Approximation of surfaces in quantitative 3-D reconstructions

In serial section reconstructions, a series of planar profiles are taken representing curves on the surface of the structure to be reconstructed. For a number of quantitative serial section methods, approximation of a surface is done by the formation of tiles between points of adjacent profiles. As generally proposed, finding this approximation has been difficult due to the inordinately large number of possible solutions resulting from different combinations of tiles between points. Current algorithms have either applied heuristic criteria to force the formation of only one solution, or have searched all acceptable combinations for one that minimizes some cost function. The algorithm presented has been developed to choose the tiling which minimizes the estimated error when the tile approximation of the surface is used in subsequent quantitative algorithms such as the calculation of surface area.