esa-sceva/satcom-chunk-collection huggingface dataset:
# Human Activity Recognition Using CSI Information with Nexmon
## 6 CSI Data Collection  
For the CSI data collection, it is necessary to enable monitoring mode on the receiver using Nexmon patched firmware and using the nexutil utility tuning the NIC on the same  
Figure 3: Human activities and effect on Wi-Fi signals propagation.  
channel and frequency band as the used router and transmitter. The detailed guide is available on the Nexmon GitHub repository [[https://github.com/seemoo-lab/nexmon](https://github.com/seemoo-lab/nexmon)]([https://github.com/seemoo-lab/nexmon](https://github.com/seemoo-lab/nexmon)) or [[https://github.com/seemoo-lab/nexmon_csi](https://github.com/seemoo-lab/nexmon_csi)]([https://github.com/seemoo-lab/nexmon_csi](https://github.com/seemoo-lab/nexmon_csi)) [7] for the CSI data collection.  
In another experiment with Asus RT-AC86U, the experimental setup was similar, where Intel NUC was used as TX without patching and Asus RT-AC86U as RX in monitoring mode on 80 MHz with patched Nexmon firmware.  
For each activity, the Raspberry Pi 3B+ without patching any firmware was used to create some network traffic with UDP packets. Another Raspberry Pi 3B+, Pi 4B was configured at 40 MHz at channel 36 (the European region selected for the geographical area) in monitoring mode with patched firmware. A Fritzbox dual-band router was used as a Wi-Fi network bridge at channel 36 with 40 MHz bandwidth with a spectrum of 5 GHz frequency band. There was no patching of the firmware done on the Fritzbox router. It acts as the Wi-Fi media between transmitter Pi and receiver Pi.  
After enabling the monitor mode, whenever there was traffic on the network, the CSI data could be captured using the user datagram protocol (UDP) packets with the sender address as 10.10.10.10 and broadcasted packets to the destination address 255.255.255.255. Using the tcpdump tool or Wireshark, the CSI data packets were dumped into the.pcap files for later analysis.  
All data generated in the experiments and used in this work is available online ([[https://dx.doi.org/10.21227/xr6j-0255](https://dx.doi.org/10.21227/xr6j-0255)]([https://dx.doi.org/10.21227/xr6j-0255](https://dx.doi.org/10.21227/xr6j-0255))) see remark in \"Sample Availability\" below.
# ISAC towards 6G Satellite-Terrestrial Communications: Principles, Status, and Prospects
## 2 The Development Status and Key Technology Of ISAC
### Prototypes Studies
#### 2.3.1 Prototype Based on the Sub-6 GHzFrequency Band  
In [31], an ISAC system based on OFDM was developed. The system operates at a central frequency of 4 GHz with a bandwidth of 400 MHz. This system enables indoor target localization and tracking. The sensing signal processing includes basic processing, interference suppression, and system calibration. Considering the prototype's signal bandwidth and constrained by the coherent processing interval, algorithm optimization is proposed to enhance the resolution performance of the system.
# Future Perspectives for Gamma-ray Burst Detection from Space
## 3 eXTP  
### Mission Overview  
The enhanced X-ray Timing and Polarimetry mission ([[https://www.isdc.unige.ch/](https://www.isdc.unige.ch/)]([https://www.isdc.unige.ch/](https://www.isdc.unige.ch/)) extp/) (eXTP) is designed to study mainly the state of matter under extreme conditions of density, gravity, and magnetic field [21]. The core science objectives of the mission are focused on the determination of the equation of state of matter at supra-nuclear density and the study of the dynamics of accretion/ejection flows under the influence of strong gravitational fields. Thanks to an extensive suite of innovative instruments, the eXTP is designed also to be a general observatory for astrophysics, providing broad capabilities in the X-ray domain (0.5-50 keV) to conduct timing, spectral, and polarimetric observations of a wide variety of galactic and extra-galactic sources. Although the mission is not focusing on GRB science, the availability of a large FoV and sensitive instrument, the WFM (see below), makes the eXTP an important contributor to the possible detection and study of these events in the future.  
The eXTP is planned to be the next flagship-class mission led by China, and it is currently in an advanced design phase, where virtually all payload elements have reached a relatively mature technology and could be ready for implementation (see Figure 3). The mission is being studied by a large collaboration including a wide scientific community in China and many European member states. At present, a launch of opportunity has still to be identified, and the programmatics are being cleared in order to possibly bring the eXTP into space in 2028-2029.  
