Abstract

Color quantization is an important operation with numerous applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. However, despite its popularity as a general purpose clustering algorithm, K-means has not received much respect in the color quantization literature because of its high computational requirements and sensitivity to initialization. In this paper, a fast color quantization method based on K-means is presented. The method involves several modifications to the conventional (batch) K-means algorithm, including data reduction, sample weighting, and the use of the triangle inequality to speed up the nearest-neighbor search. Experiments on a diverse set of images demonstrate that, with the proposed modifications, K-means becomes very competitive with state-of-the-art color quantization methods in terms of both effectiveness and efficiency.

© 2009 Optical Society of America

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    [CrossRef]
  3. Y. Deng and B. Manjunath, “Unsupervised segmentation of color-texture regions in images and video,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 800-810 (2001).
    [CrossRef]
  4. O. Sertel, J. Kong, G. Lozanski, A. Shanaah, U. Catalyurek, J. Saltz, and M. Gurcan, “Texture classification using nonlinear color quantization: application to histopathological image analysis,” in IEEE International Conference on Acoustics, Speech and Signal Processing 2008, ICAASP 2008 (IEEE, 2008), pp. 597-600.
    [CrossRef]
  5. C.-T. Kuo and S.-C. Cheng, “Fusion of color edge detection and color quantization for color image watermarking using principal axes analysis,” Pattern Recogn. 40, 3691-3704 (2007).
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  6. Y. Deng, B. Manjunath, C. Kenney, M. Moore, and H. Shin, “An efficient color representation for image retrieval,” IEEE Trans. Image Process. 10, 140-147 (2001).
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    [CrossRef]
  10. M. Gervautz and W. Purgathofer, “A simple method for color quantization: octree quantization,” in New Trends in Computer Graphics (Springer-Verlag, 1988), pp. 219-231.
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  11. S. Wan, P. Prusinkiewicz, and S. Wong, “Variance-based color image quantization for frame buffer display,” Color Res. Appl. 15, 52-58 (1990).
    [CrossRef]
  12. M. Orchard and C. Bouman, “Color quantization of images,” IEEE Trans. Signal Process. 39, 2677-2690 (1991).
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    [CrossRef]
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  16. S. Cheng and C. Yang, “Fast and novel technique for color quantization using reduction of color space dimensionality,” Pattern Recogn. Lett. 22, 845-856 (2001).
    [CrossRef]
  17. Y. Sirisathitkul, S. Auwatanamongkol, and B. Uyyanonvara, “Color image quantization using distances between adjacent colors along the color axis with highest color variance,” Pattern Recogn. Lett. 25, 1025-1043 (2004).
    [CrossRef]
  18. K. Kanjanawanishkul and B. Uyyanonvara, “Novel fast color reduction algorithm for time-constrained applications,” J. Visual Commun. Image Represent 16, 311-332 (2005).
    [CrossRef]
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    [CrossRef]
  20. R. Balasubramanian and J. Allebach, “A new approach to palette selection for color images,” J. Electron. Imaging 17, 284-290 (1991).
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    [CrossRef]
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    [CrossRef]
  23. L. Brun and M. Mokhtari, “Two high speed color quantization algorithms,” in Proceedings of the First International Conference on Color in Graphics and Image Processing (IEEE, 2000), pp. 116-121.
  24. H. Kasuga, H. Yamamoto, and M. Okamoto, “Color quantization using the fast K-means algorithm,” Syst. Comput. Jpn. 31, 33-40 (2000).
