Tricoche Xavier, Kindlmann Gordon, Westin Carl-Fredrik
Computer Science Department, Purdue University.
IEEE Trans Vis Comput Graph. 2008 Nov-Dec;14(6):1627-34. doi: 10.1109/TVCG.2008.148.
We introduce a versatile framework for characterizing and extracting salient structures in three-dimensional symmetric second-order tensor fields. The key insight is that degenerate lines in tensor fields, as defined by the standard topological approach, are exactly crease (ridge and valley) lines of a particular tensor invariant called mode. This reformulation allows us to apply well-studied approaches from scientific visualization or computer vision to the extraction of topological lines in tensor fields. More generally, this main result suggests that other tensor invariants, such as anisotropy measures like fractional anisotropy (FA), can be used in the same framework in lieu of mode to identify important structural properties in tensor fields. Our implementation addresses the specific challenge posed by the non-linearity of the considered scalar measures and by the smoothness requirement of the crease manifold computation. We use a combination of smooth reconstruction kernels and adaptive refinement strategy that automatically adjust the resolution of the analysis to the spatial variation of the considered quantities. Together, these improvements allow for the robust application of existing ridge line extraction algorithms in the tensor context of our problem. Results are proposed for a diffusion tensor MRI dataset, and for a benchmark stress tensor field used in engineering research.
我们引入了一个通用框架，用于表征和提取三维对称二阶张量场中的显著结构。关键的见解是，张量场中的退化线（由标准拓扑方法定义）恰好是一种称为模式的特定张量不变量的折痕（脊线和谷线）。这种重新表述使我们能够将科学可视化或计算机视觉中经过充分研究的方法应用于张量场中拓扑线的提取。更一般地说，这一主要结果表明，其他张量不变量，如分数各向异性（FA）等各向异性度量，可以在同一框架中代替模式，以识别张量场中的重要结构特性。我们的实现解决了所考虑的标量度量的非线性以及折痕流形计算的平滑性要求所带来的特定挑战。我们使用平滑重建核和自适应细化策略的组合，该策略会根据所考虑量的空间变化自动调整分析的分辨率。这些改进共同使得现有的脊线提取算法能够在我们问题的张量背景下稳健应用。给出了扩散张量磁共振成像数据集以及工程研究中使用的基准应力张量场的结果。
