by horizontally and steadily moving the phone in front of our body (VULA) or holding the phone still and rotating our body for \(360^{\circ}\) (VUCA), and reading the results of direction finding from the phone.
## 3 Control Strategies  
Considering the stability and precision of the teleoperation system, we integrate some control strategies into the system's control mode. As shown in Figure 2, the operator gives a command to the haptic device to obtain an actual trajectory \(S_{m1}\), and \(S_{m}\) is a filtered trajectory. After receiving the operation signal, the robot follows the haptic device and generates a trajectory \(S_{s}\). \(S_{e}\) is the position error of \(S_{m}\) and \(S_{s}\). \(J_{m}^{+}\) and \(J_{s}^{+}\) are the pseudo-inverse of the Jacobian of the master device and the slave device, respectively. \(q_{md}\), \(q_{m}\) are the master desired joint velocity, the master joint angle. \(q_{sd}\), \(q_{s}\) are the slave desired joint velocity and the slave joint angle. \(\tau_{m}\), \(\tau_{s}\) and \(\tau_{o}\) are the master torque and the slave torque generated by the PD controller, and the torque generated by the operator.
## 3 Results
### Model Verification Example
#### 3.1.2 Using the Algorithm for Model Verification
\begin{table}
\begin{tabular}{c c c} \hline
**Phase** & **Step** & **Result/Comment** \\ \hline \(1\) & \(S_{r}=S_{r}\cup\{((d-1,s,m_{s},i_{s}))\}\) & \(S_{r}=\left\{\left(\begin{array}{c}0,\\ \{(0,0),(1,1),(2,2),(3,3),(4,4),(5,5)\},\\ ((1,0),(2,0))\end{array}\right)\right\}\) \\ \hline \(1\) & \(Phase3(...)\) \\ \hline \(3\) & \(n_{w},t_{f},m_{r},m_{full},n_{x},(A_{d},n_{d}),W_{c}=\\ First_{M}(W_{c})\) & \(n_{w}=0\) \\ & \(t_{f}=f_{1}\) \\ & \(m_{r}=\{(0,0),(1,1),(2,2),(3,3)\}\) \\ & \(m_{full}=\{(0,0),(1,1),(2,2),(3,3),(4,4),(5,5)\}\) \\ & \(n_{x}=6\) \\ & \(A_{d}=\{1\}\) \\ & \(n_{d}=1\) \\ & \(W_{c}=W_{c}\setminus\{e_{1}\}=\{e_{2}\}\) \\ \hline \(3\) & \(i_{n}=Objects_{U}(i_{c},(A_{d},n_{d}))\) & \(i_{n}=((1,1),(2,0))\) \\ \hline \(3\) & \(A_{f}=Objects_{F}(i_{n},d)\) & \(A_{f}=\emptyset\) \\ \hline \(3\) & \(t_{tra}=Corr_{Tra}(t_{f})\) & \(t_{tra}=\text{first row of Table \ref{table}}\) \\ \hline \(3\) & \(i_{c}=i_{n}\) & \(i_{c}=(1,1),(2,0)\) \\ \hline \(3\) & \(r=Corr_{R}(t_{tra})\) & \(r=\text{reaction rule \emph{mov1}}\) \\ \hline \(3\) & \(result=Phase(s_{c},m_{c},r,s_{0},m_{0},n_{x})\) & Phase 4 completed without error \\ \hline \(3\) & \(s_{c},m_{c},n_{x}=result\) & \(s_{c}=\)\(\bigcup\limits_{(a)}\bigcup\limits_{(a)}\bigcup\limits_{(a)}\bigcup\limits_{(a)}\) \\ & & \(m_{c}=\{(0,0),(1,1),(2,3),(3,2),(4,4),(5,5)\}\) \\ & & (\(m_{c}\) is calculated in the same way as \(m_{full}^{\prime}\) in Phase 2) \\ & & \(n_{x}=6\) \\ \hline \(3\) & \(n_{w},t_{f},m_{r},m_{full},n_{x},(A_{d},n_{d}),W_{c}=\\ First_{M}(W_{c})\) & \(n_{w}=1\) \\ & & \(t_{f}=f_{2}\) \\ & & \(m_{r}=\{(2,0),(3,1),(4,2),(5,3)\}\) \\ & & \(m_{full}=\{(0,0),(1,1),(2,3),(3,2),(4,4),(5,5)\}\) \\ & & \(n_{x}=6\) \\ & & \(A_{d}=\{2\}\) \\ & & \(n_{d}=1\) \\ & & \(W_{c}=W_{c}\setminus\{e_{2}\}=\emptyset\) \\ \hline \(3\) & \(i_{n}=Objects_{U}(i_{c},(A_{d},n_{d}))\) & \(i_{n}=((1,1),(2,1))\) \\ \hline \(3\) & \(A_{f}=Objects_{F}(i_{n},d)\) & \(A_{f}=\emptyset\) \\ \hline \(3\) & \(t_{tra}=Corr_{Tra}(t_{f})\) & \(t_{tra}=\text{second row of Table \ref{table}}\) \\ \hline \(3\) & \(i_{c}=i_{n}\) & \(i_{c}=((1,1),(2,1))\) \\ \hline \(3\) & \(r=Corr_{R}(t_{tra})\) & \(r=\text{reaction rule \emph{mov2}}\) \\ \hline \(4\) & \(r_{l}=Corr_{Rad}(r)\) & \(r_{l}=\)\(\bigcup\limits_{(a)}\bigcup\limits_{(a)}\bigcup\limits_{(a)}\) \\ \hline \(4\) & \(c_{1}=IsUpdatePossible(s_{0},m_{0},r_{l},m_{r})\) & \(c_{1}=false\) \\ \hline \end{tabular}
\end{table} 
Table 16: Subsequent steps of the algorithm in the model validation example.
