Skip to main content
Log in

The color quantization problem solved by swarm-based operations

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

The objective of the color quantization problem is to reduce the number of different colors of an image, in order to obtain a new image as similar as possible to the original. This is a complex problem and several solution techniques have been proposed to solve it. Among the most novel solution methods are those that apply swarm-based algorithms. These algorithms define an interesting solution approach, since they have been successfully applied to solve many different problems. This paper presents a color quantization method that combines the Artificial Bee Colony algorithm with the Ant-tree for Color Quantization algorithm, creating an improved version of a previous method that combines artificial bees with the K-means algorithm. Computational results show that the new method significantly reduces computing time compared to the initial method, and generates good quality images. Moreover, this new method generates better images than other well-known color quantization methods such as Wu’s method, Neuquant, Octree or the Variance-based method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. An NY, Pun CM (2014) Color image segmentation using adaptive color quantization and multiresolution texture characterization. SIViP 18(5):1–12. https://doi.org/10.1007/s11760-012-0340-2

    Google Scholar 

  2. Araújo AR, Costa DC (2009) Local adaptive receptive field self-organizing map for image color segmentation. Image Vis Comput 27(9):1229–1239. https://doi.org/10.1016/j.imavis.2008.11.014

    Article  MathSciNet  Google Scholar 

  3. Atsalakis A, Papamarkos N (2006) Color reduction and estimation of the number of dominant colors by using a self-growing and self-organized neural gas. Eng Appl Artif Intell 19(7):769–786. https://doi.org/10.1016/j.engappai.2006.05.004

    Article  Google Scholar 

  4. Azzag H, Venturini G, Oliver A, Guinot C (2007) A hierarchical ant based clustering algorithm and its use in three real-world applications. Eur J Oper Res 179(3):906–922. https://doi.org/10.1016/j.ejor.2005.03.062

    Article  MATH  Google Scholar 

  5. Balasubramani K, Marcus K (2013) A comprehensive review of artificial bee colony algorithm. Int J Comput Technol 5(1):15–28

    Article  Google Scholar 

  6. Barbalho JM, Duarte A, Neto D, Costa JA, Netto ML (2001) Hierarchical SOM applied to image compression. In: Proceedings of the international joint conference on neural networks, IJCNN’01, vol 1. IEEE, pp 442–447

  7. Brun L, Trémeau A (2003) Color quantization. Digital color imaging handbook, pp 589–638

  8. Celebi ME (2009) 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, pp 876–880

  9. Celebi ME (2011) Improving the performance of k-means for color quantization. Image Vis Comput 29 (4):260–271. https://doi.org/10.1016/j.imavis.2010.10.002

    Article  Google Scholar 

  10. Celebi ME, Wen Q, Hwang S (2015) An effective real-time color quantization method based on divisive hierarchical clustering. J Real-Time Image Proc 10(2):329–344. https://doi.org/10.1007/s11554-012-0291-4

    Article  Google Scholar 

  11. Chang CH, Xu P, Xiao R, Srikanthan T (2005) New adaptive color quantization method based on self-organizing maps. IEEE Trans Neural Netw 16(1):237–249 . https://doi.org/10.1109/TNN.2004.836543

    Article  Google Scholar 

  12. Chen X, Kwong S, Feng JF (2002) A new compression scheme for color-quantized images. IEEE Trans Circuits Syst Video Techn 12(10):904–908. https://doi.org/10.1109/TCSVT.2002.804896

    Article  Google Scholar 

  13. Cheng G, Yang J, Wang K, Wang X (2006) Image color reduction based on self-organizing maps and growing self-organizing neural networks. In: Proceedings of the sixth international conference on hybrid intelligent systems, HIS’06. IEEE, p 24, DOI https://doi.org/10.1109/HIS.2006.264907

  14. Cheng SC, Yang CK (2001) A fast and novel technique for color quantization using reduction of color space dimensionality. Pattern Recogn Lett 22(8):845–856. https://doi.org/10.1016/S0167-8655(01)00025-3

    Article  MATH  Google Scholar 

  15. Corder GW, Foreman DI (2009) Comparing two related samples: the Wilcoxon signed ranks test. Wiley Online Library, pp 38–56

