Efficient Computation of a Simplified Medial Axis

Journal of Computing and Information Science in Engineering

Volumn 3, Issue 4, 2003, Pages 274-284

  Foskey, Mark ^a   Lin, Ming C ^b   Manocha, Dinesh ^b  

^a UNIVERSITY OF NORTH CAROLINA SCHOOL OF MEDICINE   (United States)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR FUNCTION; VOLUME DISCRETIZATION;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER GRAPHICS; COMPUTER HARDWARE; ERROR ANALYSIS; FUNCTIONS; MATHEMATICAL MODELS;

MATRIX ALGEBRA;

EID: 1642484428     PISSN: 15309827     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1631582     Document Type: Conference Paper

References (36)

1. Blum, H., 1967, "A Transformation for Extracting New Descriptors of Shape," Models for the Perception of Speech and Visual Form, W. Wathen-Dunn, Ed. MIT Press, pp. 362-380.
2. Amenta, N., Choi, S., and Kolluri, R., 2001, "The Power Crust, " Proc. ACM Symposium on Solid Modeling and Applications, pp. 249-260.
3. Dey, T. K., and Zhao, W., 2002, "Approximate Medial Axis as a Voronoi Subcomplex," Proc. ACM Symposium on Solid Modeling and Applications, pp. 356-366.
4. Storti, D. W., Turkiyyah, G. M., Ganter, M. A., Lim, C. T., and Stal, D. M., 1997, "Skeleton-Based Modeling Operations on Solids," Proc. ACM Symposium on Solid Modeling and Applications, pp. 141-154.
5. Lam, L., Lee, S.-W., and Chen, C. Y., 1992. "Thinning Methodologies - A Comprehensive Survey," IEEE Trans. Pattern Anal. Mach. Intell., 14(9), pp. 869-885.
6. Zhang, Y. Y., and Wang, P. S. P., 1993, "Analytical Comparison of Thinning Algorithms," Int. J. Pattern Recognit. Artif. Intell., 7, pp. 1227-1246.
7. Danielsson, P. E., 1980, "Euclidean Distance Mapping," Computer Graphics and Image Processing, 14, pp. 227-248.
8. Ragnemalm, I., 1993, "The Euclidean Distance Transformation in Arbitrary Dimensions," Pattern Recogn. Lett., 14, pp. 883-888.
9. Vleugels, J., and Overmars, M., 1995, Approximating generalized Voronoi diagrams in any dimension, Tech. Rep. UU-CS-1995-14, Department of Computer Science, Utrecht University.
10. Hoff, K., Culver, T., Keyser, J., Lin, M., and Manocha, D., 1999, "Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware," Proc. ACM SIGGRAPH, pp. 277-286.
11. Siddiqi, K., Bouix, S., Tannenbaum, A., and Zucker, S. W., 1999, "The Hamilton-Jacobi Skeleton," International Conference on Computer Vision, pp. 828-834.
12. Etzion, M., and Rappoport, A., 1999, "Computing the Voronoi Diagram of a 3-D Polyhedron by Separate Computation of its Symbolic and Geometric Parts," Proc. ACM Symposium on Solid Modeling and Applications, pp. 167-178.
13. Milenkovic, V., 1993, "Robust Construction of the Voronoi Diagram of a Polyhedron." Proc. 5th Canad. Conf. Comput. Geom., pp. 473-478.
14. Reddy, J., and Turkiyyah, G., 1995, "Computation of 3D Skeletons Using a Generalized Delaunay Triangulation Technique," Comput.-Aided Des., 27, pp. 677-694.
15. Chiang, C.-S., 1992, "The Euclidean distance transform," Ph.D. Thesis, Dept. Comput. Sci., Purdue Univ., West Lafayette, IN, Aug, Report CSD-TR 92-050.
16. Sherbrooke, E. C., Patrikalakis, N. M., and Brisson, E., 1995, "Computation of the Medial Axis Transform of 3-D Polyhedra," Proc. ACM Symposium on Solid Modeling and Applications, pp. 187-199.
