Sliding at first order: Higher-order momentum distributions for discontinuous image registration
This work addresses a specific challenge in medical image analysis for researchers and practitioners, offering an incremental improvement over existing LDDMM methods by enabling better modeling of sliding motions.
The paper tackles the problem of representing sliding motions in deformable image registration, which is challenging for smooth warp methods like LDDMM, by extending LDDMM with zeroth- and first-order momenta and a non-differentiable kernel to handle discontinuous deformations at boundaries while maintaining diffeomorphic deformations in homogeneous regions. Results on artificial images and the DIR-Lab 4DCT dataset demonstrate the approach's effectiveness in capturing plausible sliding motion.
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.