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.
CACM October, 1977
Fuchs, H.
Kedem,Z. M.
Uselton, S. P.
