3-D MICROSTRUCTURE GENERATION OF FRUIT TISSUE USING A NOVEL ELLIPSOID TESSELLATION ALGORITHM

A novel algorithm for the 3-D geometric tissue reconstruction from 2-D slices of synchrotron tomographic images was developed. The boundaries of 2-D cells on individual slices were digitized by an in-house software program written in Matlab (The Mathworks, Natick, MA) to establish the coordinates and the slice index of individual cells. Then, ellipsoids that fit these sets of points were determined using a Least Squared Fitted Ellipsoids (LSFEs) algorithm. The latter algorithm is the modified version of Minimum Volume Circumscribing Ellipsoid (MVCE) algorithm that produces minimum volume ellipsoids that enclose all points in a set. Using LSFEs, the size of the MVCEs were optimized to fit the set of points in a least square sense. The 3-D model tissue geometry was then generated from these sets of ellipsoids, which were truncated when neighboring volumes overlapped. As a result, a virtual three-dimensional microstructure consisting of truncated ellipsoids fills up the entire three-dimensional volume with the same number and size of cells and void spaces as that of the tomographic images. The LSFEs were interfaced in to ANSYS 11 (ANSYS, Inc., Canonsburg, PA) for finite volume geometric reconstruction and meshing.