Figure 2: Representative grasp (effective area times FoV) of the WXT as a function of photon energy (black). As a comparison, the grasp parameters of several X-ray-focusing telescopes are overplotted. Adapted from Figure 10 in [20].
# Laser Absorption Sensing Systems: Challenges, Modeling, and Design Optimization
## 1 Introduction  
### Overview of Laser Absorption Sensor Developments and Applications  
Laser absorption spectroscopy (LAS) has served as a useful tool for both fundamental and practical studies in energy and power systems since its earliest demonstration as a species diagnostic method in combustion-related environments over forty years ago [1; 2]. In addition to the non-contact characteristics of most optically based methods (e.g., emission, Schlieren imaging, laser-induced fluorescence, particle image velocimetry), LAS benefits from the species-specific nature of molecular spectroscopy, therefore is capable of achieving highly quantitative and selective measurements of a number of important species parameters including gas composition, temperature, pressure, and velocity. The use of narrow-linewidth, tunable, low-power semiconductor lasers, on the other hand, offers the opportunity for real-time, time-resolved, and long-term stable field monitoring systems that can be realized under various measurement scenarios.  
Up towards the early 2000s, gas sensors based on tunable diode laser absorption spectroscopy (TDLAS) were extensively applied in continuous emission monitoring and process controls and diffused in process industries as an accepted technique [3; 4]. The maturity and commercializationof opto-electronic devices, thanks to the booming telecommunication industry, has allowed TDLAS sensors to evolve from laboratory-scale benchtop experimental tools to a robust industrial technology. With further reduction in cost and size, portable and field-deployable systems can be made. Using smart optical-mechanical designs and sophisticated signal processing schemes, some of these sensors are able to operate in the field without operator intervention for over 10 years [5].  
Today, the design, control, and optimization of complex energy and propulsion systems poses unprecedented challenges for sensor technology. The extreme conditions associated with combustion that are typically unfriendly for optical systems, such as high temperature, pressure, and velocity, mechanical vibrations, high dust levels, and corrosiveness, make LAS still one of the best available contactless sensor techniques for harsh environments. However, extraction and interpretation of high-quality, quantitative information under such complicated, demanding conditions requires deeper understanding of the target environments and tailoring the sensor design to specific measurement goals. While state-of-the-art laser technology for novel single-mode mid-infrared and hyperspectral laser sources continues to offer much more freedom in choosing the spectral features and designing LAS sensors, much remains to be studied in improving their reliability, accuracy, and precision.
# Analysis and Evaluation of Performance Gains and Tradeoffs for Massive MIMO Systems
## Appendix A Derivation of Multiplexing Gain under Imperfect Channel Estimation  
The multiplexing gain under imperfect channel estimation is given by  
\[G_{MUX}^{imperf.CSI}=\frac{d}{d\log_{2}p_{d}}\sum\limits_{k=1}^{K}E\left( \left(\frac{T_{coh}-\tau_{p}}{T_{coh}}\right)\log_{2}\left(1+\frac{Mf_{MRT}p_{p }p_{d\ell k}\beta_{\ell k\ell}^{2}}{Mf_{MRT}p_{p}\sum\limits_{j\
eq\ell}^{L} p_{djk}\beta_{jk\ell}^{2}+\sigma_{n}^{2}}\right)\right), \tag{10}\]  
Then, under favorable condition and \(M{\rightarrow}\infty\) with (19) and (20), we have  