  16. Dekker AH (1994) Kohonen neural networks for optimal colour quantization. Netw Comput Neural Syst 5 (3):351–367. https://doi.org/10.1088/0954-898X/5/3/003

    Article  MathSciNet  MATH  Google Scholar 

  17. Deng Y, Manjunath B (2001) Unsupervised segmentation of color-texture regions in images and video. IEEE Trans Pattern Anal Mach Intell 23(8):800–810. https://doi.org/10.1109/34.946985

    Article  Google Scholar 

  18. Fritzke B (1995) A growing neural gas network learns topologies. In: Proceedings of the 1995 conference on advances in neural information processing systems, pp 625–632

  19. Garey M, Johnson D, Witsenhausen H (1982) The complexity of the generalized Lloyd-max problem (corresp.) IEEE Trans Inf Theory 28(2):255–256. https://doi.org/10.1109/TIT.1982.1056488

    Article  MATH  Google Scholar 

  20. Gervautz M, Purgathofer W (1990) A simple method for color quantization: Octree quantization. In: Glassner AS (ed) Graphics gems. USA, San Diego, pp 287–293. https://doi.org/10.1007/978-3-642-83492-9_20

  21. Ghanbarian AT, Kabir E, Charkari NM (2007) Color reduction based on ant colony. Pattern Recogn Lett 28(12):1383–1390. https://doi.org/10.1016/j.patrec.2007.01.019

  22. Heckbert P (1982) Color image quantization for frame buffer display. In: Proceedings of the 9th annual conference on computer graphics and interactive techniques, SIGGRAPH ’82. ACM, New York, pp 297–307. https://doi.org/10.1145/800064.801294

  23. Hu YC, Su BH (2008) Accelerated k-means clustering algorithm for colour image quantization. The Imaging Sci J 56(1):29–40. https://doi.org/10.1179/174313107X176298

    Article  MathSciNet  Google Scholar 

  24. Jain AK (2010) Data clustering: 50 years beyond k-means. Pattern Recogn Lett 31 (8):651–666. https://doi.org/10.1007/978-3-540-87479-9_3

    Article  Google Scholar 

  25. Joy G, Xiang Z (1993) Center-cut for color-image quantization. Visual Comput 10(1):62–66. https://doi.org/10.1007/BF01905532

    Article  Google Scholar 

  26. Kanjanawanishkul K, Uyyanonvara B (2005) Novel fast color reduction algorithm for time-constrained applications. J Vis Commun Image Represent 16(3):311–332. https://doi.org/10.1016/j.jvcir.2004.07.002

    Article  Google Scholar 

  27. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report TR-06. Tech. rep. Erciyes University, Engineering Faculty, Computer Engineering Department

  28. Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132. https://doi.org/10.1016/j.amc.2009.03.090

  29. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471. https://doi.org/10.1007/s10898-007-9149-x

  30. Karaboga D, Ozturk C (2011) A novel clustering approach: Artificial bee colony (ABC) algorithm. Appl Soft Comput 11(1):652–657. https://doi.org/10.1016/j.asoc.2009.12.025

  31. Karaboga D, Akay B, Ozturk C (2007) Artificial bee colony (ABC) optimization algorithm for training feed-forward neural networks. In: International conference on modeling decisions for artificial intelligence. Springer, pp 318–329. https://doi.org/10.1007/978-3-540-73729-2_30

  32. Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42(1):21–57. https://doi.org/10.1007/s10462-012-9328-0

    Article  Google Scholar 

  33. Kasuga H, Yamamoto H, Okamoto M (2000) Color quantization using the fast k-means algorithm. Syst Comput Japan 31 (8):33–40. https://doi.org/10.1002/1520-684X(200007)31:8<33::AID-SCJ4>3.0.CO;2-C

  34. Kohonen T (1998) The self-organizing map. Neurocomput 21(1-3):1–6. https://doi.org/10.1016/S0925-2312(98)00030-7

    Article  MATH  Google Scholar 

  35. Linde Y, Buzo A, Gray R (1980) An algorithm for vector quantizer design. IEEE Trans Commun 28 (1):84–95. https://doi.org/10.1109/TCOM.1980.1094577

