Lattice points enumeration for image coding

Proceedings - 1999 International Conference on Information Intelligence and Systems, ICIIS 1999

Volumn , Issue , 1999, Pages 482-489

  Serra Sagristà, Joan ^a   Borrell, Joan ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE COMPRESSION; MATHEMATICAL TRANSFORMATIONS;

COMPRESSION SCHEME; FINITE BOUNDARY; GEOMETRIC PROPERTIES; IMAGE STATISTICS; LATTICE BOUNDARY; MINIMUM DISTORTIONS; MODEL TRANSFORMS; VECTOR QUANTIZERS;

IMAGE CODING;

EID: 0005203861     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICIIS.1999.810319     Document Type: Conference Paper

References (32)

1. J. Barlaud, P. Sole, T. Gaidon, M. Antonini, and P. Mathieu. Pyramidal lattice vector quantization for multiscale image coding. IEEE Transactions on Image Processing, 3(4):367-380, 1994.
2. F. Chen, Z. Gao, and J. Villasenor. Lattice vector quantization of generalized gaussian sources. IEEE Transactions on Information Theory, IT-43(1):92-103, 1997.
3. J. Conway and N. Sloane. A fast encoding method for lattice codes and quantizers. IEEE Transactions on Information Theory, IT-29(6):820-824, 1983.
4. J. Conway and N. Sloane. Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice. IEEE Transactions on Information Theory, IT-32(l):41-50, 1986.
5. J. Conway and N. Sloane. Sphere Packings, Lattices and Groups, volume 290 of Grundlehren der mathematischen Wissenschaften. Springer Verlag, New York, USA, 1992.
6. J. Conway and N. Sloane. Low-dimensional lattices VII: Coordination sequences. Proc. Royal Soc. London, Series A, 453:2369-2389, 1997.
7. J. Conway and N. J. Sloane. Fast quantizing and decoding algorithms for lattice quantizers and codes. IEEE Transactions on Information Theory, IT-28(2):227-232, March 1982.
8. T. Fischer. A pyramid vector quantizer. IEEE Transactions on Information Theory, IT-32(4):568-583, 1986.
9. T. Fischer. Geometric source coding and vector quantization. IEEE Transactions on Information Theory, IT-35(1): 137-145, 1989.
10. T. Fischer and Z. Mohdyusof. Subband image coding using a fixed-rate lattice vector quantizer. In Proceedings IEEE International Conference on Image Processing, volume I of III, pages 101-105. IEEE Signal Processing Society, IEEE Computer Society Press, October 1995.
11. T. Fischer and J. Pan. Enumeration encoding and decoding algorithms for pyramid cubic lattice and trellis code. IEEE Transactions on Information Theory, IT-41(6):2056-2061, 1995.
12. G. Forney Jr. Coset codes I: Introduction and geometrical classification. IEEE Transactions on Information Theory, IT-34(Sept.): 1123-1151, 1988.
13. G. Forney Jr. Coset codes II: Binary lattices and related codes. IEEE Transactions on Information Theory, IT-34(Sept.):l 152-1187, 1988.
14. A. Gersho. Asymptotically optimal block quantization. IEEE Transactions on Information Theory, IT-25(4):373-380, 1979.
15. A. Gersho. On the structure of vector quantizers. IEEE Transactions on Information Theory, IT-28(2): 157-166, March 1982.
16. A. Gersho and R. M. Gray. Vector Quantization and Signal Compression. Kluwer Academic Publisher, Boston, USA, 1992.
17. J. Gibson and K. Sayood. Advances in Electronics and Electron Physics, volume 72, chapter Lattice quantization, pages 259-332. Academic Press, 1988.
18. B. Girod and T. Senoo. Vector quantization for entropy coding of image subbands. IEEE Transactions on Image Processing, 1(4):526-532, 1992.
19. R. Graham, D. Knuth, and O. Patashnik. Concrete mathematics: a foundation for computer science. Addison-Wesley, USA, sixth edition, 1990.
20. R. M. Gray and D. L. Neuhoff. Quantization. IEEE Transactions on Information Theory, IT-44(6):2325-2383, 1998. Invited paper.
21. H. Klock, J. Serra-Sagrista, and J. Buhmann. Conditional wavelet coding techniques in image and video compression. In preparation, 1999.
22. W. Li, H. Cao, S. Li, F. Ling, S. Segan, H. Sun, J. Wus, and Y. Zhang. A video coding algorithm using vector-based techniques. IEEE Transactions on Circuits and Systems for Video Technology, 7(1): 146-157, 1997.
23. H. Marshall. Combinatorial Theory. Discrete Mathematics. John Wiley & Sons, USA, 1986.
24. P. W. Moo. Asymptotic analysis of lattice-based quantization. PhD thesis, University of Michigan, Adviser: Prof. David L. Neuhoff, 1998.
25. M. Petkovsek, H. Wilf, and D. Zeilberger. A=B. AK Peters, Ltd., Wellesley, MA, USA, January 1996.
26. J. Riordan. Combinatorial Identities. Tracts on Probability and Statistics. John Wiley & Sons, USA, 1968.
27. J. Serra-Sagrista. On counting lattice points in pyramids. Submitted for publication to Discrete Mathematics, Elsevier, 1999.
28. J. Serra-Sagrista. On combinatorial equalities of coordination sequences. In Proc. of FPSAC '99 (11th International Conference on Formal Power Series and Algebraic Combinatorics), pages 519-529, Barcelona (Catalonia), June 1999.
29. M. Shnaider and A. Papliriski. Image coding through D lattice quantization of wavelet coefficients. Graphical Models and Image Processing, 59(4): 193-294, 1997.
30. P. Sole. Counting lattice points in pyramids. Discrete Mathematics, 139(1-3, May):381-392, 1995.
31. C. Wang, H. Cao, W. Li, and K. Tzeng. Lattice labeling algorithms for vector quantization. IEEE Transactions on Circuits and Systems for Video Technology, 8(2):206-220, 1998.
32. H. S. Wilf. The 'snake oil' method for proving combinatorial identities. In J. Siemons, editor, Surveys in Combinatorics, volume 141 of London Mathematical Society Lecture Note Series, pages 208-217, Great Britain, 1989. London Mathematical Society, Cambridge University Press.