论文标题
离散方向和矢量场中奇异点和索引估计的鲁棒性度量
A robustness measure for singular point and index estimation in discretized orientation and vector fields
论文作者
论文摘要
离散矢量场中奇异点或拓扑缺陷的鉴定发生在不同的地区，从宇宙微波背景的极化到液晶到指纹识别和生物医学成像。由于其离散的性质，缺陷及其拓扑电荷不能连续地取决于每个向量，但是一旦向量变化超过阈值，它们就会不断变化。考虑到矢量级别上可接受的变化的阈值，我们为离散缺陷估计器开发了鲁棒性度量。在这里，我们比较了离散矢量或方向字段中缺陷估计的不同模板路径。在缺陷周围采样原型矢量场模式表明，鲁棒性随模板路径的长度而增加，但在向量上存在噪声的情况下较少。因此，除了“单像素”缺陷分析外，我们发现针对相对较小的模板的噪声的分辨率和鲁棒性之间的分辨率和鲁棒性之间的最佳权衡，该缺陷分析不能排除零鲁棒性。提出的鲁棒性测量为离散矢量场中缺陷的不确定性定量铺平了道路。
The identification of singular points or topological defects in discretized vector fields occurs in diverse areas ranging from the polarization of the cosmic microwave background to liquid crystals to fingerprint recognition and bio-medical imaging. Due to their discrete nature, defects and their topological charge cannot depend continuously on each single vector, but they discontinuously change as soon as a vector changes by more than a threshold. Considering this threshold of admissible change at the level of vectors, we develop a robustness measure for discrete defect estimators. Here, we compare different template paths for defect estimation in discretized vector or orientation fields. Sampling prototypical vector field patterns around defects shows that the robustness increases with the length of template path, but less so in the presence of noise on the vectors. We therefore find an optimal trade-off between resolution and robustness against noise for relatively small templates, except for the "single pixel" defect analysis, which cannot exclude zero robustness. The presented robustness measure paves the way for uncertainty quantification of defects in discretized vector fields.
