Multiscale spatial segregation analysis in digital images: from biofilms, oats and raisins to Covid-19 epidemics

Abstract Quantifying the degree of spatial segregation of two components is relevant in many fields, including microbiology, population biology and epidemics. Spatial segregation is spatial scale-dependant – from a great distance the components may appear to be well mixed, but a closer look can reveal strong separation. Typically, this information is encoded in a digital image that represents the binary system, e.g., a microscopy image of two species biofilm or a state map of virus-infected and virus-uninfected people. To decode spatial segregation information, we have developed quantitative measures for evaluating the degree of the spatial scale-dependent segregation of two components in a digital image. The constructed algorithm implementing new segregation measures was successfully applied to mixed species biofilms and bacterial suspensions, where we detected different spatial scale-dependent segregation levels. To demonstrate the versatility of our multiscale segregation analysis approach, we have also applied it to SARS-CoV-2-infected population density maps of Italy during the “first wave” of the epidemic. Our data suggests that the first community quarantine imposed by the Italian government at the end of February 2020 was ineffective; however, after the full-country “lockdown”, the segregation stopped decreasing, indicating an efficient community quarantine.