Univ. Bordeaux, IMS, UMR 5218, F-33400 Talence, France.
Microsc Microanal. 2013 Dec;19(6):1678-87. doi: 10.1017/S1431927613013548. Epub 2013 Oct 24.
Though three-dimensional (3D) imaging gives deep insight into the inner structure of complex materials, the stereological analysis of 2D snapshots of material sections is still necessary for large-scale industrial applications for reasons related to time and cost constraints. In this paper, we propose an original framework to estimate the orientation distribution of generalized cylindrical structures from a single 2D section. Contrary to existing approaches, knowledge of the cylinder cross-section shape is not necessary. The only requirement is to know the area distribution of the cross-sections. The approach relies on minimization of a least squares criterion under linear equality and inequality constraints that can be solved with standard optimization solvers. It is evaluated on synthetic data, including simulated images, and is applied to experimental microscopy images of fibrous composite structures. The results show the relevance and capabilities of the approach though some limitations have been identified regarding sensitivity to deviations from the assumed model.
尽管三维（3D）成像可以深入了解复杂材料的内部结构，但出于时间和成本限制等原因，对于大规模的工业应用，仍需要对材料截面的二维（2D）快照进行体视学分析。在本文中，我们提出了一种从单个 2D 截面估计广义圆柱形结构的取向分布的原始框架。与现有方法不同，不需要知道圆柱横截面的形状。唯一的要求是知道横截面的面积分布。该方法依赖于线性等式和不等式约束下的最小二乘准则的最小化，可以使用标准的优化求解器来解决。该方法在合成数据（包括模拟图像）上进行了评估，并应用于纤维复合材料结构的实验显微镜图像。结果表明了该方法的相关性和能力，尽管针对偏离假设模型的敏感性方面存在一些局限性。
