  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.
