Optimal surface estimation and thresholding of confocal microscope images of biofilms using Beer's Law

Beer's Law explains how light attenuates into thick specimens, including thick biofilms. We use a Bayesian optimality criterion, the maximum of the posterior probability distribution, and computationally efficiently fit Beer's Law to the 3D intensity data collected from thick living biofilms by a confocal scanning laser microscope. Using this approach the top surface of the biofilm and an optimal image threshold can be estimated. Biofilm characteristics, such as bio-volumes, can be calculated from this surface. Results from the Bayesian approach are compared to other approaches including the method of maximum likelihood or simply counting bright pixels. Uncertainty quantification (i.e., error bars) can be provided for the parameters of interest. This approach is applied to confocal images of stained biofilms of a common lab strain of Pseudomonas aeruginosa, stained biofilms of Janthinobacterium isolated from the Antarctic, and biofilms of Staphylococcusaureus that have been genetically modified to fluoresce green.