Unsuccessful implementations of Besag’s edge correction term at non-binary fields of view ( with respect to radius at different event densities).

The normalized and centered K-function (), as described by Lagache et al, was calculated at different particle intensities and radii using simulated square fields of view measuring 256 x 256 pixels, with a homogeneous Poisson distribution of particles (Complete Spatial Randomness). Densities are expressed in particles per pixel. The black line represents the mean and the dotted lines represent the upper and lower critical quantiles (Q01 and Q99). Each mean/quantile was determined using a set of 1000 simulations. Panel A: Applying Besag’s correction term only to edge pixels, by dividing the pixels within a given radius by the area of an ideal circle of the same radius. It can be seen that is no longer centered around zero at high particle intensities. Panel B: Same as panel A, but dividing by a pixelated circle rather than an ideal one. Like panel A, it can be seen that is no longer centered on zero at high intensities. Panel C: For comparison, was calculated without applying any edge correction terms. It can be seen that edge effects play a significant role at high particle intensities, making deviate remarkably from zero.