    [CrossRef]
  25. Y.-L. Huang and R.-F. Chang, “A fast finite-state algorithm for generating RGB palettes of color quantized images,” J. Inf. Sci. Eng. 20, 771-782 (2004).
  26. Y.-C. Hu and M.-G. Lee, “K-means based color palette design scheme with the use of stable flags,” J. Electron. Imaging 16, 033003 (2007).
    [CrossRef]
  27. Y.-C. Hu and B.-H. Su, “Accelerated K-means clustering algorithm for colour image quantization,” Imaging Sci. J. 56, 29-40 (2008).
    [CrossRef]
  28. Z. Xiang, “Color image quantization by minimizing the maximum intercluster distance,” ACM Trans. Graphics 16, 260-276 (1997).
    [CrossRef]
  29. O. Verevka and J. Buchanan, “Local K-means algorithm for colour image quantization,” in Proceedings of the Graphics/Vision Interface Conference (ACM, 1995), pp. 128-135.
  30. P. Scheunders, “Comparison of clustering algorithms applied to color image quantization,” Pattern Recogn. Lett. 18, 1379-1384 (1997).
    [CrossRef]
  31. M. E. Celebi, “An effective color quantization method based on the competitive learning paradigm,” in Proceedings of the International Conference on Image Processing, Computer Vision, and Pattern Recognition (2009), pp. 876-880.
  32. D. Ozdemir and L. Akarun, “Fuzzy algorithm for color quantization of images,” Pattern Recogn. 35, 1785-1791 (2002).
    [CrossRef]
  33. G. Schaefer and H. Zhou, “Fuzzy clustering for colour reduction in images,” Telecommun. Syst. 40, 17-25 (2009).
    [CrossRef]
  34. Z. Bing, S. Junyi, and P. Qinke, “An adjustable algorithm for color quantization,” Pattern Recogn. Lett. 25, 1787-1797 (2004).
    [CrossRef]
  35. A. Dekker, “Kohonen neural networks for optimal colour quantization,” Network Comput. Neural Syst. 5, 351-367 (1994).
    [CrossRef]
  36. N. Papamarkos, A. Atsalakis, and C. Strouthopoulos, “Adaptive color reduction,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern. 32, 44-56 (2002).
    [CrossRef]
  37. C.-H. Chang, P. Xu, R. Xiao, and T. Srikanthan, “New adaptive color quantization method based on self-organizing maps,” IEEE Trans. Neural Netw. 16, 237-249 (2005).
    [CrossRef] [PubMed]
  38. Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84-95 (1980).
    [CrossRef]
  39. G. Gan, C. Ma, and J. Wu, Data Clustering: Theory, Algorithms, and Applications (SIAM, 2007).
    [CrossRef]
  40. P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, “Clustering large graphs via the singular value decomposition,” Mach. Learn. 56, 9-33 (2004).
    [CrossRef]
  41. S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28, 129-136 (1982).
    [CrossRef]
  42. E. Forgy, “Cluster analysis of multivariate data: efficiency vs. interpretability of classification,” Biometrics 21, 768 (1965).
  43. S. Phillips, “Acceleration of K-means and related clustering algorithms,” in Proceedings of the 4th International Workshop on Algorithm Engineering and Experiments (2002), pp. 166-177.
  44. T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, “An efficient K-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 881-892 (2002).
    [CrossRef]
  45. S. Har-Peled and A. Kushal, “Smaller coresets for K-median and K-means clustering,” in Proceedings of the 21st Annual Symposium on Computational Geometry (2004), pp. 126-134.
  46. C. Elkan, “Using the triangle inequality to accelerate K-means,” in Proceedings of the 20th International Conference on Machine Learning (2003), pp. 147-153.
  47. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms (Springer-Verlag, 1981).
  48. J. F. Kolen and T. Hutcheson, “Reducing the time complexity of the fuzzy C-means algorithm,” IEEE Trans. Fuzzy Syst. 10, 263-267 (2002).
    [CrossRef]
  49. Uncompressed full-resolution images are available at http://www.lsus.edu/faculty/~ecelebi/color_quantization.htm.