# A Novel Deep Learning Method for Predicting RNA-Protein Binding Sites
## 3 Results
### Prediction Results for the Debiased Datasets  
To evaluate the effectiveness of the proposed debiasing method, both the context-average debiasing method and the RPI-Net random debiasing method were evaluated in this experiment. HPNet-r uses the random debiasing method, while HPNet-m uses the context-average debiasing method. The experimental results are shown in Table 3; the mean AUC for RPI-Net was 0.927, the mean AUC for HPNet-r was 0.930, and the mean AUC for HPNet-m was 0.933. HPNet-r performed better than RPI-Net, and HPNet-m performed better than HPNet-r. Although RPI-Net automatically extracts features from secondary structures and sequences through a GCN and LSTM and has improved prediction accuracy, it ignores the hierarchical features of secondary structures, resulting in a slightly lower accuracy than HPNet-r and HPNet-m.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Mean AUC** \\ \hline RPI-Net & 0.927 \\ HPNet-r & 0.930 \\ HPNet-m & 0.933 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean AUCs of three debiasing methods.  
Figure 5: The accuracy and loss training processes for SFRS1, HNRNRNC, TIA1, IGF2 BP1-3, PUM2, and QKI.  
Figure 6 shows the performance results for the three methods with debiased data. It can be observed that the performance of HPNet-r was better than that of RPI-Net with some proteins, with the most significant improvement observed with the protein ZC3H7B at 7.5%. The box diagram in Figure 7 demonstrates that the median for HPNet-r was smaller than for RPI-Net, but the range for HPNet-r was smaller than for RPI-Net, indicating that HPNet had better stability. The median and average values for HPNet-m were more significant than those for HPNet-r, confirming the effectiveness of the context-average debiasing method proposed in this research. It can be seen from Figure 8 that when the data were debiased, the AUCs of most proteins decreased. The AUCs of several proteins, such as ALKBH5, CAPRIN1, and MOV10, decreased significantly. The reduced performance of ALKBH5 can be attributed to the small dataset, while the deviations in the dataset for CAPRIN1 and MOV10, which were obtained in the PAR-CLIP experiment, were relatively large.
