A Tournament of Transformation Models: B-Spline-based Vs. Mesh-based Multi-Objective Deformable Image Registration

The transformation model is an essential component of any deformable imageregistration approach. It provides a representation of physical deformationsbetween images, thereby defining the range and realism of registrations thatcan be found. Two types of transformation models have emerged as popularchoices: B-spline models and mesh models. Although both models have beeninvestigated in detail, a direct comparison has not yet been made, since themodels 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 solversor evolutionary algorithms. Multi-objective optimization methods, which aim tofind a diverse set of high-quality trade-off registrations, are increasinglyacknowledged to be important in deformable image registration. Since thesemethods search for a diverse set of registrations, they can provide a morecomplete picture of the capabilities of different transformation models, makingthem suitable for a comparison of models. In this work, we conduct the firstdirect comparison between B-spline and mesh transformation models, byoptimizing both models with the same state-of-the-art multi-objectiveoptimization method, the Multi-Objective Real-Valued Gene-pool Optimal MixingEvolutionary Algorithm (MO-RV-GOMEA). The combination with B-splinetransformation models, moreover, is novel. We experimentally compare bothmodels on two different registration problems that are both based on pelvic CTscans of cervical cancer patients, featuring large deformations. Our results,on three cervical cancer patients, indicate that the choice of transformationmodel can have a profound impact on the diversity and quality of achievedregistration outcomes.