There are several choices of weight functions, . The most basic, that we have opted to use, is that of the neighbourhood of 4 most adjacent positions, as shown by the dark grey in Figure 1, with each position being weighted relative to the other positions.
Another possibility is that of taking the most adjacent positions and the diagonally adjacent positions, as shown by the dark and light grey in Figure 1. Here, each of the most adjacent positions would have a relative weight of and each of the diagonally opposite positions would have a relative weight of , this way the sum of the weights is still unity and no scaling of the central pixel value occurs.
Note that the 26 element, three dimensional neighbourhood is not necessarily a better neighbourhood to take than the above 8 element two dimensional neighbourhood. While all 26 elements are still local to the central position, the microscopes that create these images usually do so in a layered fashion, that is, they scan a layer of fixed at a time. Thus weighting functions are better taken where all the elements considered are within a single, two dimensional layer of fixed .