\[G_{MUX}^{imperf.CSI}=\frac{d}{d\log_{2}p_{d}}\sum\limits_{k=1}^{K}E\left( \left(1-\frac{\tau}{T_{coh}}\right)\log_{2}\left(1+\frac{p_{d\ell k}\beta_{ \ell k\ell}^{2}}{\sum\limits_{j\
eq\ell}^{L}p_{djk}\beta_{jk\ell}^{2}}\right) \right), \tag{11}\]  
After doing the required derivative for (11) and make some simplification, so we have  
\[G_{MUX}^{imperf.CSI}=\left(1-\frac{\tau}{T_{coh}}\right)\sum\limits_{k=1}^{K }\frac{\left(p_{djk}\beta_{\ell k\ell}^{2}-p_{d\ell k}\beta_{\ell k\ell}^{2} \right)}{\left(\left(\sum\limits_{j\
eq\ell}^{L}p_{djk}\beta_{jk\ell}^{2} \right)+p_{d\ell k}\beta_{\ell k\ell}^{2}\right)\sum\limits_{j\
eq\ell}^{L}p_ {djk}}, \tag{12}\]  
with \(D_{jL}=diag\left\{\beta_{jL},\beta_{jL},...,\beta_{jKL}\right\}\) and \(P_{jL}=diag\left\{p_{jL},p_{j2L},...,p_{jKL}\right\}\) substituting \(\sum\limits_{k=1}^{K}\beta_{jKL}=tr(D_{jL})\) and \(\sum\limits_{k=1}^{K}p_{jKL}=tr(P_{jL})\) in the above expression, then we obtain  
\[G_{MUX}^{imperf.CSI}=\left(1-\frac{\tau}{T_{coh}}\right)\frac{tr(D_{\ell\ell} ^{2})\left[tr(p_{dj})-tr(p_{d\ell})\right]}{\sum\limits_{j\
eq\ell}^{L}\left[ tr(p_{dj}D_{j\ell})^{2}+tr(p_{d\ell}D_{\ell\ell}^{2})tr(p_{dj})\right]}, \tag{13}\]
## 3 Results and Discussion  
### Volatile Composition of Single-Dose Espresso Coffee-Based Blends  
Figure 1a presents a 3D GC \(\times\) GC-ToFMS chromatogram plot obtained in full scan acquisition mode of an espresso coffee brew from Blend 6 in which several hundred compounds were observed. Figure 1b shows an extracted ion chromatogram of diagnostic ions for varietal compounds (_m/z_ 93, 161, and 204), as the terpenic ones, which allowed a rapid identification of a particular type of volatiles. This highlights the importance of using a highly sensitive and high throughput technique to overcome the complexity of coffee samples, detecting both the major compounds as well as the ones present in trace amounts, namely those relevant to distinguishing among coffees with different geographical origins [19]. Figure 1: Blowup of a GC \(\times\) GC-ToFMS surface plot obtained in (**a**) full-scan and (**b**) extracted ion (_m/z_ 93, 161, and 204) acquisition modes for espresso coffee brew from Blend 6. To determine the volatile profile of single-dose espresso capsule coffee-based blends, a range of eight commercial samples was studied by HS-SPME/GC \(\times\) GC-ToFMS, differing in the labeled blend intensity (Blends 1 to 3, intensity 1 \(<\) 2 \(<\) 3) and origins (Blend 4, Jamaica, Blend 5, Tanzania, and Blend 6, Ethiopia), a decaffeinated blend (Blend Dec), and a blend supplemented (Blend Sup) with natural plant extracts of guarana (_Paullinia cupana_) and ginseng (_Panax ginseng_). A total of 390 volatile compounds (ranging from 381 to 386 in coffee powders and 380 to 387 in espresso brews), distributed over 17 chemical families, including acids (4), alcohols (12), aldehydes (26), esters (40), furan compounds (63), hydrocarbons (25), ketones (60), volatile phenols (5), oxazoles (9), pyrazines (36), pyridines (9), pyrroles (11), sulfur compounds (12), terpenic compounds (29), norisoprenoids (6), thiazoles (19), and thiophene compounds (24), was determined in the assayed single-dose coffee capsule blends (Table 1, chromatograms in Figure S1 and chromatographic details in Table S1). These chemical families were already reported in different coffee samples [5; 6; 9; 21] commonly associated with industrial coffee production during fermentation (acids, alcohols, aldehydes, and esters) and roasting processes (furan compounds, ketones, pyrazines, pyridines, and pyrroles), as well as plant varietal compounds, thus they were already present in the green coffee beans (terpenic compounds and norisoprenoids) [19; 20; 21].