2009

G. Schaefer and H. Zhou, “Fuzzy clustering for colour reduction in images,” Telecommun. Syst. 40, 17-25 (2009).
[CrossRef]

2008

Y.-C. Hu and B.-H. Su, “Accelerated K-means clustering algorithm for colour image quantization,” Imaging Sci. J. 56, 29-40 (2008).
[CrossRef]

2007

Y.-C. Hu and M.-G. Lee, “K-means based color palette design scheme with the use of stable flags,” J. Electron. Imaging 16, 033003 (2007).
[CrossRef]

C.-T. Kuo and S.-C. Cheng, “Fusion of color edge detection and color quantization for color image watermarking using principal axes analysis,” Pattern Recogn. 40, 3691-3704 (2007).
[CrossRef]

2005

K. Kanjanawanishkul and B. Uyyanonvara, “Novel fast color reduction algorithm for time-constrained applications,” J. Visual Commun. Image Represent 16, 311-332 (2005).
[CrossRef]

C.-H. Chang, P. Xu, R. Xiao, and T. Srikanthan, “New adaptive color quantization method based on self-organizing maps,” IEEE Trans. Neural Netw. 16, 237-249 (2005).
[CrossRef] [PubMed]

2004

P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, “Clustering large graphs via the singular value decomposition,” Mach. Learn. 56, 9-33 (2004).
[CrossRef]

Z. Bing, S. Junyi, and P. Qinke, “An adjustable algorithm for color quantization,” Pattern Recogn. Lett. 25, 1787-1797 (2004).
[CrossRef]

Y.-L. Huang and R.-F. Chang, “A fast finite-state algorithm for generating RGB palettes of color quantized images,” J. Inf. Sci. Eng. 20, 771-782 (2004).

Y. Sirisathitkul, S. Auwatanamongkol, and B. Uyyanonvara, “Color image quantization using distances between adjacent colors along the color axis with highest color variance,” Pattern Recogn. Lett. 25, 1025-1043 (2004).
[CrossRef]

2002

D. Ozdemir and L. Akarun, “Fuzzy algorithm for color quantization of images,” Pattern Recogn. 35, 1785-1791 (2002).
[CrossRef]

T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, “An efficient K-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 881-892 (2002).
[CrossRef]

J. F. Kolen and T. Hutcheson, “Reducing the time complexity of the fuzzy C-means algorithm,” IEEE Trans. Fuzzy Syst. 10, 263-267 (2002).
[CrossRef]

N. Papamarkos, A. Atsalakis, and C. Strouthopoulos, “Adaptive color reduction,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern. 32, 44-56 (2002).
[CrossRef]

2001

S. Cheng and C. Yang, “Fast and novel technique for color quantization using reduction of color space dimensionality,” Pattern Recogn. Lett. 22, 845-856 (2001).
[CrossRef]

Y. Deng, B. Manjunath, C. Kenney, M. Moore, and H. Shin, “An efficient color representation for image retrieval,” IEEE Trans. Image Process. 10, 140-147 (2001).
[CrossRef]

Y. Deng and B. Manjunath, “Unsupervised segmentation of color-texture regions in images and video,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 800-810 (2001).
[CrossRef]

2000

H. Kasuga, H. Yamamoto, and M. Okamoto, “Color quantization using the fast K-means algorithm,” Syst. Comput. Jpn. 31, 33-40 (2000).
[CrossRef]

1998

C.-K. Yang and W.-H. Tsai, “Color image compression using quantization, thresholding, and edge detection techniques all based on the moment-preserving principle,” Pattern Recogn. Lett. 19, 205-215 (1998).
[CrossRef]

1997

Z. Xiang, “Color image quantization by minimizing the maximum intercluster distance,” ACM Trans. Graphics 16, 260-276 (1997).
[CrossRef]

P. Scheunders, “Comparison of clustering algorithms applied to color image quantization,” Pattern Recogn. Lett. 18, 1379-1384 (1997).
[CrossRef]

1996

C.-Y. Yang and J.-C. Lin, “RWM-cut for color image quantization,” Comput. Graph. 20, 577-588 (1996).
[CrossRef]

