# Trackerless 3D Freehand Ultrasound Reconstruction: A Review
## 3 Results
### Quantitative Outcomes
#### 3.3.1 Analysis of Ablation Experiments
After calibration of the IMU with the ground truth tracking data, the acceleration showed high noise in absolute values, but a correct trend over a wider range. A temporal and multi-branch structure was employed that effectively utilized the low signal-to-noise ratio (SNR) of the IMU acceleration data. Additionally, they introduced a multi-modal online self-supervised strategy, leveraging IMU data as weak labels to constrain the predicted parameters. In a subsequent study, [PERSON] et al. [21] further tackled the challenges of the acceleration noise of an individual sensor by employing four IMUs. This approach integrated a modal-level self-supervised strategy that fused multiple IMU data sources, mitigating the noise effects of one IMU and reducing output discrepancies. The improvement in MAE and reported drift measures of the described approaches is shown in Table 3.  
The enhancement of baseline models through the integration of contextual and temporal information ranged from minor adjustments to substantial architectural changes. For instance, [PERSON] et al. [16; 26] transitioned from 2D to 3D CNNs, employing 3D residual blocks and convolutional kernels. This shift allowed for more effective extraction of feature mappings along the axis of the channel, corresponding to the temporal direction of the sweep in this context. This approach showed that a configuration with five frames yielded significant enhancements over two frames [16]. Further integration of contextual and temporal data was achieved through the implementation of various consistency losses within network architectures. [PERSON] et al. [21] employed a sequence-level self-consistency strategy, while [PERSON] et al. [20] utilized frame \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Addition** & **Dataset** & \begin{tabular}{c} **Transformation** \\ **Parameter** \\ \end{tabular} & \begin{tabular}{c} **Improvement in** \\ **MAE (\%)** \\ \end{tabular} & \begin{tabular}{c} **Improvement in** \\ **Drift Measures (\%)** \\ \end{tabular} \\ \hline \begin{tabular}{c} [PERSON] et al. [23] \\ B \(\rightarrow\) F \\ \end{tabular} & 1 IMU & \(1\) & \(t_{x}\) & 69.07 & FD: 61.89 \\  & & & \(t_{y}\) & 63.54 & \\  & & & \(t_{z}\) & 23.91 & \\  & & & \(\theta_{x}\) & 96.35 & \\  & & & \(\theta_{y}\) & 97.15 & \\  & & & \(\theta_{z}\) & 96.76 & \\ \hline \begin{tabular}{c} [PERSON] et al. [19] \\ A \(\rightarrow\) B \\ \end{tabular} & 1 IMU & \(1\) & \(\theta_{x},\theta_{y},\theta_{z}\) & 23.58 & FDR: 14.43 \\  & & 2 & 42.53 & FDR: 13.48 \\ \hline \begin{tabular}{c} [PERSON] et al. [21] \\ A \(\rightarrow\) B \\ \end{tabular} & 4 IMUs & \(1\) & \(\theta_{x},\theta_{y},\theta_{z}\) & 26.39 & FDR: 19.07 \\  & & 2 & 17.49 & FDR: 11.98 \\ \hline \
\begin{tabular}{c} [PERSON] et al. [20] \\ \end{tabular} &
\begin{tabular}{c} Optical Flow + \\ Canny Edge \\ \end{tabular} & \(1\) & \(\theta_{x},\theta_{y},\theta_{z}\) & 2.21 & FDR: 19.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative improvements of evaluation metrics due to the incorporation of additional inputs in CNNs. level contextual consistency (FCC) and path-level similarity constraints (PSCs). These strategies led to improvements in MAE and FDR, as detailed in Table 4.  
More extensive modifications in network architecture were explored by [PERSON] et al. [22], who evaluated the use of recurrent neural networks (RNNs) with LSTM modules and feed-forward (ff) CNNs. Those models are known to effectively handle sequential data over long periods. Since no significant difference between these models was found, it was suggested that ff-CNNs are equally competent in modeling US sequences compared to more specialized RNNs. Long-term dependencies were embedded in the network architecture by analyzing sequences of a length M of past (i) and (j) future frames, ranging from 2 to 100.