Automated iterative three-dimensional registration of positron emission tomography images

Two types of image similarity measures, the sum of absolute differences (SAD) and the stochastic sign change (SSC), were compared for three-dimensional registration of images from PET. To test the accuracy of both registration methods, 30 FDG brain studies, 40 13N-ammonia cardiac studies and 20 FDG liver tumor studies (where each image set contained 15 image planes, 128 x 128 pixels per plane) were made into worse case conditions by creating image sets of low counts and extreme defects. These images were then registered to the reference images that had been moved in three dimensions into a random set of known translations, rotations and normalization factors (x, y, z, theta, rho, sigma, nf). Neither method required any external fiduciary markers or operator interventions to register a set of images. The optimization of the image similarity (using the SAD or SSC) was performed with the simplex method and registration was completed within 10 min of computation time on a low-end workstation. Overall, the SAD method had an average inplane (x, y) registration error of 0.5 +/- 0.5 mm, a z-axis registration error of 1.1 +/- 1.1 mm, an inplane rotational error of 0.5 +/- 0.4 degrees, an out-of-plane rotational error of 1.1 +/- 1.2 degrees and a normalization factor error of 0.015 +/- 0.016. The SSC method had an average inplane (x, y) registration error of 0.6 +/- 0.5 mm, a z-axis registration error of 1.1 +/- 1.1 mm, an inplane rotational error of 0.7 +/- 0.5 degrees, an out-of-plane rotational error of 1.0 +/- 1.2 degrees and a normalization factor error of 0.014 +/- 0.014. This study demonstrates that either the SAD or SSC method for measuring image similarity, combined with the simplex method for function optimization, are accurate methods for registration of a wide variety of PET images including low count studies and those with marked interval changes in the pattern of count distribution.