## 6 Numerical Analysis
### Residual Mid-Span Displacement  
One of the main goals of implementing SMA wires in LRBs is to reduce the residual displacement of the deck after strong earthquakes and decrease the repairing cost. Residual displacement is the lateral displacement that remains in the deck at the end of the earthquake. This value can be extracted from the displacement history curve of each point of the bridge's deck. Here, the mid-span residual displacement is calculated, which also represents the residual displacement at the place of the mid-pier isolators. The mid-span residual displacement under all ground motion records, for the LRB isolated and the three SMA-LRB isolated bridges, is calculated and illustrated in Table 7. Besides, the reduction ratios of the residual displacement of the SMA-LRBs with respect to the LRBs are shown. The most significant reductions are under synthetic records number 3 of the RSN 8606 and RSN 8  
Due to the self-centering capability of the SMA wires, the residual displacement of the benchmark bridge equipped with SMA-LRBs is much smaller than that of the bridge with LRBs. Furthermore, amongst the three wires' arrangements, the optimized double-cross is the most successful device in reducing the residual displacement, from 52.16% to 98.67% under various records. This range for the straight arrangement is between 51.55% and 93.25%, and for the cross wires is from 42.51% to 82.17%. Figure 18 graphically compares the mid-span residual displacement for different isolators.
## 5 Experimental Tests
### The HIL Experimental Setup and Description  
The component parts of the rotational speed system, mainly including a propeller, a DC motor with an ESC (\(D\)U\(\Lambda\)LSKY(r) XM6355 DA and XC9036 HV, Shanghai, China), a subminiature encoder with resolution of 20 (JL25, Changchun Institute of Optics, Changchun, Jilin, China), and a digital signal processor (DSP)-based hardware platform with an optional high resolution external timer module, are shown in Figure 4. The software of the nonlinear adaptive control system runs on the hardware platform that can provide reliable support for high precision timer and synchronization operations. The subminiature high resolution incremental encoder is mounted on the end of the main drive shaft to measure the actual rotational speed of the propeller. The command signal generator, including a MAV mathematical model and an autopilot, is normally used to generate the command signal used as input to the rotational speed system according to the flight missions. The schematic diagram of the experimental setup is shown in Figure 4, but to be safe, the MAV is fixed to a post.  
Figure 3: The nonlinear adaptive control diagram.  
Considering that the propeller only rotates in a fixed direction, namely a clockwise direction or a counter-clockwise direction, the actual rotational speed of the propeller can be determined by scanning the interval time between two neighboring A-phase or B-phase pulses from the incremental encoder, which is implemented based on the high resolution external timer module on the hardware platform.  
The predefined parameters are described as follows:  
1. Model parameters: \(a_{m1}=1.0\times 10^{-4}\), \(a_{m0}=5.0\times 10^{-3}\), \(b_{m}=7.5\times 10^{-2}\);
2. Initial values of adjustable parameters: \(k_{a_{1}}\left(0\right)=4.0\times 10^{-4}\), \(k_{a_{0}}\left(0\right)=0\), \(k_{b_{0}}\left(0\right)=5.5\times 10^{-3}\);
3. Adjustable parameter: \(k_{b}\left(t\right)=1.5\times 10^{-2}\); Adaptive learning algorithm: \(\lambda_{a_{1}}=1.0\times 10^{-5}\), \(\lambda_{a_{0}}=2.0\times 10^{-7}\), \(\lambda_{b_{0}}=1.0\times 10^{-4}\), \(\mu=100\left(a_{m1}\dot{e}+a_{m0}e\right)\);
4. Soft limiting elements: \(\dot{k}_{a_{1}},\dot{k}_{a_{0}},\dot{k}_{b_{0}},\dot{k}_{b}\in\left(-1.0\times 1 0^{-3},\,1.0\times 10^{-3}\right)\);
5. Linear controller: PID controller.  
On the one hand, the proper choice of the initial values of adjustable parameters can speed up the convergence rates of the adjustable parameters, while, on the other hand, from Equations (7) and (9), \(k_{b}\) can be artificially fixed to reduce the learning variables and simplify the adaptive learning task without any modification of the adaptive laws, both of which can contribute to the adaptive learning performance. Otherwise, the adaptive learning process of adjustable parameters probably lasts longer. Then, a series of real-time HIL experimental tests are conducted to assess the control performance of the proposed nonlinear adaptive control scheme based on the above assumption.
