Diffeomorphic Matching and Dynamic Deformable Surfaces in 3d Medical Imaging
Diffeomorphic Matching and Dynamic Deformable Surfaces in 3d Medical Imaging
复制标题
3D 医学成像中的微分同形匹配和动态可变形表面
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Little
中科院分区：
文献类型：
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作者：
R. Azencott;R. Glowinski;Jiwen He;A. Jajoo;Yipeng Li;A. Martynenko;R. Hoppe;S. Benzekry;S. Little
摘要本文在Hilbert空间的非纯变换基础上，用变分方法研究了曲线曲面一类子流形的最优匹配问题。在一个抽象的设置，最佳匹配制定为一个最小化问题，涉及行动的正规Borel措施被认为是支持措施的参考和目标子流形上的仿射。目标函数由两部分组成，测量动态变形表面的弹性能量和匹配的质量。为了使问题的计算访问，我们使用再生核希尔伯特空间的径向内核和加权和狄拉克措施，从而产生的非纯点匹配和金额的解决方案的有限维最小化问题。我们提出了一个匹配算法的基础上的一阶必要的最优性条件，其中包括一个初始值问题的动力系统的轨迹描述的变形的表面和最终的时间与伴随方程的问题。该算法的性能说明了从医学图像分析的例子的数值结果。
Abstract We consider optimal matching of submanifolds such as curves and surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. In an abstract setting, the optimal matching is formulated as a minimization problem involving actions of diffeomorphisms on regular Borel measures considered as supporting measures of the reference and the target submanifolds. The objective functional consists of two parts measuring the elastic energy of the dynamically deformed surfaces and the quality of the matching. To make the problem computationally accessible, we use reproducing kernel Hilbert spaces with radial kernels and weighted sums of Dirac measures which gives rise to diffeomorphic point matching and amounts to the solution of a finite dimensional minimization problem. We present a matching algorithm based on the first order necessary optimality conditions which include an initial-value problem for a dynamical system in the trajectories describing the deformation of the surfaces and a final-time problem associated with the adjoint equations. The performance of the algorithm is illustrated by numerical results for examples from medical image analysis.