1994

Z. Xiang and G. Joy, “Color image quantization by agglomerative clustering,” IEEE Comput. Graphics Appl. 14, 44-48 (1994).
[CrossRef]

A. Dekker, “Kohonen neural networks for optimal colour quantization,” Network Comput. Neural Syst. 5, 351-367 (1994).
[CrossRef]

1993

G. Joy and Z. Xiang, “Center-cut for color image quantization,” Visual Comput. 10, 62-66 (1993).
[CrossRef]

1991

R. Balasubramanian and J. Allebach, “A new approach to palette selection for color images,” J. Electron. Imaging 17, 284-290 (1991).

M. Orchard and C. Bouman, “Color quantization of images,” IEEE Trans. Signal Process. 39, 2677-2690 (1991).
[CrossRef]

1990

S. Wan, P. Prusinkiewicz, and S. Wong, “Variance-based color image quantization for frame buffer display,” Color Res. Appl. 15, 52-58 (1990).
[CrossRef]

R. S. Gentile, J. P. Allebach, and E. Walowit, “Quantization of color images based on uniform color spaces,” J. Electron. Imaging 16, 11-21 (1990).

1989

W. H. Equitz, “A new vector quantization clustering algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 37, 1568-1575 (1989).
[CrossRef]

1982

P. Heckbert, “Color image quantization for frame buffer display,” ACM SIGGRAPH Comput. Graph. 16, 297-307 (1982).
[CrossRef]

S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28, 129-136 (1982).
[CrossRef]

1980

Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84-95 (1980).
[CrossRef]

1965

E. Forgy, “Cluster analysis of multivariate data: efficiency vs. interpretability of classification,” Biometrics 21, 768 (1965).

Akarun, L.

D. Ozdemir and L. Akarun, “Fuzzy algorithm for color quantization of images,” Pattern Recogn. 35, 1785-1791 (2002).
[CrossRef]

Allebach, J.

R. Balasubramanian and J. Allebach, “A new approach to palette selection for color images,” J. Electron. Imaging 17, 284-290 (1991).

Allebach, J. P.

R. S. Gentile, J. P. Allebach, and E. Walowit, “Quantization of color images based on uniform color spaces,” J. Electron. Imaging 16, 11-21 (1990).

Atsalakis, A.

N. Papamarkos, A. Atsalakis, and C. Strouthopoulos, “Adaptive color reduction,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern. 32, 44-56 (2002).
[CrossRef]

Auwatanamongkol, S.

Y. Sirisathitkul, S. Auwatanamongkol, and B. Uyyanonvara, “Color image quantization using distances between adjacent colors along the color axis with highest color variance,” Pattern Recogn. Lett. 25, 1025-1043 (2004).
[CrossRef]

Balasubramanian, R.

R. Balasubramanian and J. Allebach, “A new approach to palette selection for color images,” J. Electron. Imaging 17, 284-290 (1991).

Bezdek, J. C.

J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms (Springer-Verlag, 1981).

Bing, Z.

Z. Bing, S. Junyi, and P. Qinke, “An adjustable algorithm for color quantization,” Pattern Recogn. Lett. 25, 1787-1797 (2004).
[CrossRef]

Bouman, C.

M. Orchard and C. Bouman, “Color quantization of images,” IEEE Trans. Signal Process. 39, 2677-2690 (1991).
[CrossRef]

Brun, L.

L. Brun and A. Trémeau, Digital Color Imaging Handbook (CRC Press, 2002), pp. 589-638.

L. Brun and M. Mokhtari, “Two high speed color quantization algorithms,” in Proceedings of the First International Conference on Color in Graphics and Image Processing (IEEE, 2000), pp. 116-121.

Buchanan, J.

O. Verevka and J. Buchanan, “Local K-means algorithm for colour image quantization,” in Proceedings of the Graphics/Vision Interface Conference (ACM, 1995), pp. 128-135.

Buzo, A.

Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84-95 (1980).
[CrossRef]

Catalyurek, U.

O. Sertel, J. Kong, G. Lozanski, A. Shanaah, U. Catalyurek, J. Saltz, and M. Gurcan, “Texture classification using nonlinear color quantization: application to histopathological image analysis,” in IEEE International Conference on Acoustics, Speech and Signal Processing 2008, ICAASP 2008 (IEEE, 2008), pp. 597-600.
[CrossRef]

Celebi, M. E.

M. E. Celebi, “An effective color quantization method based on the competitive learning paradigm,” in Proceedings of the International Conference on Image Processing, Computer Vision, and Pattern Recognition (2009), pp. 876-880.

Chang, C.-H.

C.-H. Chang, P. Xu, R. Xiao, and T. Srikanthan, “New adaptive color quantization method based on self-organizing maps,” IEEE Trans. Neural Netw. 16, 237-249 (2005).
[CrossRef] [PubMed]

Chang, R.-F.

Y.-L. Huang and R.-F. Chang, “A fast finite-state algorithm for generating RGB palettes of color quantized images,” J. Inf. Sci. Eng. 20, 771-782 (2004).

Cheng, S.

S. Cheng and C. Yang, “Fast and novel technique for color quantization using reduction of color space dimensionality,” Pattern Recogn. Lett. 22, 845-856 (2001).
[CrossRef]

Cheng, S.-C.

C.-T. Kuo and S.-C. Cheng, “Fusion of color edge detection and color quantization for color image watermarking using principal axes analysis,” Pattern Recogn. 40, 3691-3704 (2007).
[CrossRef]

Dekker, A.

A. Dekker, “Kohonen neural networks for optimal colour quantization,” Network Comput. Neural Syst. 5, 351-367 (1994).
[CrossRef]

Deng, Y.

Y. Deng, B. Manjunath, C. Kenney, M. Moore, and H. Shin, “An efficient color representation for image retrieval,” IEEE Trans. Image Process. 10, 140-147 (2001).
[CrossRef]

Y. Deng and B. Manjunath, “Unsupervised segmentation of color-texture regions in images and video,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 800-810 (2001).
[CrossRef]

Drineas, P.

P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, “Clustering large graphs via the singular value decomposition,” Mach. Learn. 56, 9-33 (2004).
[CrossRef]

Elkan, C.

C. Elkan, “Using the triangle inequality to accelerate K-means,” in Proceedings of the 20th International Conference on Machine Learning (2003), pp. 147-153.

Equitz, W. H.

W. H. Equitz, “A new vector quantization clustering algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 37, 1568-1575 (1989).
[CrossRef]

Forgy, E.

E. Forgy, “Cluster analysis of multivariate data: efficiency vs. interpretability of classification,” Biometrics 21, 768 (1965).

Frieze, A.

P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, “Clustering large graphs via the singular value decomposition,” Mach. Learn. 56, 9-33 (2004).
[CrossRef]

Gan, G.

G. Gan, C. Ma, and J. Wu, Data Clustering: Theory, Algorithms, and Applications (SIAM, 2007).
[CrossRef]

Gentile, R. S.

R. S. Gentile, J. P. Allebach, and E. Walowit, “Quantization of color images based on uniform color spaces,” J. Electron. Imaging 16, 11-21 (1990).

Gervautz, M.

M. Gervautz and W. Purgathofer, “A simple method for color quantization: octree quantization,” in New Trends in Computer Graphics (Springer-Verlag, 1988), pp. 219-231.
[CrossRef]

Gomez, J.

L. Velho, J. Gomez, and M. Sobreiro, “Color image quantization by pairwise clustering,” in X Brazilian Symposium on Computer Graphics and Image Processing 1977 (IEEE Computer Society, 1997), pp. 203-210.
[CrossRef]

Gray, R.

Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84-95 (1980).
[CrossRef]

Gurcan, M.

