In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a non-differentiable kernel. This allows to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deformation model from the viewpoint of discontinuous systems. To evaluate our approach, we conduct experiments on both artificial images and the publicly available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach in capturing plausible sliding motion.

翻译：本文提出了一种捕捉滑移运动的新可变形图像配准方法。大变形微分同胚度量映射（LDDMM）配准方法因构造特性生成平滑扭曲场，故在表征滑移运动时面临挑战。为解决该问题，我们通过引入结合零阶与一阶动量及非可微核函数扩展了LDDMM。这一方法既能表征切换边界处的不连续形变，又能保持同质区域内的微分同胚形变。我们从不连续系统视角对提出的形变模型进行了数学分析。为评估方法性能，我们在人工图像及公开DIR-Lab 4DCT数据集上开展了实验。结果表明，本方法在捕捉合理滑移运动方面具有有效性。