Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most popular ways of quantifying cloudiness are based on power spectrum or correlation function on the one hand or the Laplacian pyramid on the other hand. Here, we recall the mathematical basis of the first approach comprehensively, derive a cloudiness index, and demonstrate its practical estimation. We prove that the Laplacian pyramid as well as other quantities characterizing cloudiness like the range of interaction and the intensity of small-angle scattering are very closely related to the power spectrum. Finally, we show that the power spectrum is easy to be measured image analytically and carries more information than the alternatives.

翻译：云层或云层形成是工业界通常使用的概念,以解决非交织物和纸质中与同质的偏差。根据图像数据测量云层指数是工业质量保证的一项共同任务。两种最常用的云层量化方式是一方面以电力频谱或相关功能为基础,另一方面以拉普拉西亚金字塔为基础。这里,我们回顾第一种方法的数学基础,全面得出云层指数,并展示其实际估计。我们证明拉普拉西亚金字塔以及其他以云层特征为特征的数量,如相互作用范围和小交错散的强度,都与电力频谱密切相关。最后,我们表明,电频谱很容易通过分析来测量图像,并且比替代物有更多的信息。