Two High Speed Quantization Algorithms Luc Brun Myriam Mokhtari L.E.R.I. Reims University (I.U.T.)
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Transcript of Two High Speed Quantization Algorithms Luc Brun Myriam Mokhtari L.E.R.I. Reims University (I.U.T.)
![Page 1: Two High Speed Quantization Algorithms Luc Brun Myriam Mokhtari L.E.R.I. Reims University (I.U.T.)](https://reader035.fdocuments.net/reader035/viewer/2022062519/5697bffb1a28abf838cc0ce9/html5/thumbnails/1.jpg)
Two High Speed Quantization Algorithms
Luc BrunMyriam Mokhtari
L.E.R.I. Reims University (I.U.T.)
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Contents
Quantization algorithms
Our Methods
Discussion
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Quantization algorithms
Reduce the number of colours
Number of colours: 141,000 Number of colours: 16
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Quantization Algorithms
Applications
Display
Compression
Classification
Segmentation
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Quantization steps
Create clusters
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Quantization steps
Create clusters: Squared error
Partition error
K
iiCSEPE
1
)()(
Cx
CxxfCSE2
KCCP ,,1
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Quantization steps
Create clusters
Compute means
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Quantization steps
Create clusters
Compute means
Create output image (inverse colormap)
Quantization Inverse colormap dithtering
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Type of quantization methods
Three kind of Methods
Top-down
Bottom-up
Split & Merge
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Top-down methods
Recursive split of the image color set
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Bottom-up methods
For each colour c in the image colour set
Select K “empty” clusters
Aggregate c to its closest cluster
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Split and Merge methods
Select N>K clusters (split step)
Merge these clusters to obtain the K final clusters (merge step)
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Our Method: Split step
Create a uniform quantization.
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Our Method: Merge Step
Create a graph
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Our Method: Merge Step
Create a graph: Cluster Adjacency Graph
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Our Method: Merge Step
Merge of clusters: Ci and Cj
Minimize the partition error Select i0 and j0 such that:
2
, )()'( ji
ji
ji
ji CCCC
CCPEPE
jinji
ji
ji
Min ,,1),(
, 200
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: Merge Step
Merge clusters: Edge contraction
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Our Method: First Inverse colormap
Given a colour c
Find its enclosing clusterFind its enclosing meta-clusterMap c to its mean
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Our Method: Second Inverse colormap
Given a color cFind its enclosing clusterFind the adjacent meta-clustersMap c to the closest mean
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Our Method: Results
Compared to the Top-down method [Wu-91] Image quality:
First inverse colormap: slightly lowerSecond 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
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Our method: Results
First inverse colormap Second inverse colormap
Wu 91 Xiang 97
Original
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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
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Discussion: Short History
Top down methods Intensively explored since 1982 [Heckbert 82]
Bottom-up methods Restricted to simple Heuristics
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Discussion: Short History
Number of clusters
Partition Error
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Discussion: Short History
Top down methods Bottom-up methods
Split & Merge methodsFirst attempts based on top-down algorithms.
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Conclusion Possible improvements
Uniform quantization Avoid empty clusters
Merge Step Find a better heuristic
Inverse colormap No improvement needed.
Combinatorial optimisation ?
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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