Diffeomorphic spectral matching of cortical surfaces.

Accurate matching of cortical surfaces is necessary in many neuroscience applications. In this context diffeomorphisms are often sought, because they facilitate further statistical analysis and atlas building. Present methods for computing diffeomorphisms are based on optimizing flows or on inflating surfaces to a common template, but they are often computationally expensive. It typically takes several hours on a conventional desktop computer to match a single pair of cortical surfaces having a few hundred thousand vertices. We propose a very fast alternative based on an application of spectral graph theory on a novel association graph. Our symmetric approach can generate a diffeomorphic correspondence map within a few minutes on high-resolution meshes while avoiding the sign and multiplicity ambiguities of conventional spectral matching methods. The eigenfunctions are shared between surfaces and provide a smooth parameterization of surfaces. These properties are exploited to compute differentials on highly folded cortical surfaces. Diffeomorphisms can thus be verified and invalid surface folding detected. Our method is demonstrated to attain a vertex accuracy that is at least as good as that of FreeSurfer and Spherical Demons but in only a fraction of their processing time. As a practical experiment, we construct an unbiased atlas of cortical surfaces with a speed several orders of magnitude faster than current methods.

在许多神经科学应用中，皮质表面的精确匹配是必要的。在此背景下，常常寻求微分同胚，因为它们有助于进一步的统计分析和图谱构建。现有的计算微分同胚的方法基于优化流或基于将表面膨胀到一个通用模板，但它们通常计算成本高昂。在传统的台式计算机上，匹配一对具有几十万个顶点的皮质表面通常需要几个小时。我们提出一种基于在一种新型关联图上应用谱图理论的非常快速的替代方法。我们的对称方法能够在高分辨率网格上在几分钟内生成一个微分同胚对应映射，同时避免了传统谱匹配方法的符号和多重性模糊问题。本征函数在表面之间共享，并提供表面的平滑参数化。这些特性被用于计算高度折叠的皮质表面上的微分。因此，可以验证微分同胚并检测到无效的表面折叠。我们的方法经证明可达到至少与FreeSurfer和Spherical Demons一样好的顶点精度，但处理时间仅为它们的一小部分。作为一个实际实验，我们构建了一个皮质表面的无偏图谱，其速度比当前方法快几个数量级。