2925	 Optimal Surface Reconstruction from Planar Contours	 In many scientific and technical endeavors a three-dimensional solid must be reconstructed from serial sections either to aid in the comprehension of the object s structure or to facilitate its automatic manipulation and analysis. This paper presents a general solution to the problem of constructing a surface over a set of cross-sectional contours. This surface to be composed of triangular tiles is constructed by separately determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum cost cycles in a directed toroidal graph. A new fast algorithm for finding such cycles is utilized. Also developed is a closed-form expression in term of the number of contour poin ts for an upper bound on the number of operations required to execute the algorithm. An illustrated example which involves the construction of a minimum area surface describing a human head is included. surface reconstruction contour data serial sections three-dimensional computer graphics minimum cost paths continuous tone displays
