A geometric model for measurement of surface distance, surface area, and volume from tomographic images

Surface area and volume are essential measurements in the morphometric assessment of anatomical structures. New algorithms were developed to measure (1) distance along a curve, (2) surface area, and (3) volume using data extracted from tomographic images as a geometrical surface model. The model is a list of coordinates and normal vectors for each voxel or point gathered from the surface of a selected object. The resulting surface-based pointlist is also used for high-speed rendering of surfaces. Differential arclength and surface area are measured with high numeric precision by using the absolute value of the maximum component of the unit normal vector (MUNC) to approximate their values. These differential values are summed to measure distance along a curve and surface area. A discrete form of the Divergence theorem, also using the MUNC, is used to calculate volume. The intrinsic accuracy of the measurement algorithms was evaluated using computer generated pointlists of circles, ellipses, spheres, and ellipsoids. Compared to standard measurement techniques, the new algorithms provided the greatest accuracy and least shape-related bias for measurement of distance, surface area, and volume. Feasibility of using the new algorithms to measure physical objects was tested with CT images of spherical, egg-shaped, and irregular shaped objects. The Dividing Cubes algorithm was used to segment and create pointlists from the CT data. Volume and surface area measurements from CT data compared extremely well with reference values for most objects tested (errors less than 2%).