Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (STED) scanning microscopy that provides molecule counts in automatically generated image segments and offers statistical guarantees in form of asymptotic confidence intervals. To this end, we first apply a multiscale scanning procedure on STED microscopy measurements of the sample to obtain a system of significant regions, each of which contains at least one molecule with prescribed uniform probability. This system of regions will typically be highly redundant and consists of rectangular building blocks. To choose an informative but non-redundant subset of more naturally shaped regions, we hybridize our system with the result of a generic segmentation algorithm. The diameter of the segments can be of the order of the resolution of the microscope. Using multiple photon coincidence measurements of the same sample in confocal mode, we are then able to estimate the brightness and number of the molecules and give uniform confidence intervals on the molecule counts for each previously constructed segment. In other words, we establish a so-called molecular map with uniform error control. The performance of the algorithm is investigated on simulated and real data.

翻译：从荧光显微测量中量化分子数量是细胞生物学和医学研究中的重要课题。本文提出一种用于超分辨率（STED）扫描显微成像的连续算法，该算法能够在自动生成的图像片段中提供分子计数，并以渐近置信区间的形式提供统计保证。为此，我们首先对样本的STED显微测量数据应用多尺度扫描程序，获得一组显著区域，每个区域以预设的一致概率包含至少一个分子。这组区域通常高度冗余，由矩形基本单元组成。为选择一组信息丰富且非冗余、形状更自然的子区域，我们将该组结果与通用分割算法的输出进行杂交。各片段的直径可达到显微镜分辨率的量级。利用同一样本在共聚焦模式下的多光子符合测量，我们能够估计分子的亮度和数量，并为每个先前构建的片段上的分子计数提供一致置信区间。换言之，我们建立了一种具有一致误差控制的所谓分子图谱。该算法的性能已通过模拟数据和真实数据进行了验证。