# Validation Analysis of Drought Monitoring Based on FY-4 Satellite
## 2 Materials and Methods
### Methods
#### 2.3.3 Correlation Analysis  
The MCI site data and SHRI raster data were correlated with TVDI by the Pearson coefficient. The calculation formula is:  
\[\mathrm{x}=\frac{\sum_{i=1}^{n}\left(\mathrm{x_{i}-\overline{x}}\right)\left( \mathrm{y_{i}-\overline{y}}\right)}{\sqrt{\sum_{i=1}^{n}\left(\mathrm{x_{i}- \overline{x}}\right)^{2}}\sqrt{\sum_{i=1}^{n}\left(\mathrm{y_{i}-\overline{y} }\right)^{2}}}. \tag{4}\]
## 2 Multi-UAV Cooperative Persistent Monitoring Path Planning Model
### Multi-UAV Collaborative Monitoring Constraints  
Let \(K\) denote the maximum length of the monitoring horizon. Let the binary variable matrix \(Y^{m}\in\mathbb{R}^{K\times(N+|U|)}\) denote whether a node is monitored by UAV \(m\), \(m\in M_{UAV}\). For \(\forall i\in V^{\prime}\), the element \(y^{m}_{K:}=1\) represents that the node \(i\) is monitored by UAV \(m\) at time \(k\), and \(y^{m}_{K:}=0\) represents that the node \(i\) is not monitored by UAV \(m\) at time \(k\). \(Y^{m}\) represents the monitoring of all nodes by UAV \(m\) in the entire monitoring time horizon.  
Let the binary variable matrix \(X\in\mathbb{R}^{K\times(N+|U|)}\) represent whether a node is monitored by any UAV in the group, where the element \(x_{k,i}=1\) represents that there is at least one UAV monitoring node \(i\) at time \(k\), and the element \(x_{k,i}=0\) represents that node \(i\) is not monitored by any UAV at time \(k\). The matrix \(X\) stands for the monitored situation of all nodes in the monitoring time horizon, and can be obtained by combining all \(Y^{m}\), \(m=1\), \(2\),..., \(M\). The relationship between \(X\) and \(Y^{m}\) is \(X=Y^{1}\cup Y^{2}\ldots\cup Y^{M}\). The constraints are as follows:  
\[x_{k,i}=\left\{\begin{array}{l}0,\text{if }\sum\limits_{m=1}^{M}y^{m}_{k,i}=0, \\ 1,\text{otherwise, i.e., }\sum\limits_{m=1}^{M}y^{m}_{k,i}=1\end{array}\right. \tag{1}\]  
where \(i\in V,k\in\{1,2,\ldots,K\}\)  
\[\sum\limits_{m=1}^{M}y^{m}_{k,i}\leq 1,i\in V^{\prime},k\in\{1,2,\ldots,K\} \tag{2}\]  
\[\sum\limits_{k=1}^{K}x_{k,i}\geq 1,i\in V \tag{3}\]  
\[\sum\limits_{i=1}^{N+|U|}x_{k,i}=MEquation (2) indicates that at any time \(k\), a node is monitored by, at most, one UAV, that is, multiple UAVs cannot appear at the same location at the same time. Equation (3) indicates that within the monitoring horizon \(K\), each node must be visited at least once. Equation (4) indicates that a UAV only has one position at a certain time \(k\).
