Reliability and Capture Range

Because the optimization procedures used in most implementations of chamfer matching are simple downhill searchers, the algorithm can be caught in local minimum of the cost function and produce a suboptimal or downright wrong result. The probability that the match winds up in a local minimum depends on the distance (in the search space) between the starting position and the correct match. For this reason, often measures are taken to reduce this distance (by manual or automatic prematching).

To test a registration procedure for reliability and capture range, it is restarted repeatedly with a random translation, rotation, and scaling from a well-chosen reference match. The "capture range" is defined as the distance (expressed as an average displacement vector length for the random transformation) at which 10% of the registrations fail. A failure is a match that deviates significantly from the reference match. The reliability is measured by generating random transformations according to the assumed clinical distribution of initial mismatches and counting the number of failures. A typical capture range for 3D image registration using chamfer matching is 2-5 cm, depending on the quality of the image segmentation. At capture ranges below 4 cm a prematch (for instance, on the skin surface) is required to ensure adequate reliability. With such measures, a reliability on the order of 95% or better can be obtained for CT-MRI registration of the head or of the pelvis. The remaining failures are corrected by restarting the match from a manual prematch.

The capture range was measured this way for CT-CT, CT-MRI, and CT-SPECT registration of the head [34]. The capture

TABLE 3 Difference (st. dev.) in resulting translation (mm) and rotation (degrees) between chamfer matching on bone and volume matching based on mutual information for CT-MRI registrationa

Translation (mm) along axis Rotation (degrees around)

AP HF LR AP HF LR 3D mean 3D maximum

Brain (n = 15) 0.53 0.45 0.24 0.29 0.17 0.60 1.43 2.82

range was 6 cm for CT-CT and CT-MRI and 3 cm for CT-SPECT. A capture range of 4 cm is adequate for reliable unattended clinical operation. In conclusion, the accuracy and reliability of our method are adequate for CT-CT and CT-MRI correlation, while CT-SPECT correlation must be improved further.

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