Chapter 26 - Difference Image vs Ratio Image Error Function Forms in PET-PET Realignment

Abstract

This chapter presents a mathematical analysis of common modality image registration. Two alternative formulas are compared for computing registration error, the basis of these being the computation of image differences versus ratios. The theory suggests that the difference image method should be numerically more stable as well as more immune to noise. To test the theory, a Hoffman brain phantom is repeatedly scanned in one position, and images of variable statistical quality and spatial frequency content are prepared. These data are then submitted for realignment according to either the difference or the ratio image method. The difference image error function yielded consistently better precision in all but the most blurred data, in which case the two methods performed comparably. The precision advantage of the difference image method was attributable mainly to better determination of angular registration error as a consequence of reduced sensitivity to noise, and therefore greater tolerance of increased spatial frequency bandwidth. These results indicate that a modest improvement in realignment precision can be achieved by the use of error functions based on image differences as opposed to ratios.