Utilizing Minkowski functionals for image analysis: a marching square algorithm - Mecke, Klaus; Jacobs, Karin; et al. (Journal of Statistical Mechanics-Theory and Experiment, 2008)
Comparing noisy experimental image data with statistical models requires a quantitative analysis of grey-scale images beyond mean values and two-point correlations. A real-space image analysis technique is introduced for digitized grey-scale images, based on Minkowski functionals of thresholded patterns. A novel feature of this marching square algorithm is the use of weighted side lengths for pixels, so that boundary lengths are captured accurately. As examples to illustrate the technique we study surface topologies emerging during the dewetting process of thin films and analyse spinodal decomposition as well as turbulent patterns in chemical reaction-diffusion systems. The grey-scale value corresponds to the height of the film or to the concentration of chemicals, respectively. Comparison with analytic calculations in stochastic geometry models reveals a remarkable agreement of the examples with a Gaussian random field. Thus, a statistical test for non-Gaussian features in experimental data becomes possible with this image analysis technique-even for small image sizes. Implementations of the software used for the analysis are offered for download.
Keywords: patterns; liquid films (experiment); pattern formation (theory); pattern formation (experiment)