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Tree Triangular Coding Image Compression Algorithms

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Lossy Image Compression

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Abstract

This chapter presents four new image compression algorithms namely, Three-triangle decomposition scheme, Six-triangle decomposition scheme, Nine-triangle decomposition scheme and the Delaunay Triangulation Scheme. Performance of these algorithms is evaluated using standard test images. The asymptotic time complexity of Three-, Six-, and Nine-triangle decomposition algorithms is the same: O(nlogn) for coding and θ(n), for decoding. The time complexity of the Delaunay triangulation algorithm is O(n 2 logn) for coding and O(nlogn) for decoding, where n is the number of pixels in the image.

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References

  1. Distasi R, Nappi M, Vitulano S (1997) Image compression by B-tree triangular coding. IEEE Trans Commun 45(9):1095–1100

    Article  Google Scholar 

  2. Dimento LJ, Brekovich SY (1990) The compression effects of the binary tree overlapping method on digital imagery. IEEE Trans Commun 38:1260–1265

    Article  Google Scholar 

  3. Radha H, Leonadi R, Vetterli M (1991) A multiresolution approach to binary tree representation of Images. Proc ICASSP 91:2653–2656

    Google Scholar 

  4. Strobach P (1989) Image coding based on quadtree–structured recursive least squares approximation. Proc IEEE ICAASP 89:1961–1964

    Google Scholar 

  5. Wu X (1992) Image coding by adaptive tree-structured segmentation. IEEE Trans Inf Theory 38(6):1755–1767

    Article  MATH  Google Scholar 

  6. Davoine F, Svensson J, Chassery J-M (1995) A mixed triangular and quadrilateral partition for fractal image coding. In: Proceedings of the international conference on image processing (ICIP ‘95)

    Google Scholar 

  7. VC Da Silva, JM De Carvalho (2000) Image compression via TRITREE decomposition. In: Proceedings of the XIII Brazilian symposium on computer graphics and image processing (SIBGRAPI)

    Google Scholar 

  8. Li X, Knipe J, Cheng H (1997) Image compression and encryption using tree structures. Pattern Recogn Lett 18:1253–1259

    Article  Google Scholar 

  9. Kotlov A (2001) Note: tree width and regular triangulations. Discret Math 237:187–191

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu X, Fang Y (1995) A segmentation-based predictive multiresolution image coder. IEEE Trans Image Process 4:34–47

    Article  Google Scholar 

  11. Radha H, Vetterli M, Leonardi R (1996) Image compression using binary space partitioning trees. IEEE Trans image process 5(12):1610–1623

    Article  Google Scholar 

  12. Samet H (1984) The quadtree and related Hierarchical data structures. ACM Comput Surv 16(2):187–260

    Article  MathSciNet  Google Scholar 

  13. Babuska I, Aziz AK (1976) On the angle condition in the finite element method. Siam J Numer Anal 13(2):214–226

    Article  MathSciNet  MATH  Google Scholar 

  14. Rippa S (1992) Long and thin triangles can be good for linear interpolation. Siam J Numer Anal 29(1):257–270

    Article  MathSciNet  MATH  Google Scholar 

  15. Plaza A, Rivara M-C (2002) On the adjacencies of triangular meshes based on skeleton-regular partitions. J Comput Appl Math 140:673–693

    Article  MathSciNet  MATH  Google Scholar 

  16. Mitchell SA (1997) Approximating the maximum-angle covering triangulation. Comput Geom 7:93–111

    Article  MathSciNet  MATH  Google Scholar 

  17. Szelinski R (1990) Fast surface interpolation using hierarchical basis functions. IEEE Trans Pattern Anal Mach Intell 12:513–528

    Article  Google Scholar 

  18. Vreelj B, Vaidyanathan PP (2001) Efficient implementation of all digital interpolation. IEEE Trans image process 10(11):1639–1646

    Article  Google Scholar 

  19. Li J, Chen CS (2002) A simple efficient algorithm for interpolation between different grids in both 2D and 3D. Math Comput Sim 58:125–132

    Article  MATH  Google Scholar 

  20. Chuah C-S, Leou J-J (2001) An adaptive image interpolation algorithm for image/video processing. Pattern Recogn 34:2383–2393

    Article  MATH  Google Scholar 

  21. Boissonnant JD, Cazals F (2002) Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comput Geom 22:185–203

    Article  MathSciNet  Google Scholar 

  22. Antonini M, Barlaud M, Mathieu P, Daubechies I (1992) Image coding using the wavelet transform. IEEE Trans Image Process 1(2):205–220

    Article  Google Scholar 

  23. Vore BAD, Jawerth B, Lucien BJ (1992) Image compression through wavelet transform coding. IEEE Trans Inf Theory 38:719–746

    Article  Google Scholar 

  24. Jacquin AE (1992) Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans Image Process 1:18–30

    Article  Google Scholar 

  25. Helsingius M, Kuosmanen P, Astola J (2000) Image compression using multiple transforms. Signal Process Image Commun 15:513–529

    Article  Google Scholar 

  26. Prasad MVNK, Mishra VN, Shukla KK (2003) Space partitioning based image compression using quality measures. Appl Soft Comput Elsevier Sci 3:273–282

    Article  Google Scholar 

  27. Bramble JH, Zlamal M (1970) Triangular elements in the finite elements method. Math Comput 24(112):809–820

    Article  MathSciNet  Google Scholar 

  28. Waldron S (1998) The error in linear interpolation at the vertices of a simplex. Siam J Numer Anal 35:1191–1200

    Article  MathSciNet  MATH  Google Scholar 

  29. Aurenhammer F (1991) Voronoi diagrams—a survey of a fundamental geometric data structure. ACM Comput Surv 23(3):345–405

    Article  Google Scholar 

  30. Guibas L, Stolfi J (1985) Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams. ACM Trans Graph 4(2):74–123

    Article  MATH  Google Scholar 

  31. Su P, Drysdale RLS (1995) A comparison of sequential delaunay triangulation algorithms, 1lth Symposium computational geometry, Vancouver, B.C. Canada, pp 61–70

    Google Scholar 

  32. Shewchuk JR (1999) Lecture notes on delaunay mesh generation. University of California, Berkeley, p 20

    Google Scholar 

  33. Letrattanapanich S, Bose NK (2002) High resolution image formation from low resolution frames using delaunay triangulation. IEEE Trans Image Process 11(12):1427–1441

    Article  MathSciNet  Google Scholar 

  34. Davoine F, Antonini M, Chassery J-M, Barlaud M (1996) Fractal image compression based on delaunay triangulation and vector quantization. IEEE Trans Image Process 5(2):338–346

    Article  Google Scholar 

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Correspondence to K. K. Shukla .

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Shukla, K.K., Prasad, M.V. (2011). Tree Triangular Coding Image Compression Algorithms. In: Lossy Image Compression. SpringerBriefs in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-2218-0_2

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  • DOI: https://doi.org/10.1007/978-1-4471-2218-0_2

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  • Online ISBN: 978-1-4471-2218-0

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