How to calculate local void ratio

Hi,
i want to calculate local void ratio inside a sample. And i have tried two methods
For the first method, i have try to use "variable...mass"function to calculate the mass of particles in a given region i have set in advance . Then i can derive the local void ratio.but this method always overestimate or underestimate the void ratio because of the existing of particles intersecting with the region boundary.
For the second method , i used "fix... ave/euler"command to calculate Cell-based averages of volume fraction.But i can not determine the arrangement of cells and the size of cell must be at least 3 multiple of maximum cutoff limits the use of this command.
so i want to know is there any other better methods to calculate the local void ratio?
thanks,
K.cheng