The transformation model is an essential component of any deformable image registration approach. It provides a representation of physical deformations between images, thereby defining the range and realism of registrations that can be found. Two types of transformation models have emerged as popular choices: B-spline models and mesh models. Although both models have been investigated in detail, a direct comparison has not yet been made, since the models are optimized using very different optimization methods in practice. B-spline models are predominantly optimized using gradient-descent methods, while mesh models are typically optimized using finite-element method solvers or evolutionary algorithms. Multi-objective optimization methods, which aim to find a diverse set of high-quality trade-off registrations, are increasingly acknowledged to be important in deformable image registration. Since these methods search for a diverse set of registrations, they can provide a more complete picture of the capabilities of different transformation models, making them suitable for a comparison of models. In this work, we conduct the first direct comparison between B-spline and mesh transformation models, by optimizing both models with the same state-of-the-art multi-objective optimization method, the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The combination with B-spline transformation models, moreover, is novel. We experimentally compare both models on two different registration problems that are both based on pelvic CT scans of cervical cancer patients, featuring large deformations. Our results, on three cervical cancer patients, indicate that the choice of transformation model can have a profound impact on the diversity and quality of achieved registration outcomes.
Taking a multi-objective optimization approach to deformable image registration has recently gained attention, because
such an approach removes the requirement of manually tuning the weights of all the involved objectives. Especially for
problems that require large complex deformations, this is a non-trivial task. From the resulting Pareto set of solutions one
can then much more insightfully select a registration outcome that is most suitable for the problem at hand. To serve as
an internal optimization engine, currently used multi-objective algorithms are competent, but rather inefficient. In this
paper we largely improve upon this by introducing a multi-objective real-valued adaptation of the recently introduced
Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) for discrete optimization. In this work, GOMEA is
tailored specifically to the problem of deformable image registration to obtain substantially improved efficiency. This
improvement is achieved by exploiting a key strength of GOMEA: iteratively improving small parts of solutions,
allowing to faster exploit the impact of such updates on the objectives at hand through partial evaluations. We performed
experiments on three registration problems. In particular, an artificial problem containing a disappearing structure, a pair
of pre- and post-operative breast CT scans, and a pair of breast MRI scans acquired in prone and supine position were
considered. Results show that compared to the previously used evolutionary algorithm, GOMEA obtains a speed-up of
up to a factor of ~1600 on the tested registration problems while achieving registration outcomes of similar quality.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.