Efficient computation of enclosed volume and surface area from the same triangulated surface representation

We demonstrate that the volume enclosed by triangulated surfaces can be computed efficiently in the same elegant way the volume enclosed by digital surfaces can be computed by digital surface integration. Although digital surfaces are effective and efficient for visualization and volume measurement, their drawback is that surface area measurements derived from them are inaccurate. On the other hand, triangulated surfaces give more accurate surface area measurements, but volume measurements and visualization are less efficient. Our data structure (called t-shell) for representing triangulated digital surfaces retains advantages and overcomes difficulties of both the digital and the triangulated surfaces. We create a lookup table with area and volume contributions for each of the 256 Marching Cubes configurations. When scanning the shell (e.g., while creating it), the surface area and volume are incrementally computed by using the lookup table and the current x co-ordinate, where the sign of the x component of the triangle normal indicates the sign of the volume contribution. We have computed surface area and volume for digitized mathematical phantoms, physical phantoms, and real objects. The experiments show that triangulated surface area is more accurate, triangulated volume follows digital volume closely, and that the values get closer to the true value with decreasing voxel size.