Cyclic Interlaced Quadtree Algorithms for Quincunx Multiresolution

Journal of Algorithms

Volumn 27, Issue 1, 1998, Pages 97-128

  Hebert, D J ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001974159     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.1998.0925     Document Type: Article

References (29)

1. H. S. M. Coxeter, "Regular Polytopes," Dover, New York, 1973.
2. K. Georg, Generation of triangulations by reflections, Utilitas Math. 16 (1979), 123-129.
3. H. Sagan, "Space Filling Curves," Springer-Verlag, Berlin/New York, 1994.
4. M. C. Rivara, Mesh refinement processes based on the generalized bisection of simplices, SIAM J. Numer. Anal. 21 (1984), 604-613.
5. J. M. Maubach, "Iterative Methods for Non-linear Partial Differential Equations," N.W.O. Center for Mathematics and Computer Science, Amsterdam, 1991 (ISBN 90-9004007-2).
6. J. M. Maubach, Local bisection refinement for n-simplicial grids generated by reflections, SIAM J. Sci. Comput. 16 (1995), 210-227.
7. D. J. Hebert, Symbolic local refinement of tetrahedral grids, J. Symbolic Comput. 17 (1994), 457-472.
8. H. Samet, "Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS," Addison-Wesley, Reading, MA, 1989.
9. G. Dutton, Locational properties of quaternary triangular meshes, in "Proceedings of the Fourth International Symposium on Spatial Data Handling, Zurich, 1990," pp. 901-910.
10. M. F. Goodchild and Y. Shiren, A hierarchical spatial data structure for global geographic information systems, CVGIP: Graphical Models and Image Processing, 54 (1992), 33-41.
11. G. Fekete, Rendering and Managing Spherical Data with Sphere Quadtrees, in "Proceedings of Visualization 90, San Francisco, 1990."
12. H. K.-C. Chang and C.-Y. Liou, Parallel implementation of linear quadtree codes using the n Cube 2 supercomputer system, Internat. J. Supercomputer Appl. 9 (1995), 220-231.
13. P. Zwart, Multivariate splines with nondegenerate partitions, SIAM J. Numer. Anal. 10 (1973), 665-673.
14. C. de Boor, K. Höllig, and S. Riemenschnieder, "Box Splines," Springer-Verlag, Berlin/New York, 1993.
15. I. Daubechies, "Ten Lectures on Wavelets #61," CBMS-NSF Conference Series in Applied Mathematics, SIAM, Philadelphia, 1992.
16. A. Cohen and I. Daubechies, Non-separable bidimensional wavelet bases, Rev. Math. Iberoamericana 9 (1993), 51-137.
17. d), Math. Comp., to appear.
18. E. P. Simoncelli and E. H. Adelson, Non-separable extensions of quadrature mirror filters to multiple dimensions, Proc. IEEE 78 (1990), 652-663.
19. J. Kovacevic and M. Vetterli, Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for R", IEEE Trans. Inform. Theory. 28 (1992), 533-555.
20. D. J. Hebert, A box spline subdivision pyramid algorithm, Appl. Math. Lett., to appear.
21. D. J. Hebert and H. J. Kim, Image encoding with triangulation wavelets, Proc. SPIE 2569 (1995), 381-392.
22. J. A. Provine and R. M. Ragayyan, Lossless compression of peanoscanned images, J. Electronic Imaging 3 (1994), 176-181.
23. H. J. Kim, "Unified Image Compression Using Reversible and Fast Biorthogonal Wavelet Transforms," thesis, University of Pittsburgh, 1996.
24. G. Strang and T. Nguyen, "Wavelets and Filter Banks," Wellesley-Cambridge Press, 1996.
25. E. R. Dougherty and R. Giardina, "Image Processing - Continuous to Discrete," Vol. 1, 1987.
26. D. J. Hebert and H. J. Kim, A fast-wavelet compass edge detector, Proc. SPIE 2825 (1996), 432-442.
27. A. P. Schröder and W. Sweldens, Spherical wavelets: Efficiently representing functions on the sphere, Computer Graphics Proceedings (SIGGRAPH 95) pp. 161-172, ACM, 1995.
28. M. Girardi and W. Sweldens, A new class of unbalanced Haar wavelets that form an unconditional basis for Lp on general measure spaces, J. Fourier Anal. Appl., to appear.
29. C. K. Chui, K. Jetter, and J. Stöckler, Wavelets and frames on the four-directional mesh, in "Wavelets, Theory, Algorithms, and Applications," (C. K. Chui, L. Montejusco, and L. Puccio, Eds.), pp. 213-230, 1994.