We would like to thank the reviewers for their insightful comments which will help us improve the article. Impact of the noise parameter: We will add Fig.(a) below in appendix. It supports the theoretical claim of Sec.2.3 that the noise parameter is of little importance. Model 1. is unrealistic: A more natural model is ICA based solutions for cleaning EEG or fMRI data). The difference between algorithms is small.

In the context of medical Augmented Reality (AR) applications, object tracking is a key challenge and requires a significant amount of annotation masks. As segmentation foundation models like the Segment Anything Model (SAM) begin to emerge, zero-shot segmentation requires only minimal human participation obtaining high-quality object masks. We introduce a HoloLens-Object-Labeling (HOLa) Unity and Python application based on the SAM-Track algorithm that offers fully automatic single object annotation for HoloLens 2 while requiring minimal human participation. HOLa does not have to be adjusted to a specific image appearance and could thus alleviate AR research in any application field. We evaluate HOLa for different degrees of image complexity in open liver surgery and in medical phantom experiments. Using HOLa for image annotation can increase the labeling speed by more than 500 times while providing Dice scores between 0.875 and 0.982, which are comparable to human annotators. Our code is publicly available at: https://github.com/mschwimmbeck/HOLa

In computer-assisted orthopedic surgery (CAOS), accurate pre-operative to intra-operative bone registration is an essential and critical requirement for providing navigational guidance. This registration process is challenging since the intra-operative 3D points are sparse, only partially overlapped with the pre-operative model, and disturbed by noise and outliers. The commonly used method in current state-of-the-art orthopedic robotic system is bony landmarks based registration, but it is very time-consuming for the surgeons. To address these issues, we propose a novel partial-to-full registration framework based on gradient-SDF for CAOS. The simulation experiments using bone models from publicly available datasets and the phantom experiments performed under both optical tracking and electromagnetic tracking systems demonstrate that the proposed method can provide more accurate results than standard benchmarks and be robust to 90% outliers. Importantly, our method achieves convergence in less than 1 second in real scenarios and mean target registration error values as low as 2.198 mm for the entire bone model. Finally, it only requires random acquisition of points for registration by moving a surgical probe over the bone surface without correspondence with any specific bony landmarks, thus showing significant potential clinical value.