    Article  Google Scholar 

  36. Liu GH, Yang JY (2013) Content-based image retrieval using color difference histogram. Pattern Recogn 46(1):188–198. https://doi.org/10.1016/j.patcog.2012.06.001

    Article  Google Scholar 

  37. Omran M, Engelbrecht AP, Salman A (2005a) A color image quantization algorithm based on particle swarm optimization. Inform (Slovenia) 29(3):261–270

    MATH  Google Scholar 

  38. Omran M, Engelbrecht AP, Salman A (2005b) Particle swarm optimization method for image clustering. Int J Pattern Recognit Artif Intell 19(03):297–321. https://doi.org/10.1142/S0218001405004083

    Article  Google Scholar 

  39. Orchard MT, Bouman CA (1991) Color quantization of images. IEEE Trans Signal Proc 39(12):2677–2690. https://doi.org/10.1109/78.107417

    Article  Google Scholar 

  40. Özdemir D, Akarun L (2002) A fuzzy algorithm for color quantization of images. Pattern Recogn 35 (8):1785–1791. https://doi.org/10.1016/S0031-3203(01)00170-4

    Article  MATH  Google Scholar 

  41. Ozturk C, Hancer E, Karaboga D (2014) Color image quantization: a short review and an application with artificial bee colony algorithm. Inform 25(3):485–503. https://doi.org/10.15388/Informatica.2014.25

    Google Scholar 

  42. Palomo EJ, Domínguez E (2014) Hierarchical color quantization based on self-organization. J Math Imaging Vis 49(1):1–19. https://doi.org/10.1007/s10851-013-0433-8

    Article  Google Scholar 

  43. Papamarkos N, Atsalakis AE, Strouthopoulos CP (2002) Adaptive color reduction. IEEE Trans Syst Man Cybern B Cybern 32(1):44–56. https://doi.org/10.1109/3477.979959

    Article  MATH  Google Scholar 

  44. Park HJ, Cha EY, Kim KB (2015) An effective color quantization method using color importance-based self-organizing maps. Neural Netw World 25(2):121–137. https://doi.org/10.14311/NNW.2015.25.006

    Article  Google Scholar 

  45. Pérez-Delgado ML (2015) Colour quantization with ant-Tree. Appl Soft Comput 36:656–669. https://doi.org/10.1016/j.asoc.2015.07.048

    Article  Google Scholar 

  46. Pérez-Delgado ML (2018a) Campus Viriato images. http://audax.zam.usal.es/web/mlperez/fotos_campus.html. Accessed 19.10.18

  47. Pérez-Delgado ML (2018b) Source code for colour quantization. http://audax.zam.usal.es/web/mlperez/cq.html. Accessed 20.07.18

  48. Phung SL, Bouzerdoum A, Chai D (2005) Skin segmentation using color pixel classification: analysis and comparison. IEEE Trans Pattern Anal Mach Intell 27(1):148–154. https://doi.org/10.1109/TPAMI.2005.17

    Article  Google Scholar 

  49. Ponti M, Nazaré TS, Thumé GS (2016) Image quantization as a dimensionality reduction procedure in color and texture feature extraction. Neurocomputing 173:385–396. https://doi.org/10.1016/j.neucom.2015.04.114

    Article  Google Scholar 

  50. Şaykol E, Güdükbay U, Ulusoy Ö (2005) A histogram-based approach for object-based query-by-shape-and-color in image and video databases. Image Vis Comput 23(13):1170–1180. https://doi.org/10.1016/j.imavis.2005.07.015

    Article  Google Scholar 

  51. Schaefer G, Zhou H (2009) Fuzzy clustering for colour reduction in images. Telecommun Syst 40(1):17–25. https://doi.org/10.1007/s11235-008-9143-8

    Article  Google Scholar 

  52. Scheunders P (1997) A genetic c-means clustering algorithm applied to color image quantization. Pattern Recogn 30(6):859–866. https://doi.org/10.1016/S0031-3203(96)00131-8

    Article  Google Scholar 

  53. Shukran MAM, Chung YY, Yeh WC, Wahid N, Zaidi AMA (2011) Artificial bee colony based data mining algorithms for classification tasks. Mod Appl Sci 5(4):217–231. https://doi.org/10.5539/mas.v5n4p217

