Co-localization analysis is a popular method for quantitative analysis in fluorescence microscopy imaging. The localization of marked proteins in the cell nucleus allows a deep insight into biological processes in the nucleus. Several metrics have been developed for measuring the co-localization of two markers, however, they depend on subjective thresholding of background and the assumption of linearity. We propose a robust method to estimate the bivariate distribution function of two color channels. From this, we can quantify their co- or anti-colocalization. The proposed method is a combination of the Maximum Entropy Method (MEM) and a Gaussian Copula, which we call the Maximum Entropy Copula (MEC). This new method can measure the spatial and nonlinear correlation of signals to determine the marker colocalization in fluorescence microscopy images. The proposed method is compared with MEM for bivariate probability distributions. The new colocalization metric is validated on simulated and real data. The results show that MEC can determine co- and anti-colocalization even in high background settings. MEC can, therefore, be used as a robust tool for colocalization analysis.

中文翻译：

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通过最大熵联结在荧光显微镜下进行共定位分析

共定位分析是荧光显微镜成像中一种流行的定量分析方法。标记蛋白质在细胞核中的定位可以深入了解细胞核中的生物过程。已经开发了几个度量标准来测量两个标记的共定位，但是，它们取决于背景的主观阈值和线性假设。我们提出了一种稳健的方法来估计两个颜色通道的双变量分布函数。由此，我们可以量化它们的共定位或反共定位。所提出的方法是最大熵方法 (MEM) 和高斯 Copula 的组合，我们称之为最大熵 Copula (MEC)。这种新方法可以测量信号的空间和非线性相关性，以确定荧光显微镜图像中的标记共定位。将所提出的方法与 MEM 进行二元概率分布的比较。新的共定位度量在模拟和真实数据上得到验证。结果表明，即使在高背景设置下，MEC 也可以确定共定位和反共定位。因此，MEC 可以用作共定位分析的强大工具。