Optimal surface reconstruction from planar contours

Abstract

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 terms of the number of contour points, 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.

A mean three-dimensional atlas of the human thalamus: Generation from multiple histological data

“…Surface-tiling (Fuchs et al, 1977) reconstructs meshes by triangulating outlines of adjacent sections. While the algorithm produces topologically correct meshes for thin or elongated structures, it relies on the fact that the outlines are parallel.…”

Polyhedral perturbations that preserve topological form

“…In many applied fields, including tolerancing and metrology (Hillyard and Braid, 1978a;Hillyard and Braid, 1978b;Gossard et al, 1988;Jayaraman and Srinivasan, 1989;Srinivasan and Jayaraman, 1989;Rossignac and Requicha, 1986;Boyer and Stewart, 1991;Boyer and Stewart, 1992;Stewart, 1993), solid modeling (M~intyl~i, 1988, p.110), engineering design (Heisserman and Woodbury, 1992), finite element analysis (Kumar and Gossard, 1992), surface reconstruction (Hoppe et al, 1993), computer graphics (Edelsbrunner and Miicke, 1994), path planning in robotics (Latombe, 1991, p. 91), fairing procedures (Rando and Roulier, 1991), image analysis (Serra, 1982, p. 69), and medical imaging (Peters et al, 1992;Fuchs, 1977), it is natural to require that a perturbed object should have the same topological form as a given original object S.…”

Recent development on computer aided tissue engineering — a review

“…However, the transformation from contours to surface is more problematic, often requiring operator guidance in connecting contours from adjacent slices [93]. More sophisticated use of contouring employs methods adapted from computer graphics to blend adjacent contours into a solid surface similar to the popular graphics process called morphing.…”