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Two High Speed Quantization Algorithms

This paper presents innovative high-speed quantization algorithms developed by Luc Brun and Myriam Mokhtari at Reims University. It delves into various quantization methods including top-down, bottom-up, and split & merge strategies aimed at significantly reducing color numbers from 141,000 to 16. The discussion highlights the effectiveness of creating clusters, computing means, and implementing an inverse colormap dithering approach. Results demonstrate substantial improvements in both image quality and computing speed compared to existing methods. It concludes with suggestions for future enhancements in uniform quantization and heuristic approaches.

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Two High Speed Quantization Algorithms

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  1. Two High Speed Quantization Algorithms Luc Brun Myriam Mokhtari L.E.R.I. Reims University (I.U.T.)

  2. Contents • Quantization algorithms • Our Methods • Discussion

  3. Quantization algorithms • Reduce the number of colours Number of colours: 141,000 Number of colours: 16

  4. Quantization Algorithms • Applications • Display • Compression • Classification • Segmentation

  5. Quantization steps • Create clusters

  6. Quantization steps • Create clusters: • Squared error • Partition error

  7. Quantization steps • Create clusters • Compute means

  8. Quantization steps • Create clusters • Compute means • Create output image (inverse colormap) Inverse colormap dithtering Quantization

  9. Type of quantization methods • Three kind of Methods • Top-down • Bottom-up • Split & Merge

  10. Top-down methods • Recursive split of the image color set

  11. Bottom-up methods • Select K “empty” clusters • For each colour c in the image colour set Aggregate c to its closest cluster

  12. Split and Merge methods • Select N>K clusters (split step) • Merge these clusters to obtain the K final clusters (merge step)

  13. Our Method: Split step • Create a uniform quantization.

  14. Our Method: Merge Step • Create a graph

  15. Our Method: Merge Step • Create a graph: Cluster Adjacency Graph

  16. Our Method: Merge Step • Merge of clusters: Ci and Cj • Minimize the partition error • Select i0 and j0 such that:

  17. Our Method: Merge Step • Merge clusters: Edge contraction

  18. Our Method: Merge Step • Merge clusters: Edge contraction

  19. Our Method: Merge Step • Merge clusters: Edge contraction

  20. Our Method: Merge Step • Merge clusters: Edge contraction

  21. Our Method: Merge Step • Merge clusters: Edge contraction

  22. Our Method: Merge Step • Merge clusters: Edge contraction

  23. Our Method: Merge Step • Merge clusters: Edge contraction

  24. Our Method: First Inverse colormap • Given a colour c • Find its enclosing cluster • Find its enclosing meta-cluster • Map c to its mean

  25. Our Method: Second Inverse colormap • Given a color c • Find its enclosing cluster • Find the adjacent meta-clusters • Map c to the closest mean

  26. Our Method: Results • Compared to the Top-down method [Wu-91] • Image quality: • First inverse colormap: slightly lower • Second Inverse colormap: Improved • Computing time  15 time faster • Compared to the Bottom-up method [Xiang-97] • Image quality: Improved [Tremeau-96] • Computing time  10 time faster

  27. Our method: Results First inverse colormap Second inverse colormap Original Wu 91 Xiang 97

  28. Discussion: The idea • Merge at each step the two closest clusters. • Reduce the amount of data (uniform quantization) • Apply an expansive heuristic:O(n2) (merge step)  Split & Merge strategy

  29. Discussion: Short History • Top down methods • Intensively explored since 1982 [Heckbert 82] • Bottom-up methods • Restricted to simple Heuristics

  30. Discussion: Short History Partition Error Number of clusters

  31. Discussion: Short History • Top down methods • Bottom-up methods • Split & Merge methods • First attempts based on top-down algorithms.

  32. Conclusion Possible improvements • Uniform quantization • Avoid empty clusters • Merge Step • Find a better heuristic • Inverse colormap • No improvementneeded. Combinatorial optimisation ?

  33. References • [Wu 91] Xiaolin Wu and K. Zhang. A better tree structured vector quantizer. In Proceedings of the IEEE Data Compression Conference, pages 392-401. IEEE Computer Society Press, 1991. • [Xiang-97] Color Image quantization by minimizing the maximum inter-cluster distance. ACM Transactions on Graphics, 16(3):260-276, July 1997. • [Tremeau-96] A. Tremeau, E. Dinet and E. Favier. Measurement and display of color image differences based on visual attention. Journal of Imaging Science and Technology, 40(6):522-534, 1996.IS&T/SID • http://www.univ-reims.fr/Labos/LERI/membre/luc

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