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We pursue a novel morphometric analysis to detect sources in very-high-energygamma-ray counts maps by structural deviations from the background noise.Because the Minkowski functionals from integral geometry quantify the shape ofthe counts map itself, the morphometric analysis includes unbiased structureinformation without prior knowledge about the source. Their distributionprovides access to intricate geometric information about the background. Wecombine techniques from stochastic geometry and statistical physics todetermine the joint distribution of all Minkowski functionals. We achieve anaccurate characterization of the background structure for large scan windows(with up to $15\times15$ pixels), where the number of microstates varies overup to 64 orders of magnitude. Moreover, in a detailed simulation study, weconfirm the statistical significance of features in the background noise anddiscuss how to correct for trial effects. We also present a local correction ofdetector effects that can considerably enhance the sensitivity of the analysis.In the third paper of this series, we will use the here derived refinedstructure characterization for a more sensitive data analysis that can detectformerly undetected sources.

Morphometric analysis in gamma-ray astronomy using Minkowski functionals: II. Joint structure quantification