Probabilistic analysis of small-scale print defects with aligned 2D measurements

Abstract

We present an analysis of the pointwise relationship between the reflectance of print and the surface topography of the paper before printing. We have measured the surface topography and reflectance of paper before and after printing in a sheet-fed pilot offset printing press. The 2D measurement maps have been aligned to obtain local print reflectance and surface topography values for every spatial position on the samples. In contrast to the various deterministic modeling approaches, which imply an a priori defined underlying mathematical model, we apply probabilistic analysis. Therefore we first estimate joint probability density functions (pdfs) of local topography and print reflectance using Gaussian Mixture Models (GMMs). From these pdfs we select paper regions with unusual properties, i.e. regions from the tails of the pdfs. These anomaly maps are analyzed for interrelations between the print reflectance and surface topography, its gradient and local variance. The degree of interrelation is characterized by the mutual information (MI), a measure to quantify statistical dependence without making assumptions about the linear or nonlinear nature of the regression dependence. The significance of the MI values is confirmed by simulation based statistical hypothesis testing. The objective is to offer answers to the question: How does the observation of an exceptional topography point on the paper surface change our information about whether the print quality attainable at that point will be exceptional or not? The results suggest that topography in combination with its local variance have the most prominent interrelation to small scale print anomalies. Furthermore it is shown that regions with abnormal topography have at least ten-fold higher probability to exhibit exceptionally high print reflectance, compared to randomly selected regions.