...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>ESAIM: Proceedings and Surveys >Deformation field correction to preserve topology for image registration
【24h】

Deformation field correction to preserve topology for image registration

机译：变形场校正以保留用于图像配准的拓扑

获取原文
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this paper, the author addresses the issue of designing a theoretically well-motivated and computationally efficient method ensuring topology preservation on image-registration-related deformation fields. The model is motivated by a mathematical characterization of topology preservation for a deformation field mapping two subsets of Z2, namely, positivity of the four approximations to the Jacobian determinant of the deformation on a square patch. The first step of the proposed algorithm thus consists in correcting the gradient vector field of the deformation at the discrete level in order to fulfill this positivity condition. Once this step is achieved, it thus remains to reconstruct the deformation field, given its full set of discrete gradient vectors. The author propose to decompose the reconstruction problem into independent problems of smaller dimensions, yielding a natural parallelization of the computations and enabling us to reduce drastically the computational time (up to 80 in some applications). For each subdomain, a functional minimization problem under Lagrange interpolation constraints is introduced and its well-posedness is studied: existence/uniqueness of the solution, characterization of the solution, convergence of the method when the number of data increases to infinity, discretization with the Finite Element Method and discussion on the properties of the matrix involved in the linear system. Numerical simulations based on OpenMP parallelization and MKL multi-threading demonstrating the ability of the model to handle large deformations (contrary to classical methods) and the interest of having decomposed the problem into smaller ones are provided.
机译：在本文中，作者解决了设计理论上动机良好且计算效率高的方法的问题，该方法可确保在与图像配准相关的变形场上保留拓扑。该模型是通过对变形场映射Z2的两个子集（即四个近似值对方形块上的变形的雅可比行列式的正性）进行映射的变形场的拓扑保留的数学表征而激发的。因此，所提出算法的第一步是在离散水平上校正变形的梯度矢量场，以满足该正性条件。一旦完成此步骤，给定其完整的离散梯度矢量集，就可以重建变形场。作者建议将重构问题分解为较小尺寸的独立问题，从而自然地并行化计算，并使我们能够大幅度减少计算时间（在某些应用中最多可减少80个）。对于每个子域，引入了一个在Lagrange插值约束下的函数最小化问题，并研究了其适度性：解的存在/唯一性，解的特征，当数据数量增加到无穷大时方法的收敛性，有限元方法和线性系统中涉及的矩阵性质的讨论。提供了基于OpenMP并行化和MKL多线程的数值模拟，证明了模型处理大变形的能力（与经典方法相反），并且有兴趣将问题分解为较小的变形。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号