Nonrigid image registration is an important task for many medical imaging applications. In particular, for radiation oncology it is desirable to track respiratory motion for thoracic cancer treatment. B-splines are convenient for modeling nonrigid deformations, but ensuring invertibility can be a challenge. This paper describes sufficient conditions for local invertibility of deformations based on B-spline bases. These sufficient conditions can be used with constrained optimization to enforce local invertibility. We also incorporate these conditions into nonrigid image registration methods based on a simple penalty approach that encourages diffeomorphic deformations. Traditional Jacobian penalty methods penalize negative Jacobian determinant values only at grid points. In contrast, our new method enforces a sufficient condition for invertibility directly on the deformation coefficients to encourage invertibility globally over a 3-D continuous domain. The proposed penalty approach requires substantially less compute time than Jacobian penalties per iteration.

中文翻译：

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鼓励局部可逆性的 B 样条非刚性图像配准的简单正则化器

非刚性图像配准是许多医学成像应用的重要任务。特别是，对于放射肿瘤学而言，需要跟踪呼吸运动以进行胸癌治疗。B 样条曲线便于对非刚性变形进行建模，但确保可逆性可能是一个挑战。本文描述了基于 B 样条基的变形局部可逆性的充分条件。这些充分条件可与约束优化一起使用以强制执行局部可逆性。我们还基于鼓励微分变形的简单惩罚方法将这些条件合并到非刚性图像配准方法中。传统的雅可比惩罚方法仅在网格点处惩罚负的雅可比行列式值。相比之下，我们的新方法直接在变形系数上强制可逆性的充分条件，以促进 3-D 连续域上的全局可逆性。与雅可比惩罚相比，每次迭代所提出的惩罚方法需要的计算时间要少得多。