    Google Scholar 

  54. Sirisathitkul Y, Auwatanamongkol S, Uyyanonvara B (2004) Color image quantization using distances between adjacent colors along the color axis with highest color variance. Pattern Recogn Lett 25(9):1025–1043. https://doi.org/10.1016/j.patrec.2004.02.012

    Article  Google Scholar 

  55. Tsai CF, Jhuang CA, Liu CW (2008) Gray image compression using new hierarchical self-organizing map technique. In: ICICIC’08; 3rd international conference on innovative computing information and control. IEEE, pp 544–544. https://doi.org/10.1109/ICICIC.2008.298

  56. Uchiyama T, Arbib MA (1994) An algorithm for competitive learning in clustering problems. Pattern Recogn 27(10):1415–1421. https://doi.org/10.1016/0031-3203(94)90074-4

    Article  Google Scholar 

  57. Verevka O, Buchanan JW (1995) The local k-means algorithm for colour image quantization. In: Proceedings of graphics interface ’95, Québec. Canadian Information Processing Society, Canada, pp 128–128, https://doi.org/10.20380/GI1995.15

  58. Wan S, Prusinkiewicz P, Wong S (1990) Variance-based color image quantization for frame buffer display. Color Res Appl 15(1):52–58. https://doi.org/10.1002/col.5080150109

    Article  Google Scholar 

  59. Wang CH, Lee CN, Hsieh CH (2007) Sample-size adaptive self-organization map for color images quantization. Pattern Recogn Lett 28 (13):1616–1629. https://doi.org/10.1016/j.patrec.2007.04.005

    Article  Google Scholar 

  60. Wang J, Yang WJ, Acharya R (1997) Color clustering techniques for color-content-based image retrieval from image databases. In: Proceedings of the IEEE international conference on multimedia computing and systems’ 97. IEEE, pp 442–449, https://doi.org/10.1109/MMCS.1997.609755

  61. Wang XY, Yu YJ, Yang HY (2011) An effective image retrieval scheme using color, texture and shape features. Comput Stand Interfaces 33(1):59–68. https://doi.org/10.1016/j.csi.2010.03.004

    Article  Google Scholar 

  62. Weber A (2018) USC-SIPI image database. http://sipi.usc.edu/database/database.php/. Accessed 19.10.18

  63. Wen Q, Celebi ME (2011) Hard versus fuzzy c-means clustering for color quantization. EURASIP J Adv Signal Proc 2011(1):1–12. https://doi.org/10.1186/1687-6180-2011-118

    Article  Google Scholar 

  64. Wu X (1991) Efficient statistical computations for optimal color quantization. In: Graphics gems, vol II. Academic Press, pp 126–133, DOI https://doi.org/10.1016/B978-0-08-050754-5.50035-9

  65. Wu X (1992) Color quantization by dynamic programming and principal analysis. ACM Trans Graph 11 (4):348–372. https://doi.org/10.1145/146443.146475

    Article  MATH  Google Scholar 

  66. Yang CK, Tsai WH (1998) Color image compression using quantization, thresholding, and edge detection techniques all based on the moment-preserving principle. Pattern Recogn Lett 19(2):205–215. https://doi.org/10.1016/S0167-8655(97)00166-9

    Article  MathSciNet  Google Scholar 

  67. Yang CY, Lin JC, et al. (1996) RWM-Cut for color image quantization. Comput Graph 20(4):577–588. https://doi.org/10.1016/0097-8493(96)00028-3

    Article  Google Scholar 

  68. Zhang C, Ouyang D, Ning J (2010) An artificial bee colony approach for clustering. Expert Syst Appl 37(7):4761–4767. https://doi.org/10.1016/j.eswa.2009.11.003

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Samuel Solórzano Barruso Memorial Foundation of the University of Salamanca.

Funding

This study was funded by the Samuel Solórzano Barruso Memorial Foundation of the University of Salamanca (grant number FS/102015).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to María-Luisa Pérez-Delgado.

Ethics declarations

Conflict of interests

The author declares that she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(PDF 12.9 MB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pérez-Delgado, ML. The color quantization problem solved by swarm-based operations. Appl Intell 49, 2482–2514 (2019). https://doi.org/10.1007/s10489-018-1389-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-018-1389-6

Keywords

Navigation