Systems and methods for C-arm fluoroscope camera pose refinement with secondary movement compensation

1. A method of compensating for secondary movement of a C-arm fluoroscope, the method comprising:

receiving fluoroscopic images obtained from a fluoroscopic sweep by the C-arm fluoroscope;

detecting markers of a structure of two-dimensional (2D) markers in the fluoroscopic images to obtain detected markers;

determining movement of the markers based on the detected markers;

estimating a primary movement axis based on the movement of the markers;

determining a secondary movement axis based on the primary movement axis;

estimating a translation of the markers in a direction of the secondary movement axis;

estimating a rotation axis translation based the translation of the markers;

estimating a three-dimensional (3D) position of a rotation axis;

estimating poses for the fluoroscopic images; and

refining the poses for the fluoroscopic images based on the rotation axis translation and the 3D position of the rotation axis.

2. The method of claim 1 , wherein each marker of the structure of 2D markers is a radiopaque bead or a radiopaque marker.

3. The method of claim 1 , wherein the structure is a 2D grid pattern.

4. The method of claim 1 , wherein estimating the translation of the markers includes:

aligning each marker with the primary movement axis and the secondary movement axis to obtain an aligned signal; and

determining a difference signal of each marker for a secondary component of the aligned signal.

5. The method of claim 1 , wherein the secondary movement axis is determined by processing the primary movement axis with a Graham-Schmidt algorithm.

6. The method of claim 1 , wherein estimating the 3D position of the rotation axis includes:

fitting a plane to main camera axes of the C-arm fluoroscope over the fluoroscopic sweep; and

computing an axis normal to the plane to obtain the 3D position of the rotation axis.

7. The method of claim 1 , wherein estimating the primary movement axis of the markers includes:

determining, for each of the markers, difference vectors between pairs of detected markers in adjacent pairs of frames of the fluoroscopic images; and

computing, for each pair of frames, a weighted average of the difference vectors,

wherein weights applied to the difference vectors are distances between the pairs of detected markers.

8. The method of claim 7 , wherein estimating the primary movement axis of the markers further includes:

computing a dot product between difference vectors;

determining that the dot product is less than a threshold;

in response to determining that the dot product is less than the threshold, setting the weights of the difference vectors to zero;

recomputing, for each pair of frames, a weighted average of the difference vectors;

determining that weights of a current iteration are the same as weights of a previous iteration; and

in response to determining that the weights of a current iteration are the same as the weights of a previous iteration, stopping computing of the weighted average.

9. A method for estimating wigwag movement in a C-arm fluoroscope, the method comprising:

receiving fluoroscopic images of a structure of markers from a sweep of the C-arm fluoroscope;

obtaining two-dimensional (2D) samples of each marker of the structure of markers from the fluoroscopic images;

estimating a main movement axis of each marker based on the 2D samples of each marker;

determining a secondary movement axis of each marker based on the main movement axis of each marker;

aligning 2D samples of each marker with the main movement axis and the secondary movement axis for each marker to obtain an aligned signal of each marker;

determining a velocity signal of each marker for a secondary component of the aligned signal of each marker;

converting the velocity signals of the markers to a rotation axis translation signal; and

estimating a rotation axis for the rotation axis translation signal.

10. The method of claim 9 , wherein each marker is part of a structure of markers.

11. The method of claim 9 , wherein the structure is a 2D grid pattern.

12. The method of claim 9 , wherein estimating the rotation axis includes:

fitting a plane to main camera axes of the C-arm fluoroscope over the sweep; and

computing a normal axis to the plane to obtain the rotation axis.

13. The method of claim 9 , wherein estimating the main movement axis of each marker of the structure of markers includes:

determining, for each marker of the structure of markers, difference vectors between pairs of markers in adjacent pairs of frames of the fluoroscopic images; and

computing, for each pair of frames, a weighted average of the difference vectors,

wherein the weights applied to the difference vectors are distances between the pairs of markers.

14. The method of claim 9 , wherein the secondary movement axis is determined by processing the main movement axis of each marker of the structure of markers with a Graham-Schmidt algorithm.

15. The method of claim 9 , wherein converting the velocity signal of each marker to a rotation axis velocity signal includes:

determining a similarity ratio for each marker; and

applying the similarity ratio to each marker to obtain the rotation axis velocity signal.

16. The method of claim 9 , wherein converting the velocity signals of the markers to a rotation axis translation signal includes:

averaging the velocity signals for all markers for each of the fluoroscopic images to obtain an averaged velocity signal; and

converting the averaged velocity signal to the rotation axis translation signal.

17. The method of claim 16 , wherein converting the averaged velocity signal to the rotation axis translation signal includes integrating the averaged velocity signal across all fluoroscopic images to obtain the rotation axis translation signal.

18. The method of claim 16 , further comprising estimating a pose for each of the fluoroscopic images based on the 2D samples of the markers, the rotation axis translation signal, and the rotation axis.

19. The method of claim 18 , wherein the markers are a grid of radiopaque beads.