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assessment.md

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Although the ground-truth are available in the form of rigid transformation, we
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argue that, from experience in developing similar numerical algorithms, enforcing the algorithm output to be homogeneous transformation is not only unnecessary, but sometimes misleadingly encourages a more
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numerically challenging solution due to issues such as gimbal lock in using rotation matrix, local minima in numerical optimisation. In addition, the displacement-based representation allows flexibility for a quantitatively more accurate reconstruction (<a href="https://link.springer.com/chapter/10.1007/978-3-031-72083-3_64" target="_blank">Li et al. 2024</a>), with a near-rigid transformation, which could be sufficient for clinical use. However, there is no requirement in the internal methodology adopted, for example, the submitted algorithm can convert a single estimated rigid transformation matrix to all these four types of required displacement vectors as output.
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numerically challenging solution due to issues such as gimbal lock in using rotation matrix, local minima in numerical optimisation. In addition, the displacement-based representation allows flexibility for a quantitatively more accurate reconstruction (<a href="https://doi.org/10.1007/978-3-031-72083-3_64" target="_blank">Li et al. 2024</a>), with a near-rigid transformation, which could be sufficient for clinical use. However, there is no requirement in the internal methodology adopted, for example, the submitted algorithm can convert a single estimated rigid transformation matrix to all these four types of required displacement vectors as output.
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**Justification of the local and global reconstruction errors**
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The reconstructed scan from either local level or global level displacement are capable of representing different types of reconstruction performance, such as frame-level reconstruction error and accumulated error of the algorithm (<a href="https://doi.org/10.1109/TBME.2023.3325551" target="_blank">Li et al. 2023</a>, <a href="https://link.springer.com/chapter/10.1007/978-3-030-59716-0_49" target="_blank">Wein et al. 2020</a>). To streamline the evaluation, other monotonic metrics, such as final drift and Dice overlap, albeit commonly reported in literature (e.g. <a href="https://doi.org/10.1109/TBME.2023.3325551" target="_blank">Li et al 2023</a>), are not included. However, in practical applications, one might choose to reconstruct a sequence of ultrasound frames (as opposed to the entire scan or two adjacent frames, which are represented by local and global errors, respectively), using a pre-optimised sequence length that is most suitable to the downstream application. Without specifying a single target clinical application, these two adopted local and global errors shall represent the range of accuracy between the choices of the reconstruction length.
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The reconstructed scan from either local level or global level displacement are capable of representing different types of reconstruction performance, such as frame-level reconstruction error and accumulated error of the algorithm (<a href="https://doi.org/10.1109/TBME.2023.3325551" target="_blank">Li et al. 2023</a>, <a href="https://doi.org/10.1007/978-3-030-59716-0_49" target="_blank">Wein et al. 2020</a>). To streamline the evaluation, other monotonic metrics, such as final drift and Dice overlap, albeit commonly reported in literature (e.g. <a href="https://doi.org/10.1109/TBME.2023.3325551" target="_blank">Li et al 2023</a>), are not included. However, in practical applications, one might choose to reconstruct a sequence of ultrasound frames (as opposed to the entire scan or two adjacent frames, which are represented by local and global errors, respectively), using a pre-optimised sequence length that is most suitable to the downstream application. Without specifying a single target clinical application, these two adopted local and global errors shall represent the range of accuracy between the choices of the reconstruction length.
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## Ranking method
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The ranking follows the “aggregate then rank” strategy proposed by <a href="https://www.nature.com/articles/s41467-018-07619-7" target="_blank">Maier-Hein et al. 2018</a>.
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The ranking follows the “aggregate then rank” strategy proposed by <a href="https://doi.org/10.1038/s41467-018-07619-7" target="_blank">Maier-Hein et al. 2018</a>.
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For each test scan, the four evaluation metrics will be normalised to the range [0, 1] based on the "smallest reconstruction error" and "largest reconstruction error", respectively, using formulas below. The "smallest reconstruction error" is defined as the reconstruction error using the ground truth transformations, which is 0. The "largest reconstruction error" is the reconstruction error using transformations of identity matrix for all frames in a scan.
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