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Surface Reconstruction by Multiaxial Triangulation
November/December 1994 (vol. 14 no. 6)
pp. 28-35

Outlines for reconstructing object surfaces are traditionally drawn from sequential images in parallel planes. The method presented here instead supports complex object topologies by drawing contours from multiaxial image planes. Multiaxial triangulation of an object in a given data volume involves four steps. First, the user generates contours interactively by selecting sample planes inside the data volume, then drawing object contours from the image corresponding to this sample plane. Our algorithm for multiaxial triangulation then processes these contours to verify consistency within and between sample planes. Second, it uses the sample planes containing the contours to partition the data volume into a divided volume. The contours are partitioned against the plane boundaries, and the contour parts (chains) are associated with faces, edges, and vertices in the divided volume. Third, these chains are joined into closed loops in the divided volume. Fourth, the loops are triangulated patchwise to create the surface model.

1. C. Levinthal and R. Ware, "Three-Dimensional Reconstruction from Serial Sections,"Nature, Vol. 236, No. 5,344, 1972, pp. 207-210.
2. S. Ganapathy and T.G. Dennehy, "A New General Triangulation Algorithm for Planar Contours,"ACM Trans. Graphics, Vol. 10, No. 2, Apr. 1991, pp. 182-199.
3. H. Fuchs. Z. M. Kedem, and S. P. Uselton, "Optimal surface reconstruction from planar contours,"Commun. ACM, vol. 20, Oct. 1977.
4. E. Keppel, "Approximating Complex Surfaces by Triangulation of Contour Lines,"IBM J. Research and Development, Vol. 19, No. 1, Jan. 1975, pp. 2-11.
5. J.D. Boissonnat, "Shape Reconstruction from Planar Cross Sections,"Computer Vision, Graphics, and Image Processing, Vol. 41, No. 1, 1988, pp. 1-29.
6. Y. Shinagawa, T.L. Kunii, and Y.L. Kergosien, "Surface Coding Based on Morse Theory,"IEEE CG&A, Vol. 11, No. 5, Sept. 1991, pp. 66-78.
7. Y. Shinagawa and T.L. Kunii, "Constructing a Reeb Graph Automatically from Cross Sections,"IEEE CG&A, Vol. 11, No. 6, Nov. 1991, pp. 44-51.
8. H.N. Christiansen and T.W. Sederberg, "Conversion of Complex Contour Line Definitions into Polygonal Element Mosaics,"Computer Graphics(Proc. SIGGRAPH), Vol. 12, No. 3, Aug. 1978, pp. 187-192.
9. M. Shantz, "Surface Definition for Branching, Contour-Defined Objects,"Computer Graphics, Vol. 15, No. 2, 1981, pp. 242-258.
10. S. Ganapathy and T.G. Dennehy, "A New General Triangulation Algorithm for Planar Contours,"ACM Trans. Graphics, Vol. 10, No. 2, Apr. 1991, pp. 182-199.
11. M. Mäntylä,An Introduction to Solid Modeling, Computer Science Press, Rockville, Md., 1988.
12. A. Fournier and D. Y. Montuno, "Triangulating simple polygons and equivalent problems,"ACM Trans. Graphics, vol. 3, no. 2, pp. 153-174, Apr. 1984.

Citation:
Bradley A. Payne, Arthur W. Toga, "Surface Reconstruction by Multiaxial Triangulation," IEEE Computer Graphics and Applications, vol. 14, no. 6, pp. 28-35, Nov.-Dec. 1994, doi:10.1109/38.329091
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