Approaching problematic edge effects at non-binary fields of view and small radii.

Panel A: Three implementations of Besag’s edge correction term were tested. Note that the black region (black pixels) are considered to be outside the study region (i.e. the border between the grey and black area represents the edge of the study region), The implementations are as follows: i) Dividing the total number of pixels, located within a pre-defined radius from a given border pixel (light-gray area), by the total area of an ideal circle (area enclosed by the dotted red line). ii) Same as implementation i, but dividing by the total area of a non-ideal/pixelated circle (light-gray plus pink regions). iii) Same as implementation i, but applied for all pixels within the field of view. Hence, even for non-border pixels, the edge correction term would be obtained by dividing the area of the pixelated circle by the area of a perfect circle of the same radius. Panel B: The difference between an “ideal” circle and its pixelated counterpart at the four radii tested in this paper. Panel C: Complete Spatial Randomness (CSR) at a selected number of event densities (intensities). Each field of view measures 256 x 256 pixels. The image intensities were re-scaled for display purposes; the simulations used in Ripley’s K-function validation were set such that one intensity unit is akin to one event, at a saturation limit of 255 events per pixel (8-bit grayscale images).