“…The change in volume of each grain i, V i , between the volume from the originally segmented mesh, V i,mcubes (labeled as 'mcubes') and that from the smoothed mesh, V i,smoothed (labeled as 'smoothed'), is defined as figure 8, the errors of V i created through the smoothing process are plotted against V i,mcubes for all of the grains in (a) Microstructure I, and (b) Microstructure II, respectively. Note that most of the grains experience less than 0.2% volume changes during the smoothing procedure and that smaller grains experience larger volume changes due to the relatively poor resolution of both the original images and segmented triangles when compared to the larger ones, as one might reasonably expect [42].…”