Direct cortical mapping via solving partial differential equations on implicit surfaces
Direct cortical mapping via solving partial differential equations on implicit surfaces
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DOI：
10.1016/j.media.2007.02.001
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发表时间：
2007-06-01
影响因子：
10.9
通讯作者：
Toga, Arthur W.
中科院分区：
文献类型：
--
作者：
Shi, Yonggang;Thompson, Paul M.;Toga, Arthur W.
在本文中，我们提出了一种新的方法，皮质映射，计算两个皮质表面之间的直接映射，同时满足脑沟标志曲线的约束。通过直接计算地图，我们可以避免传统的中间参数化，并有助于简化皮层映射过程。直接映射在我们的方法被制定为一个灵活的变分能量的最小地标约束下。能量可以包括用于确保地图的平滑度的调和项和用于匹配几何特征的一般数据项。从一个适当设计的初始地图开始，我们通过求解定义在源皮质表面上的偏微分方程（PDE）来迭代地计算地图。对于数值实现，一组自适应数值方案的开发，以扩展隐式曲面上求解偏微分方程的技术，使地标约束的强制执行。在我们的实验中，我们显示了直接映射方法的灵活性，通过计算光滑的地图，从两个不同的能量的地标约束。我们还定量地比较了一组30名受试者的直接映射方法与参数映射方法的度量保持属性。最后，我们展示了直接映射方法在脑图谱构建和变异性分析中的应用。(c)2007 Elsevier B.V.保留所有权利。
In this paper, we propose a novel approach for cortical mapping that computes a direct map between two cortical surfaces while satisfying constraints on sulcal landmark curves. By computing the map directly, we can avoid conventional intermediate parameterizations and help simplify the cortical mapping process. The direct map in our method is formulated as the minimizer of a flexible variational energy under landmark constraints. The energy can include both a harmonic term to ensure smoothness of the map and general data terms for the matching of geometric features. Starting from a properly designed initial map, we compute the map iteratively by solving a partial differential equation (PDE) defined on the source cortical surface. For numerical implementation, a set of adaptive numerical schemes are developed to extend the technique of solving PDEs on implicit surfaces such that landmark constraints are enforced. In our experiments, we show the flexibility of the direct mapping approach by computing smooth maps following landmark constraints from two different energies. We also quantitatively compare the metric preserving property of the direct mapping method with a parametric mapping method on a group of 30 subjects. Finally, we demonstrate the direct mapping method in the brain mapping applications of atlas construction and variability analysis. (c) 2007 Elsevier B.V. All rights reserved.