O. Sertel, J. Kong, G. Lozanski, A. Shanaah, U. Catalyurek, J. Saltz, and M. Gurcan, “Texture classification using nonlinear color quantization: application to histopathological image analysis,” in IEEE International Conference on Acoustics, Speech and Signal Processing 2008, ICAASP 2008 (IEEE, 2008), pp. 597-600.
[CrossRef]

Har-Peled, S.

S. Har-Peled and A. Kushal, “Smaller coresets for K-median and K-means clustering,” in Proceedings of the 21st Annual Symposium on Computational Geometry (2004), pp. 126-134.

Heckbert, P.

P. Heckbert, “Color image quantization for frame buffer display,” ACM SIGGRAPH Comput. Graph. 16, 297-307 (1982).
[CrossRef]

Hu, Y.-C.

Y.-C. Hu and B.-H. Su, “Accelerated K-means clustering algorithm for colour image quantization,” Imaging Sci. J. 56, 29-40 (2008).
[CrossRef]

Y.-C. Hu and M.-G. Lee, “K-means based color palette design scheme with the use of stable flags,” J. Electron. Imaging 16, 033003 (2007).
[CrossRef]

Huang, Y.-L.

Y.-L. Huang and R.-F. Chang, “A fast finite-state algorithm for generating RGB palettes of color quantized images,” J. Inf. Sci. Eng. 20, 771-782 (2004).

Hutcheson, T.

J. F. Kolen and T. Hutcheson, “Reducing the time complexity of the fuzzy C-means algorithm,” IEEE Trans. Fuzzy Syst. 10, 263-267 (2002).
[CrossRef]

Joy, G.

Z. Xiang and G. Joy, “Color image quantization by agglomerative clustering,” IEEE Comput. Graphics Appl. 14, 44-48 (1994).
[CrossRef]

G. Joy and Z. Xiang, “Center-cut for color image quantization,” Visual Comput. 10, 62-66 (1993).
[CrossRef]

Junyi, S.

Z. Bing, S. Junyi, and P. Qinke, “An adjustable algorithm for color quantization,” Pattern Recogn. Lett. 25, 1787-1797 (2004).
[CrossRef]

Kanjanawanishkul, K.

K. Kanjanawanishkul and B. Uyyanonvara, “Novel fast color reduction algorithm for time-constrained applications,” J. Visual Commun. Image Represent 16, 311-332 (2005).
[CrossRef]

Kannan, R.

P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, “Clustering large graphs via the singular value decomposition,” Mach. Learn. 56, 9-33 (2004).
[CrossRef]

Kanungo, T.

T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, “An efficient K-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 881-892 (2002).
[CrossRef]

Kasuga, H.

H. Kasuga, H. Yamamoto, and M. Okamoto, “Color quantization using the fast K-means algorithm,” Syst. Comput. Jpn. 31, 33-40 (2000).
[CrossRef]

Kenney, C.

Y. Deng, B. Manjunath, C. Kenney, M. Moore, and H. Shin, “An efficient color representation for image retrieval,” IEEE Trans. Image Process. 10, 140-147 (2001).
[CrossRef]

Kolen, J. F.

J. F. Kolen and T. Hutcheson, “Reducing the time complexity of the fuzzy C-means algorithm,” IEEE Trans. Fuzzy Syst. 10, 263-267 (2002).
[CrossRef]

Kong, J.

O. Sertel, J. Kong, G. Lozanski, A. Shanaah, U. Catalyurek, J. Saltz, and M. Gurcan, “Texture classification using nonlinear color quantization: application to histopathological image analysis,” in IEEE International Conference on Acoustics, Speech and Signal Processing 2008, ICAASP 2008 (IEEE, 2008), pp. 597-600.
[CrossRef]

Kuo, C.-T.

C.-T. Kuo and S.-C. Cheng, “Fusion of color edge detection and color quantization for color image watermarking using principal axes analysis,” Pattern Recogn. 40, 3691-3704 (2007).
[CrossRef]

Kushal, A.

