Applied Intelligence

, Volume 49, Issue 7, pp 2482–2514 | Cite as

The color quantization problem solved by swarm-based operations

  • María-Luisa Pérez-DelgadoEmail author


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.


Color quantization Artificial ants Ant-tree algorithm Artificial bee colony algorithm Clustering 



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

Funding Information

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

Compliance with Ethical Standards

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.

Supplementary material

10489_2018_1389_MOESM1_ESM.pdf (13 mb)
(PDF 12.9 MB)


  1. 1.
    An NY, Pun CM (2014) Color image segmentation using adaptive color quantization and multiresolution texture characterization. SIViP 18(5):1–12. Google Scholar
  2. 2.
    Araújo AR, Costa DC (2009) Local adaptive receptive field self-organizing map for image color segmentation. Image Vis Comput 27(9):1229–1239. MathSciNetGoogle Scholar
  3. 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. Google Scholar
  4. 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. zbMATHGoogle Scholar
  5. 5.
    Balasubramani K, Marcus K (2013) A comprehensive review of artificial bee colony algorithm. Int J Comput Technol 5(1):15–28Google Scholar
  6. 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 442–447Google Scholar
  7. 7.
    Brun L, Trémeau A (2003) Color quantization. Digital color imaging handbook, pp 589–638Google Scholar
  8. 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 876–880Google Scholar
  9. 9.
    Celebi ME (2011) Improving the performance of k-means for color quantization. Image Vis Comput 29 (4):260–271. Google Scholar
  10. 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. Google Scholar
  11. 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 . Google Scholar
  12. 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. Google Scholar
  13. 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
  14. 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. zbMATHGoogle Scholar
  15. 15.
    Corder GW, Foreman DI (2009) Comparing two related samples: the Wilcoxon signed ranks test. Wiley Online Library, pp 38–56Google Scholar
  16. 16.
    Dekker AH (1994) Kohonen neural networks for optimal colour quantization. Netw Comput Neural Syst 5 (3):351–367. MathSciNetzbMATHGoogle Scholar
  17. 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. Google Scholar
  18. 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 625–632Google Scholar
  19. 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. zbMATHGoogle Scholar
  20. 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.
  21. 21.
    Ghanbarian AT, Kabir E, Charkari NM (2007) Color reduction based on ant colony. Pattern Recogn Lett 28(12):1383–1390.
  22. 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.
  23. 23.
    Hu YC, Su BH (2008) Accelerated k-means clustering algorithm for colour image quantization. The Imaging Sci J 56(1):29–40. MathSciNetGoogle Scholar
  24. 24.
    Jain AK (2010) Data clustering: 50 years beyond k-means. Pattern Recogn Lett 31 (8):651–666. Google Scholar
  25. 25.
    Joy G, Xiang Z (1993) Center-cut for color-image quantization. Visual Comput 10(1):62–66. Google Scholar
  26. 26.
    Kanjanawanishkul K, Uyyanonvara B (2005) Novel fast color reduction algorithm for time-constrained applications. J Vis Commun Image Represent 16(3):311–332. Google Scholar
  27. 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 DepartmentGoogle Scholar
  28. 28.
    Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132.
  29. 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.
  30. 30.
    Karaboga D, Ozturk C (2011) A novel clustering approach: Artificial bee colony (ABC) algorithm. Appl Soft Comput 11(1):652–657.
  31. 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.
  32. 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. Google Scholar
  33. 33.
    Kasuga H, Yamamoto H, Okamoto M (2000) Color quantization using the fast k-means algorithm. Syst Comput Japan 31 (8):33–40.<33::AID-SCJ4>3.0.CO;2-C
  34. 34.
    Kohonen T (1998) The self-organizing map. Neurocomput 21(1-3):1–6. zbMATHGoogle Scholar
  35. 35.
    Linde Y, Buzo A, Gray R (1980) An algorithm for vector quantizer design. IEEE Trans Commun 28 (1):84–95. Google Scholar
  36. 36.
    Liu GH, Yang JY (2013) Content-based image retrieval using color difference histogram. Pattern Recogn 46(1):188–198. Google Scholar
  37. 37.
    Omran M, Engelbrecht AP, Salman A (2005a) A color image quantization algorithm based on particle swarm optimization. Inform (Slovenia) 29(3):261–270zbMATHGoogle Scholar
  38. 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. Google Scholar
  39. 39.
    Orchard MT, Bouman CA (1991) Color quantization of images. IEEE Trans Signal Proc 39(12):2677–2690. Google Scholar
  40. 40.
    Özdemir D, Akarun L (2002) A fuzzy algorithm for color quantization of images. Pattern Recogn 35 (8):1785–1791. zbMATHGoogle Scholar
  41. 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. Google Scholar
  42. 42.
    Palomo EJ, Domínguez E (2014) Hierarchical color quantization based on self-organization. J Math Imaging Vis 49(1):1–19. Google Scholar
  43. 43.
    Papamarkos N, Atsalakis AE, Strouthopoulos CP (2002) Adaptive color reduction. IEEE Trans Syst Man Cybern B Cybern 32(1):44–56. zbMATHGoogle Scholar
  44. 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. Google Scholar
  45. 45.
    Pérez-Delgado ML (2015) Colour quantization with ant-Tree. Appl Soft Comput 36:656–669. Google Scholar
  46. 46.
    Pérez-Delgado ML (2018a) Campus Viriato images. Accessed 19.10.18
  47. 47.
    Pérez-Delgado ML (2018b) Source code for colour quantization. Accessed 20.07.18
  48. 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. Google Scholar
  49. 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. Google Scholar
  50. 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. Google Scholar
  51. 51.
    Schaefer G, Zhou H (2009) Fuzzy clustering for colour reduction in images. Telecommun Syst 40(1):17–25. Google Scholar
  52. 52.
    Scheunders P (1997) A genetic c-means clustering algorithm applied to color image quantization. Pattern Recogn 30(6):859–866. Google Scholar
  53. 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. Google Scholar
  54. 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. Google Scholar
  55. 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.
  56. 56.
    Uchiyama T, Arbib MA (1994) An algorithm for competitive learning in clustering problems. Pattern Recogn 27(10):1415–1421. Google Scholar
  57. 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,
  58. 58.
    Wan S, Prusinkiewicz P, Wong S (1990) Variance-based color image quantization for frame buffer display. Color Res Appl 15(1):52–58. Google Scholar
  59. 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. Google Scholar
  60. 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,
  61. 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. Google Scholar
  62. 62.
    Weber A (2018) USC-SIPI image database. Accessed 19.10.18
  63. 63.
    Wen Q, Celebi ME (2011) Hard versus fuzzy c-means clustering for color quantization. EURASIP J Adv Signal Proc 2011(1):1–12. Google Scholar
  64. 64.
    Wu X (1991) Efficient statistical computations for optimal color quantization. In: Graphics gems, vol II. Academic Press, pp 126–133, DOI
  65. 65.
    Wu X (1992) Color quantization by dynamic programming and principal analysis. ACM Trans Graph 11 (4):348–372. zbMATHGoogle Scholar
  66. 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. MathSciNetGoogle Scholar
  67. 67.
    Yang CY, Lin JC, et al. (1996) RWM-Cut for color image quantization. Comput Graph 20(4):577–588. Google Scholar
  68. 68.
    Zhang C, Ouyang D, Ning J (2010) An artificial bee colony approach for clustering. Expert Syst Appl 37(7):4761–4767. Google Scholar

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Authors and Affiliations

  1. 1.University of SalamancaZamoraSpain

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