Comparing Unscented and Extended Kalman Filter Algorithms in the Rigid-Body Point-Based Registration
Bibliographic record
Abstract
Rigid registration is a crucial step in guidance system designed for neurosurgery, hip surgery, spine surgery and orthopaedic surgery. These systems often rely on point-based registration to determine the rigid transformation. The points used for registration (fiducial points) can be either extracted from the object being registered or created by implanting fiducial markers on the object. The localized fiducial points are generally corrupted by the noise which is called fiducial (point) localization error. In this work, we present a new point-based registration algorithm based on the Unscented Kalman Filter (UKF) algorithm and compare it with the earlier proposed registration algorithm which is based on the Extended Kalman Filter (EKF) algorithm. By means of numerical simulations, it is shown that the UKF registration algorithm more accurately estimates the registration parameters than the EKF registration algorithm. In addition, in contrast with EKF, UKF computes the variance of the estimated registration parameters with the accuracy of at least second-order Taylor series expansion. The computed variances are valuable information that can be used to determine the accuracy of the registration at any desired target positions (target registration error). We utilize the estimated variance of the registration parameters to compute the distribution of target registration error (TRE) at a desired target location. A new formula for the distribution of TRE, based on the estimated variances, is derived, and it is shown that the computed distribution more accurately follows the real distribution that is generated by the numerical simulations, than the one obtained from the EKF registration algorithm
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".