Geometric constraint analysis and synthesis: methods for improving shape-based registration accuracy

Shape-based registration is a process for estimating the transformation between two shape representations of an object. It is used in many image-guided surgical systems to establish a transformation between preand intra-operative coordinate systems. This paper describes several tools which are useful for improving the accuracy resulting from shape-based registration: constraint analysis, constraint synthesis, and online accuracy estimation. Constraint analysis provides a scalar measure of sensitivity which is well correlated with registration accuracy. This measure can be used as a criterion function by constraint synthesis, an optimization process which generates configurations of registration data which maximize expected accuracy. Online accuracy estimation uses a conventional rootmean-squared error measure coupled with constraint analysis to estimate an upper bound on true registration error. This paper demonstrates that registration accuracy can be significantly improved via application of these methods.