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Deformable Image Registration Based on Functions of Bounded Generalized Deformation
International Journal of Computer Vision ( IF 19.5 ) Pub Date : 2021-02-04 , DOI: 10.1007/s11263-021-01439-x
Ziwei Nie , Chen Li , Hairong Liu , Xiaoping Yang

Functions of bounded deformation (BD) are widely used in the theory of elastoplasticity to describe the possibly discontinuous displacement fields inside elastoplastic bodies. BD functions have been proved suitable for deformable image registration, the goal of which is to find the displacement field between a moving image and a fixed image. Recently BD functions have been generalized to symmetric tensor fields of bounded generalized variation. In this paper, we focus on the first-order symmetric tensor fields, i.e., vector-valued functions, of bounded generalized variation. We specify these functions as functions of bounded generalized deformation (BGD) since BGD functions are natural generalizations of BD functions. We propose a BGD model for deformable image registration problems by regarding concerned displacement fields as BGD functions. BGD model employs not only the first-order but also higher-order coupling information of components of the displacement field. It turns out that BGD model allows for jump discontinuities of displacements while, in contrast to BD model, at the same time is able to employ higher-order derivatives of displacements in smooth regions. As a result, BGD model tends to capture possible discontinuities of displacements appeared around edges of the target objects while keep the smoothness of displacements inside the target objects as well. This characteristic enables BGD model to obtain better registration results than BD model and other variational models. To our knowledge, it is the first time in literature to use BGD functions for image registration. A first-order adaptive primal–dual algorithm is adopted to solve the proposed BGD model. Numerical experiments on 2D and 3D images show both effectiveness and advantages of BGD model.



中文翻译:

基于有界广义变形函数的可变形图像配准

弹塑性理论中广泛使用有界变形(BD)函数来描述弹塑性体内可能不连续的位移场。BD函数已被证明适用于可变形图像配准,其目的是找到运动图像和固定图像之间的位移场。最近,BD函数已被推广到有界广义变化的对称张量场。在本文中,我们集中于有界广义变化的一阶对称张量场,即矢量值函数。由于BGD函数是BD函数的自然概括,因此我们将这些函数指定为有界广义变形(BGD)函数。通过将有关位移场视为BGD函数,我们提出了用于可变形图像配准问题的BGD模型。BGD模型不仅采用位移场分量的一阶耦合信息,还采用高阶耦合信息。事实证明,与BD模型相比,BGD模型允许位移的跳跃不连续性,同时能够在平滑区域中采用位移的高阶导数。结果,BGD模型倾向于捕获目标对象边缘周围出现的位移的不连续性,同时也保持目标对象内部位移的平滑性。这一特性使BGD模型可以获得比BD模型和其他变体模型更好的配准结果。据我们所知,这是文献中首次使用BGD功能进行图像配准。采用一阶自适应原始对偶算法来求解所提出的BGD模型。

更新日期:2021-02-04
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