Lui Lok Ming, Thiruvenkadam Sheshadri, Wang Yalin, Chan Tony, Thompson Paul
Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA.
Med Image Comput Comput Assist Interv. 2008;11(Pt 1):494-501. doi: 10.1007/978-3-540-85988-8_59.
In this work, we find meaningful parameterizations of cortical surfaces utilizing prior anatomical information in the form of anatomical landmarks (sulci curves) on the surfaces. Specifically we generate close to conformal parametrizations that also give a shape-based correspondence between the landmark curves. We propose a variational energy that measures the harmonic energy of the parameterization maps, and the shape dissimilarity between mapped points on the landmark curves. The novelty is that the computed maps are guaranteed to give a shape-based diffeomorphism between the landmark curves. We achieve this by intrinsically modelling our search space of maps as flows of smooth vector fields that do not flow across the landmark curves, and by using the local surface geometry on the curves to define a shape measure. Such parameterizations ensure consistent correspondence between anatomical features, ensuring correct averaging and comparison of data across subjects. The utility of our model is demonstrated in experiments on cortical surfaces with landmarks delineated, which show that our computed maps give a shape-based alignment of the sulcal curves without significantly impairing conformality.
在这项工作中，我们利用皮质表面上解剖学标志（脑沟曲线）形式的先验解剖学信息，找到了皮质表面有意义的参数化方法。具体来说，我们生成了接近共形的参数化，它还在标志曲线之间给出了基于形状的对应关系。我们提出了一种变分能量，用于测量参数化映射的调和能量以及标志曲线上映射点之间的形状差异。新颖之处在于，计算得到的映射保证能在标志曲线之间给出基于形状的微分同胚。我们通过将映射的搜索空间内在地建模为不穿过标志曲线的光滑向量场流，并利用曲线上的局部表面几何来定义形状度量，从而实现这一点。这种参数化确保了解剖特征之间的一致对应，保证了跨受试者数据的正确平均和比较。我们的模型在带有划定标志的皮质表面实验中得到了验证，结果表明我们计算得到的映射给出了脑沟曲线基于形状的对齐，同时不会显著损害共形性。
