Transitive inverse-consistent image registration and evaluation
Xiujuan Geng · 2007
Image registration is widely used for finding correspondences and \t\t\t\tcomparing morphology in populations of biological forms. Due to \t\t\t\tthe shape complexity, discretized approximation of continuous \t\t\t\tspace, and so on, it is hard to find perfect registration and \t\t\t\tthe point-wise ground truth correspondence rarely exists. In \t\t\t\torder to improve registration performance, registration errors \t\t\t\tand desired properties were studied to constrain the \t\t\t\ttransformation searching space. New registration methods were \t\t\t\tdeveloped to generate correspondences with desired properties. \t\t\t\tEvaluation framework and experiments were established for \t\t\t\tmethods validation and comparison. Transitive inverse-consistent non-reference (TINR) registration \t\t\t\tmethods were developed to jointly estimate correspondences \t\t\t\tbetween groups of three images while minimizing inverse \t\t\t\tconsistency and transitivity errors. Registering three images \t\t\t\tsimultaneously provides a means for minimizing the transitivity \t\t\t\terror which is not possible when registering only two images. \t\t\t\tThe clustered TINR (CTINR) extended this method to register \t\t\t\tgroups of more than three images and was implemented by first \t\t\t\tclustering the group to sub-groups and applying the TINR method \t\t\t\tinside each sub-group. Transitive inverse-consistent implicit \t\t\t\treference (TIIR) registration methods were also developed to \t\t\t\tjointly register images to an implicit reference. By \t\t\t\tconstruction, the set of transformations are transitive and \t\t\t\tinverse consistent. The TIIR registration method was proved \t\t\t\tmathematically to provide smaller registration error compared to \t\t\t\tpair-wise registration. Few studies have been dedicated to registration evaluation. \t\t\t\tRegistration evaluation not only validates algorithm \t\t\t\tperformance, but also helps develop new registration techniques. \t\t\t\tSince ground truth correspondence is rarely known, no metric \t\t\t\talone is sufficient to valuate the registration performance. An \t\t\t\tevaluation framework and a set of metrics were developed and \t\t\t\tapplied. Curve, surface and volume-based TINR registration algorithms were \t\t\t\timplemented and evaluated. By maintaining similar similarity \t\t\t\tperformance, the transformation concatenation errors such as \t\t\t\tinverse consistency and transitivity errors were reduced \t\t\t\tsignificantly. Experiments were established to compare the CTINR \t\t\t\tand TIIR with the commonly used pair-wise group registration \t\t\t\tmethod. Results show that the CTINR method provided more \t\t\t\tconsistent transformations in terms of smaller transitivity and \t\t\t\tinverse-consistent errors, although the similarity error was \t\t\t\tslightly worse than the pair-wise group registration. The TIIR \t\t\t\tregistration provided better registration performance compared \t\t\t\tto the pair-wise group registration.