Calibrating tracking systems to remove position-dependent bias
A method for removing position-dependent bias from tracking systems computes invertible transformations between a tracking system and a reference system, and applies an inverse of the transformation to measurements in the tracking system to estimate the locations of reference points in the reference system and to determine relative bias at the measured points.
1. A method of calibrating a system used in a medical procedure, comprising:
tracking, using a tracking system, an object with features of known relative geometry in a tracking coordinate system;
comparing a measured geometry of the features with the known geometry of the features; and
determining, using a processing device, the relative position-dependent bias of the tracking system based on the comparing, wherein the relative position-dependent bias is a temporally constant, spatially varying error.
2. The method of claim 1 , wherein tracking the object comprises:
calculating an invertible transformation between known locations of a first plurality of points in a reference coordinate system and measured locations of the first plurality of points in the tracking coordinate system; and wherein comparing the measured geometry with the known geometry comprises:
applying an inverse of the invertible transformation to a measured location of a second point in the tracking coordinate system to obtain an estimated location of the second point in the reference coordinate system; and
generating a control signal representative of a difference between the estimated location of the second point in the reference coordinate system and a known location of the second point in the reference coordinate system, the difference corresponding to a relative position-dependent bias between the first plurality of points in the tracking coordinate system and the second point in the tracking coordinate system.
3. The method of claim 2 , further comprising positioning a tracked surgical instrument in the reference coordinate system with the control signal to correct for the relative position-dependent bias in the tracking coordinate system.
4. The method of claim 2 , further comprising positioning a tracked surgical target in the reference coordinate system with the control signal to correct for the relative position-dependent bias in the tracking coordinate system.
5. The method of claim 2 , wherein the first plurality of points comprises a first plurality of fiducial markers and the second point comprises a second fiducial marker, wherein the first plurality of fiducial markers and the second fiducial marker are positioned at known locations on the object.
6. The method of claim 5 , wherein the object defines the reference coordinate system.
7. The method of claim 5 , wherein the reference coordinate system comprises an x-ray imaging system.
8. The method of claim 2 , further comprising:
determining the known locations of the first plurality of points in the reference coordinate system and the known location of the second point in the reference coordinate system;
measuring the locations of the first plurality of points in the tracking coordinate system; and
measuring the location of the second point in the tracking coordinate system.
9. The method of claim 2 , further comprising determining the relative position-dependent bias for a plurality of different second points over a region of interest in the tracking coordinate system to generate a map of relative position-dependent bias over the region of interest in the tracking coordinate system.
10. The method of claim 2 , further comprising:
determining the relative position-dependent bias for a plurality of different second points bounding a region of interest in the tracking coordinate system; and
linearly interpolating the relative position-dependent bias between each of the plurality of different second points and a centroid of the first plurality of points.