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Two High Speed Quantization Algorithms

Two High Speed Quantization Algorithms. Luc Brun Myriam Mokhtari L.E.R.I. Reims University (I.U.T.). Contents. Quantization algorithm s Our Methods Discussion. Quantization algorithms. Reduce the number of colours. Number of colours: 141,000. Number of colours: 16.

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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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