Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, June 2-7, 2019, Proceedings
Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, June 2-7, 2019, Proceedings
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医学影像信息处理 - 第 26 届国际会议，IPMI 2019，中国香港，2019 年 6 月 2-7 日，会议记录
DOI：
10.1007/978-3-030-20351-1_17
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Le Folgoc L
中科院分区：
文献类型：
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作者：
Le Folgoc L
我们研究离散自旋变换，一个几何框架来操纵表面网格通过控制平均曲率。应用包括表面光顺-将网格流到例如参考球体上-和网格挤出-例如，从参考球体和曲率规范重建复杂形状。因为它们在曲率空间中操作，所以这些操作可以在大变形中非常稳定地进行，而不需要重新网格化。旋转变换添加到用于姿态不变形状分析的算法工具箱中。从数学上讲，平均曲率是形状不变的，并且通常完全表征闭合形状（与度量一起）。从计算上讲，自旋变换使这种关系变得明确。我们的工作扩展了自旋变换的离散形式。像它们的光滑对应物一样，离散自旋变换自然地接近保角（保角）。然而，这种准保形性可以被放松，以满足面积失真和角度保持之间的期望折衷。我们得出这样的限制，并提出了一个配方，它们可以有效地纳入。该方法在皮质下结构上展示。
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing – flowing a mesh onto say, a reference sphere – and mesh extrusion –e.g., rebuilding a complex shape from a reference sphere and curvature specification. Because they operate in curvature space, these operations can be conducted very stably across large deformations with no need for remeshing. Spin transformations add to the algorithmic toolbox for pose-invariant shape analysis. Mathematically speaking, mean curvature is a shape invariant and in general fully characterizes closed shapes (together with the metric). Computationally speaking, spin transformations make that relationship explicit. Our work expands on adiscreteformulation of spin transformations. Like their smooth counterpart, discrete spin transformations are naturally close to conformal (angle-preserving). This quasi-conformality can nevertheless be relaxed to satisfy the desired trade-off between area distortion and angle preservation. We derive such constraints and propose a formulation in which they can be efficiently incorporated. The approach is showcased on subcortical structures.