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. Author manuscript; available in PMC: 2017 Jul 1.
Published in final edited form as: Neuroimage. 2016 Apr 19;134:617–629. doi: 10.1016/j.neuroimage.2016.04.029

Table A1. Benchmark statistics for each of the benchmark structures (shown in Figure A1).

The geometric properties of each structure include the length of the longest dimension (L), volume (V), surface area (SA), and the ratio of volume to surface area (V/SA). Fractal dimensionality was calculated using four different methods, using either the box-counting or dilation algorithms, and either only counting the surface voxels of the structure (FDs) or also including the filled volume of the structure (FDf).

Structure Geometric Box-Counting Dilation
L V SA V/SA FDs FDf FDs FDf
Sphere 200 4,187,854 186,053 22.51 1.99 2.89 2.00 2.89
Cube 200 8,000,000 237,608 33.67 1.97 2.97 2.00 2.92
Menger-1 200 5,961,392 316,792 18.82 1.98 2.91 2.00 2.88
Menger-2 200 4,447,440 517,016 8.60 2.02 2.81 2.03 2.78
Menger-4 200 2,477,920 1,921,376 1.29 2.46 2.60 2.49 2.56
Newell Teapot 225 1,119,692 90,899 12.32 2.03 2.81 2.02 2.81
Stanford Bunny 221 2,211,262 167,897 13.17 2.03 2.81 2.01 2.82
Stanford Armadillo 225 825,402 121,628 6.77 2.03 2.68 2.02 2.69
Mug 220 1,113,980 340,802 3.27 2.14 2.53 2.13 2.56
Fiber Cup 223 245,102 69,926 3.41 1.96 2.40 2.00 2.46