Transitive inverse-consistent image registration and evaluation

Image registration is widely used for finding correspondences and comparing morphology in populations of biological forms. Due to the shape complexity, discretized approximation of continuous space, and so on, it is hard to find perfect registration and the point-wise ground truth correspondence rarely exists. In order to improve registration performance, registration errors and desired properties were studied to constrain the transformation searching space. New registration methods were developed to generate correspondences with desired properties. Evaluation framework and experiments were established for methods validation and comparison.

Transitive inverse-consistent non-reference (TINR) registration methods were developed to jointly estimate correspondences between groups of three images while minimizing inverse consistency and transitivity errors. Registering three images simultaneously provides a means for minimizing the transitivity error which is not possible when registering only two images. The clustered TINR (CTINR) extended this method to register groups of more than three images and was implemented by first clustering the group to sub-groups and applying the TINR method inside each sub-group. Transitive inverse-consistent implicit reference (TIIR) registration methods were also developed to jointly register images to an implicit reference. By construction, the set of transformations are transitive and inverse consistent. The TIIR registration method was proved mathematically to provide smaller registration error compared to pair-wise registration.

Few studies have been dedicated to registration evaluation. Registration evaluation not only validates algorithm performance, but also helps develop new registration techniques. Since ground truth correspondence is rarely known, no metric alone is sufficient to valuate the registration performance. An evaluation framework and a set of metrics were developed and applied.

Curve, surface and volume-based TINR registration algorithms were implemented and evaluated. By maintaining similar similarity performance, the transformation concatenation errors such as inverse consistency and transitivity errors were reduced significantly. Experiments were established to compare the CTINR and TIIR with the commonly used pair-wise group registration method. Results show that the CTINR method provided more consistent transformations in terms of smaller transitivity and inverse-consistent errors, although the similarity error was slightly worse than the pair-wise group registration. The TIIR registration provided better registration performance compared to the pair-wise group registration.