Bibliography

1

D. B. Karron, J. Cox, and B. Mishra, ``New findings from the spiderweb algorithm : Toward a digital morse theory,'' in Visualization in Biomedical Computing - '94 (R. A. Robb, ed.), no. 2359 in SPIE Proceedings, pp. 643-657, SPIE, SPIE, Oct. 1994.

2

D. B. Karron and J. Cox, ``Extracting 3D objects from volume data using digital morse theory,'' in Computer Vision, Virtual Reality and Robotics in Medicine (N. Ayache, ed.), no. 905 in Lecture Notes in Computer Science, (New York, NY), pp. 481-486, INRIA, INSERM, ECV net, Springer-Verlag, 1995.

3

D. Karron and J. Cox, ``Digital morse theory for anatomic modeling,'' Proceedings of IEEE BMES-EMBS first joint conference, 10 1999.

4

H. Carr, J. Snoeyink, and U. Axen, ``Computing Contour Trees in All Dimensions,'' Symposium on Discrete Algorithms 2000, p. to appear, 2000.

5

M. vanKreveld, R. vanOostrum, C. Bajaj, V. Pascucci, and D. Schikore, ``Contour Trees and Small Seed Sets for Isosurface Traversal,'' Proceedings 13th Ann ACM Symposium on Computational Geometry, pp. 212-220, 1996.

6

S. P. Tarasov and M. N. Vyalyi, ``Construction of contour trees in 3d in o(n log n) steps,'' Proceedings 14th Ann ACM Symposium on Computational Geometry, pp. 68-75, 1998.

7

D. Karron, J. Cox, and B. Mishra, ``System and Method for Surface Rendering of Internal Structures within the Interior of a Solid Object. .'' United States Patent 5,898,793, Apr. 1999.

8

A. Kaufman, ed., Volume Visualization.
IEEE Computer Society Press Tutorial, Los Alamitor, California: IEEE Computer Society Press, 1991.

9

N. Max, ``Optical models for direct volume rendering,'' IEEE Transcations on Visualization and Computer Graphics, vol. 1, June 1995.

10

C. Silva and A. Kaufman, ``PVR: High Performance Volume Rendering,'' IEEE Computational Science and Engineering 1996, 1996.

11

W. E. Lorensen and H. E. Cline, ``Marching Cubes: A High Resolution 3D Surface Construction Algorithm,'' ACM Computer Graphics, vol. 21, pp. 163-169, July 1987.

12

A. Guéziec and R. Hummel, ``Exploiting Triangulated Surface Extraction Using Tetrahedral Decomposition,'' IEEE Transactions on Visualization and Computer Graphics, vol. 1, no. 4, pp. 328-342, 1995.

13

J. L. Cox, D. B. Karron, and B. Mishra, ``The SpiderWeb Algorithm for Surface Construction from Medical Volume Data: Geometric Properties of its Surface,'' Innovations Et Technologie en Biologie et Medecine, vol. 14, pp. 634-656, Nov. 1993.

14

A. Guezic and R. Hummel, ``Exploiting triangulated isosurface extraction using tetrahedral decomposition,'' IEEE Transactions on Visualization and Computer Graphics, vol. 1, December 1995.

15

H. E. Cline, C. L. Dumoulin, H. R. H. Jr., and W. E. Lorensen, ``3D Reconstruction of the Brain from Magnetic Resonance Images Using a Connectivity Algorithm,'' Magnetic Resonance Imaging, vol. 5, pp. 345-352, July 1987.

16

K. Whang, J. Song, J. Chang, J. Kim, W. Cho, C. Park, and I.Y.Song, ``Octree-r: An adaptive octree for efficient ray tracing,'' IEEE Transactions on Visualization and Computer Graphics, vol. 1, July 1995.

17

J. Wilhelms and A. V. Gelder, ``Octrees for faster isosurface generation,'' ACM Transactions on Graphics, vol. 11, pp. 201-227, July 1992.

18

T. Itoh and K. Koyamada, ``Automatic isosurface propagation using an extrema graph and sorted boundary cell lists,'' IEEE Transactions on Visualization and Computer Graphics, vol. 1, December 1995.

19

R. Gallagher, ``Span filter: An optimization scheme for volume visualization of large finite element models,'' Proceedings of Visualization '91, 1991.

20

H. Shen and C. Johnson, ``Sweeping simplices: A fast isosurface extraction algorithm for unstructured grid,'' Proceedings on Visualization '95, 1995.

21

Y.Livnat, H. Shen, and C. Johnson, ``A near optimal isosurface extraction algorithm using the span space,'' IEEE Transactions on Visualization and Computer Graphics, vol. 2, March 1996.

22

P. Cignoni, P. Marino, C. Montani, E. Puppo, and R. Scopigno, ``Speeding up isosurface extraction using interval tree,'' IEEE Transcations on Visualization and Computer Graphics, vol. 3, April-June 1997.

23

Y. Chiang and C. Silva, ``I/O Optimal IsoSurface Extraction,'' IEEE Visualization 1997, pp. 293-300, 1997.

24

G. M. Nielson and B. Hamann, ``The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes,'' in Proceedings of Visualization 91 (G. M. Nielson and L. Rosenblum, eds.), vol. 2, pp. 83-91, 1991.

25

W. J. Schroeder, J. A. Zarge, and W. E. Lorensen, ``Decimation of triangle meshes,'' ACM Computer Graphics, vol. 26, pp. 65-70, July 1992.

Figure 1: Possible isosurface intersections with cube face.

Figure 2: The ambiguous face is the center face in 2 stacked cubes. Left-noncritical disambiguation point with sample object, Right-critical disambiguation point with sample object

Figure 3: dodo in your eye

Figure 4: A- The triangle edge from an AP to a hit shared by 2 triangles. B- The edge across a face shared by 2 triangles. C- A hit is locally a triangulation of the circle.