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.

翻译：变换模型是可变形图像配准方法的核心组成部分。它提供图像间物理形变的表示，从而定义了可实现的配准范围与真实性。B样条模型与网格模型已成为两类广泛应用的变换模型。尽管两种模型均已得到深入研究，但由于实践中采用差异显著的优化方法，至今尚未实现直接比较：B样条模型主要采用梯度下降法优化，而网格模型通常依赖有限元法求解器或进化算法。多目标优化方法旨在寻找高质量折衷配准方案的多样解集，其在可变形图像配准中的重要性日益凸显。此类方法通过搜索多样化配准方案，能更全面揭示不同变换模型的能力，因而适于模型间的比较。本研究首次在B样条与网格变换模型间进行直接比较——采用相同的最新多目标优化方法（多目标实值基因池最优混合进化算法，MO-RV-GOMEA）对两种模型进行优化。其中，B样条变换模型与该算法的结合尚属首次。我们基于宫颈癌患者盆腔CT扫描数据（涉及大形变），在两类不同配准问题上开展实验对比。针对三位宫颈癌患者的实验结果表明，变换模型的选择对配准结果的多样性与质量具有显著影响。