S. Har-Peled and A. Kushal, “Smaller coresets for K-median and K-means clustering,” in Proceedings of the 21st Annual Symposium on Computational Geometry (2004), pp. 126-134.

Lee, M.-G.

Y.-C. Hu and M.-G. Lee, “K-means based color palette design scheme with the use of stable flags,” J. Electron. Imaging 16, 033003 (2007).
[CrossRef]

Lin, J.-C.

C.-Y. Yang and J.-C. Lin, “RWM-cut for color image quantization,” Comput. Graph. 20, 577-588 (1996).
[CrossRef]

Linde, Y.

Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84-95 (1980).
[CrossRef]

Lloyd, S.

S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28, 129-136 (1982).
[CrossRef]

Lozanski, G.

O. Sertel, J. Kong, G. Lozanski, A. Shanaah, U. Catalyurek, J. Saltz, and M. Gurcan, “Texture classification using nonlinear color quantization: application to histopathological image analysis,” in IEEE International Conference on Acoustics, Speech and Signal Processing 2008, ICAASP 2008 (IEEE, 2008), pp. 597-600.
[CrossRef]

Ma, C.

G. Gan, C. Ma, and J. Wu, Data Clustering: Theory, Algorithms, and Applications (SIAM, 2007).
[CrossRef]

Manjunath, B.

Y. Deng and B. Manjunath, “Unsupervised segmentation of color-texture regions in images and video,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 800-810 (2001).
[CrossRef]

Y. Deng, B. Manjunath, C. Kenney, M. Moore, and H. Shin, “An efficient color representation for image retrieval,” IEEE Trans. Image Process. 10, 140-147 (2001).
[CrossRef]

Mokhtari, M.

L. Brun and M. Mokhtari, “Two high speed color quantization algorithms,” in Proceedings of the First International Conference on Color in Graphics and Image Processing (IEEE, 2000), pp. 116-121.

Moore, M.

Y. Deng, B. Manjunath, C. Kenney, M. Moore, and H. Shin, “An efficient color representation for image retrieval,” IEEE Trans. Image Process. 10, 140-147 (2001).
[CrossRef]

Mount, D.

T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, “An efficient K-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 881-892 (2002).
[CrossRef]

Netanyahu, N.

T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, “An efficient K-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 881-892 (2002).
[CrossRef]

Okamoto, M.

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Uncompressed full-resolution images are available at http://www.lsus.edu/faculty/~ecelebi/color_quantization.htm.

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Figures (4)

Fig. 1
Fig. 1

Test images: a, Airplane; b, Baboon; c, Boats; d, Lenna; e, Parrots; f, Peppers; g, Fish; h, Poolballs.

Fig. 2
Fig. 2

Sample quantization results for the Airplane image ( K = 32 ) : a, MMM output; b, MMM error; c, NEU output; d, NEU error; e, WSM output; f, WSM error; g, WSM-C output; h, WSM-C error.

Fig. 3
Fig. 3

Sample quantization results for the Parrots image ( K = 64 ) : a, MC output; b, MC error; c, FKM output; d, FKM error; e, WSM output; f, WSM error; g, WSM-C output; h, WSM-C error.

Fig. 4
Fig. 4

CPU time for WSM for K = { 2 , , 256 } .

Tables (4)

Tables Icon

Table 1 MSE Comparison of the Quantization Methods

Tables Icon

Table 2 CPU Time Comparison of the Quantization Methods

Tables Icon

Table 3 Performance Rank Comparison of the Quantization Methods

Tables Icon

Table 4 Stability Rank Comparison of the Quantization Methods

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

SSE = k = 1 K x i S k x i c k 2 2 ,
MSE ( X , X ̂ ) = 1 H W h = 1 H w = 1 W x ( h , w ) x ̂ ( h , w ) 2 2 ,
PSNR = 20 log 10 ( 255 MSE ) .

Metrics