## 5 Analysis  
In this section, we first explore the validity of each part of the proposed method using ablation experiments. Subsequently, we explore the validity of the ensemble in the proposed method.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Teacher** & **ResNet152** & **ResNet152** & **ResNet152** & **ResNet50** & **ResNet50** & **VGG13** & **WRN40-2** \\
**Student** & **ResNet50** & **ResNet18** & **ResNet10** & **ResNet18** & **VGG8** & **VGG8** & **WRN16-2** \\ \hline KD [14] & 79.69 & 79.86 & 77.85 & 79.72 & 73.81 & 72.98 & 74.92 \\ FitNet [41] & 80.51 & 79.24 & 78.02 & 76.27 & 73.24 & 73.22 & 73.07 \\ AT [5] & 80.41 & 80.19 & 78.45 & 78.28 & 74.01 & 73.48 & 73.97 \\ SP [42] & 80.72 & 79.87 & 78.25 & 79.32 & 73.52 & 73.49 & 74.34 \\ CC [43] & 79.89 & 79.82 & 78.06 & 77.42 & 73.48 & 73.04 & 73.18 \\ VID [44] & 79.24 & 79.67 & 77.80 & 76.79 & 73.46 & 72.97 & 74.07 \\ RKD [45] & 80.22 & 79.60 & 77.90 & 78.75 & 73.51 & 73.19 & 73.36 \\ PKT [23] & 80.57 & 79.44 & 78.41 & 78.89 & 73.61 & 73.25 & 74.42 \\ AB [46] & 81.21 & 79.50 & 78.18 & 76.77 & 73.65 & 73.35 & 72.65 \\ FT [47] & 80.37 & 79.26 & 77.53 & 76.29 & 72.98 & 73.44 & 73.33 \\ CRD [26] & 80.53 & 79.81 & 78.60 & 74.58 & 74.58 & 74.29 & 75.79 \\ SSKD [27] & 80.29 & 80.36 & 78.60 & 79.72 & 75.36 & 75.27 & 76.14 \\ HSAKD [28] & 83.33 & 82.17 & 79.75 & 81.22 & 75.20 & 75.07 & 78.20 \\ TSKD [48] & 83.09 & 81.27 & 79.34 & 81.28 & 75.63 & 75.42 & 78.31 \\ \hline MSKD (ours) & 82.37 & 81.32 & 79.38 & 81.17 & 75.74 & 75.83 & 77.58 \\ OtO (ours) & 83.20 & 81.73 & 79.74 & 81.42 & 76.05 & 76.27 & 78.57 \\ OtO* (ours) & **83.47** & **82.63** & **80.52** & **82.10** & **76.19** & **76.36** & **78.72** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of the accuracy (%) of our method with those of other KD methods for CIFAR100. The best and second-best results are shown in **bold** and underlined, respectively. “OtO*” denotes the results after data augmentation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Teacher** & **ResNet34** & **ResNet34** \\
**Student** & **ResNet18** & **ResNet34** \\ \hline Teacher & 66.40 & 66.40 \\ Student & 64.40 & 66.40 \\ \hline KD [14] & 67.90 & 68.80 \\ FitNet [41] & 64.44 & 66.18 \\ AT [5] & 66.54 & 67.16 \\ SP [42] & 67.06 & 68.36 \\ VID [44] & 66.92 & 68.08 \\ RKD [45] & 65.90 & 67.80 \\ PKT [23] & 65.76 & 68.18 \\ CRD [26] & 67.94 & 68.96 \\ AFD [49] & 68.56 & 69.58 \\ \hline MSKD (ours) & 69.04 & 70.78 \\ OtO (ours) & **69.86** & **71.38** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of accuracy (%) of the proposed method with those of other KD methods for Tiny ImageNet. The best and second-best results are shown in **bold** and underlined, respectively.
# Automatic 3D MRI-Ultrasound Registration for Image Guided Arthroscopy
## 3 Methods
### Registration
#### 3.2.2 Pre-Initialization  
During the MIS, US probe is positioned on the patellar tendon and fat pad as shown in Figure 1. We model the US view in the MRI as an oriented bounding box of the anterior knee anatomy. We use the fat pad structure to arrive at a cuboidal region that is close to the view obtained by the US, for the initialization. The infrapatellar fat pad segmentation is obtained by using the method in Section 3.1.2. The principal axes of the fat pad, which are the normals to the faces of the bounding box, are computed from the segmentation, using principal component analysis (PCA) on the points on the fat pad surface.  
We now use anatomical information to align the US beam direction to one of the axes. Given the probe placement on the patellar tendon, the fat pad, which is immediately beneath, has almost similar orientation. This enables us to align the inferior-superior direction to one of the fat pad axes directly. The centroid, \(C\), of the fat pad, projected outward gives a point on the anterior fat pad surface, which is our initialization for probe center. Of the three eigenvectors obtained, the vector, \(v_{si}\), which goes from superior to inferior direction of the fat pad, gives the rotation matrix for the US volume. Let \(p_{1}\) and \(p_{2}\) be the boundary points of the fat pad that are intercepted by \(v_{si}\). The anterior point, \(p_{1}\), gives the required translation for the US volume (refer Appendix B).  
Figure 4 shows the fat pad segmentation, the boundary points intercepted by \(v_{si}\), and the principal axes of fat pad. \(O\) is the centre of the cropped MRI image. The rotation matrix given by \(v_{si}\) and the translation vector given by \(p_{1}\) together give us the initial transform of the US.