17. Culver, T. Keyser, J., and Manocha, D., 1999, "Accurate Computation of the Medial Axis of a Polyhedron," Proc. ACM Symposium on Solid Modeling and Applications, pp. 179-190.
18. Dutta, D., and Hoffmann, C. M., 1990, "A Geometric Investigation of the Skeleton of CSG Objects," Proc. ASME Conf. Design Automation.
19. Hoffmann, C. M., 1990, "How to Construct the Skeleton of CSG Objects," Proc. 4th IMA Conf. on the Mathematics of Surfaces, Oxford University Press.
20. Boissonnat, J.-D., 1984, "Geometric Structures for Three-Dimensional Shape Representation," ACM Trans. Graphics, 3(4), pp. 266-286.
21. Dey, T. K., and Zhao, W., 2002, "Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee," European Symposium on Algorithms, pp. 387-398.
22. Turkiyyah, G. M., Storti, D. W., Ganter, M., Chen, H., and Vimawala, M., 1997, "An Accelerated Triangulation Method for Computing the Skeletons of Free-Form Solid Models," Comput.-Aided Des., 29(1), pp. 5-19.
23. Attali, D., and Boissonnat, J., 2002, "A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces, " Proc. ACM Symposium on Solid Modeling and Applications, pp. 139-146.
24. August, J., Tannenbaum, A., and Zucker, S., 1999, "On the Evolution of the Skeleton," Proc. of Int. Conf. on Computer Vision.
25. Attali, D., and Montanvert, A., 1997, "Computing and Simplifying 2D and 3D Continuous Skeletons," Comput. Vis. Image Underst., 67(3), pp. 261-273.
26. Boissonnat, J.-D., and Cazals, F., 2000. "Smooth Surface Reconstruction Via Natural Neighbor Interpolation of Distance Functions," Proc. ACM Symposium on Computational Geometry, pp. 223-232.
27. Styner, M., Gerig, G., Joshi, S., and Pizer, S., 2003, "Automatic and Robust Computation of 3D Medial Models Incorporating Object Variability," Int. J. Comput. Vis. 55, pp. 107-122.
28. Choi, S. W., and Seidel, H.-P., 2002, "Linear Onesided Stability of MAT for Weakly Injective 3D Domain," Proc. ACM Symposium on Solid Modeling and Applications, pp. 344-355.
29. Larsen, E., Gottschalk, S., Lin, M., and Manocha, D., 1999, "Fast Proximity Queries with Swept Sphere Volumes." Tech. Rep. TR99-018, Department of Computer Science, University of North Carolina. 32 pages.
30. Taubin, G., 1995, "A Signal Processing Approach to Fair Surface Design," Proc. ACM SIGGRAPH, pp. 351-358.
31. Wilmarth, S. A., Amato, N. M., and Stiller, P. F., 1999, "Motion Planning for a Rigid Body Using Random Networks on the Medial Axis of the Free Space," Proc. ACM Symposium on Computational Geometry, pp. 173-180.
32. Choi, H. I., Choi, S. W., and Moon, H. P., 1997, "Mathematical Theory of Medial Axis Transform," Pac. J. Math., 181(1), pp. 56-88.
33. Donaghy, R. J., McCune. W., Bridgett, S. J., Armstrong, C. G., Robinson, D. J., and McKeag, R. M., 1996, "Dimensional Reduction of Analysis Models," 5th International Meshing Roundtable, pp. 307-320.
34. Suresh, K., 2003, "Automating the CAD/CAE Dimensional Reduction Process," Proc. ACM Symposium on Solid Modeling and Applications, pp. 76-85.
35. Armstrong, C. G., Robinson, D. J., McKeag, R. M., Li, T. S., Bridgett, S. J., Donaghy, R. J., and McGleenan, C. A., 1995, "Medials for Meshing and More," 4th International Meshing Roundtable, pp. 277-288.
36. Quadros, W. R., Ramaswami, K., Prinz, F. B., and Gurumoorthy, B., 2000, "LayTracks: A New Approach to Automated Quadrilateral Mesh Generation using MAT," 9th International Meshing Roundtable, pp. 239-250.