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 crosssectional 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 illustrative example which involves the construction of a minimum area surface describing a human head is included.

Interactive manipulation of three dimensional binary scenes

“…1981) of the same has 144948 faces and hence requires 579792 bytes to store it. The surface representation developed by (Fuchs et al 1977) will perhaps contain fewer polygon but each polygon will need much more than four bytes to store it. Moreover these representations as well as other representations mentioned in Sect.…”

“…Once the scene has been segmented, the process of obtaining the shaded display and/or manipulation depends largely on its representation. Various schemes for encoding 3D binary scenes such as octrees (Srihari 1981), surface representation (Artzy et al 1981 ;Fuchs et al 1977), and contour representation (Tuy and Udupa 1983), have been extensively studied. A desirable representation will be concise, easy to decode/encode, and efficacious from the viewpoint of the particular application such as display, manipulation and quantitative analysis.…”

Graph-directed modelling from serial sections

“…Most of the work in this area focuses on reliable and efficient algorithms for computing a 3D-surface segment between two successive contours (Keppel 1975, Fuchs et al 1977, Christiansen and Sederberg 1978, Ganapathy and Dennehy 1982. Because a set of adjacent triangles approximates the surface segment, they are called triangulation algorithms.…”

A heuristic triangulation algorithm for multiple planar contours using an extended double branching procedure

“…A cost function, devised to obtain the maximum volume polyhedron, is assigned to each arc of the graph, and an optimal solution with respect to the criterion is obtained by finding an optimum path in this graph. Fuchs et al (1977) also reduced the surface generation problem to the problem of finding certain minimum cost cycles in a directed toroidal graph. The cost assigned to an arc was the area of the associated triangular surface tile, so that the resulting surface was the one with the minimum total surface area.…”