## 3 Inferential Statistics Results
For example, in P1 alcohol increases significantly the Euphoria (ES), where the pre-scores (Table 1) (BL, M = 3.84, SD = 1.068) were lower than the post-scores (M = 13.63, SD = 6.457) t(32) = \(-6.886\), \(p<0.001\), CI95% (\(-2.252\), \(-0.889\)), \(\beta=1.000\), while regarding caffeine, the pre-scores were also lower than the post-scores (M = 10.16, SD = 5.069) t(32) = \(-5.712\), \(p<0.001\), CI95% (\(-1.919\), \(-0.682\)), \(\beta=1.000\), but, as we can see with CI 95%, there is no significant difference between both conditions when we compare the effects of caffeine and alcohol. As for SFS, we applied a Friedman test, as mentioned above. For P1, the result is significant (\(\chi^{2}=7.01\), \(p<0.05\)), as it is the case for P2 (\(\chi^{2}=7.01\), \(p<0.05\)). But the Wilcoxon paired samples test only shows significant results for the effect of alcohol on BL in P1 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Factors** & **Sig. Mauchy’s W** & **F** & **Sig.** & **Partial Eta Squared** & **Observed Power** \\ \hline Participant 1 & EUPHORIA & 0.420 & 27.771 & \textless{}0.001 & 0.607 & 1.000 \\ \hline Participant 2 & EUPHORIA & 0.480 & 19.908 & \textless{}0.001 & 0.525 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Two-Way repeated measures ANOVA of ES for two participants. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **MD** & **ST** & **t** & \(p\) & **d 95\% (CD)** & \(\beta\) \\ \hline P1 & BL & ALCOHOL & \(-9.789\) & 1.442 & \(-6.886\) & \(<\)0.001 & \(-1.580\) (\(-2.252\), \(-0.889\)) & 1.000 \\ EUPHORIA & BL & COFFE & \(-6.316\) & 1.106 & \(-5.712\) & \(<\)0.001 & \(-1.310\) (\(-1.919\), \(-0.682\)) & 1.000 \\  & ALCOHOL & COFFE & 3.474 & 1.442 & 2.410 & 0.013 & 0.553 (0.062, 1.030) & 0.626 \\ \hline P2 & BL & ALCOHOL & \(-1.842\) & 0.574 & \(-3.221\) & 0.002 & \(-0.737\) (\(-1.238\), \(-0.220\)) & 0.859 \\ EUPHORIA & BL & COFFE & \(-3.895\) & 0.567 & \(-6.874\) & \(<\)0.001 & \(-1.577\) (\(-2.248\), \(-0.887\)) & 1.000 \\  & ALCOHOL & COFFE & \(-2.053\) & 0.703 & \(-2.920\) & 0.005 & \(-0.670\) (\(-1.162\), \(-0.163\)) & 0.789 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pairwise comparisons and \(t\)-test of EUPHORIA measures. (Z = \(-\)2949, \(p\) < 0.05), and for the effect of caffeine on BL in P2 (Z = \(-\)2.941, \(p\) < 0.05). Thus, the results from the ES and SFS are similar for both participants.
# Automatic Measurement of Inclination Angle of Utility Poles Using 2D Image and 3D Point Cloud
## 2 The Proposed Method
### Pole Mask and Depth Map Fusion
#### 2.3.2 3D Reconstruction of Utility Poles  
The transformation of the world coordinate system, camera coordinate system, image coordinate system, and pixel coordinate system will be involved in the generation of the pole. In Figure 9, \(P_{w}\) is a point in space, which is represented by \((X_{Pw}\), \(Y_{Pw}\), \(Z_{Pw})\) in the world coordinate system and \((X_{PC}\), \(Y_{PC}\), \(Z_{PC})\) in the camera coordinate system. The point \(P_{w}\) on the imaging plane is denoted by \(p\), which is represented as \((x,y)\) in the image coordinate system and \((u,v)\) in the pixel coordinate system.  
Figure 8: Mask random transformation results.  
Figure 9: Coordinate system transformation.  
The spatial point \(P_{w}\) (\(X_{Pw}\), \(Y_{Pw}\), \(Z_{Pw}\)) in the world coordinate system can be transformed into the imaging point \(p\) (\(u\), \(v\)) in the pixel coordinate by the transformation matrix, as shown in Equation (7).  
\[Z_{PC}\begin{bmatrix}u\\ v\\ 1\end{bmatrix}=\begin{bmatrix}\frac{1}{dx}\ 0\ u_{0}\\ 0\ \frac{1}{dy}\ v_{0}\\ 0\ 0\ 1\end{bmatrix}\begin{bmatrix}f\ 0\ 0\ 0\\ 0\ f\ 0\ 0\\ 0\ 0\ 1\end{bmatrix}\begin{bmatrix}R\ t\\ 0^{T}\ 1\end{bmatrix}\begin{bmatrix}X_{Pw}\\ Y_{Pw}\\ Z_{Pw}\\ 1\end{bmatrix} \tag{7}\]  
where, \(dx\) and \(dy\) represent the actual physical size of a single pixel along the \(x\)-axis and \(y\)-axis, \((u_{0},v_{0})\) is the coordinate value of the camera coordinate system origin \(o\) in the pixel coordinate system, \(f\) represents the camera focal length, and \(R\) and \(t\) represent the rotation matrix and offset vector converted from the world coordinate system to the camera coordinate system, respectively.  
Similarly, combined with the depth information provided by the depth map, the pixel points provided by the pole mask can be transformed into the spatial points in the world coordinate system by using the transformation matrix, and the frustum point cloud containing the poles and interference points can be obtained. Figure 10 illustrates the transformation results.