Local thresholding of degraded or unevenly illuminated documents using fuzzy inclusion and entropy measures

  • Athanasios C. BogiatzisEmail author
  • Basil K. Papadopoulos
Original Paper


There are applications in which the content of a scanned document needs to be recognized or improved. We often achieve this by converting our input into a binary image and this is in fact the first step in many document analysis systems or optical character recognition (OCR) processes. In cases where our input is degraded or has a non-uniform illumination, global thresholding algorithms fail to deliver adequate results. For this reason, we have to use some local thresholding techniques which binarize each pixel based on the grayscale information of its adjoining pixels. In this paper, we present a local thresholding method based on specific fuzzy inclusion and entropy measures which we introduced in some of our previous work. We use these indicators to measure specific attributes of the neighborhood of a pixel and then, based on these values, an appropriate threshold is calculated. We don’t use the histogram of the image or any statistical measures and contrast parameters depending on the input. It is an open, automated and adaptable procedure and in this presentation we see some implementations of a more general algorithm along with some specific results. Our main domain of experimentation consists of texts containing lighting “irregularities” but some remarks regarding further generalization are being made as well. We also comment on other potential of these measures and the prospect of being connected with other studies that already use fuzzy inclusion and entropy measures.


Fuzzy entropy Fuzzy inclusion Fuzzy measuring Image binarization Local thresholding 



  1. Abak T, Baris U, Sankur B (1997) The performance of thresholding algorithms for optical character recognition. In: International conference on document analysis and recognition ICDAR’97, pp 697–700Google Scholar
  2. Angelov P, Yager Y (2013) Density-based averaging-a new operator for data fusion. Inf Sci 222:163–174MathSciNetzbMATHGoogle Scholar
  3. Angelov P, Kasabov N (2005) Evolving computational intelligence systems. In: Proceedings of the 1st international workshop on genetic fuzzy systems, pp 76–82Google Scholar
  4. Angelov P, Victor J, Dourado A, Filev D (2004) On-line evolution of Takagi-Sugeno fuzzy models. In: 2nd IFAC workshop on advanced fuzzy/neural control, pp 67–72Google Scholar
  5. Bernsen J (1986) Dynamic thresholding of gray-level images. In: Proceedings of 8th international conference on pattern recognition, Paris, pp 1251–1255Google Scholar
  6. Blayvas I, Bruckstein A, Kimmel R (2006) Efficient computation of adaptive threshold surfaces for image binarization. Pattern Recognit 39:89–101Google Scholar
  7. Bogiatzis A, Papadopoulos B (2018a) Binarization of texts with varying lighting conditions using fuzzy inclusion and entropy measures. Int Conf Num Anal Appl Math 1978(1):290006Google Scholar
  8. Bogiatzis A, Papadopoulos B (2018b) Producing fuzzy inclusion and entropy measures and their application on global image thresholding. Evolving Systems 9(4):331–353Google Scholar
  9. Boulmakoul A, Laarabi MH, Sacile R (2017) An original approach to ranking fuzzy numbers by inclusion index and Bitset Encoding. Fuzzy Optim Decis Mak 16(1):23–49MathSciNetzbMATHGoogle Scholar
  10. Bronevich AG, Rozenberg IN (2014) Ranking probability measures by inclusion indices in the case of unknown utility function. Fuzzy Optim Decis Mak 13(1):49–71 Springer, USMathSciNetzbMATHGoogle Scholar
  11. Baruah RD, Angelov P (2014) DEC: dynamically evolving clustering and its application to structure identification of evolving fuzzy models. IEEE Trans Cybern 44(9):1619–1631Google Scholar
  12. Baruah RD, Angelov P (2012) Evolving local means method for clustering of streaming data. In: IEEE international conference on fuzzy systems, pp 1-8Google Scholar
  13. Cho S, Haralick R, Yi S (1989) Improvement of Kittler and Illingworth’s minimum error thresholding. Pattern Recognit 22(5):609–617Google Scholar
  14. Chow CK, Kaneko T (1972) Automatic detection of the left ventricle from cineangiograms. Comput Biomed Res 5:388–410Google Scholar
  15. Cintra ME, Monard MC, Camargo HA (2010) Data base definition and feature selection for the genetic generation of fuzzy rule bases. Evol Syst 1(4):241–252Google Scholar
  16. Cross V (2018) Relating fuzzy set similarity measures. Adv Intell Syst Comput 648:9–21Google Scholar
  17. Dey V, Pratihar DK, Datta GL (2011) Genetic algorithm-tuned entropy-based fuzzy C-means algorithm for obtaining distinct and compact clusters. Fuzzy Optim Decis Mak 10(2):153–166MathSciNetGoogle Scholar
  18. Eikvil L, Taxt T, Moen K (1991) A fast adaptive method for binarization of document images. In: Proceedings of ICDAR, France, pp 435–443Google Scholar
  19. Firdousi R, Parveen S (2014) Local thresholding techniques in image binarization. Int J Eng Comput Sci 3(3):4062–4065Google Scholar
  20. Henzgen S, Strickert M, Hullermeier E (2014) Visualization of evolving fuzzy rule-based systems. Evol Syst 5(3):175–191Google Scholar
  21. Herbst G, Bocklisch SF (2010) Recognition of fuzzy time series patterns using evolving classification results. Evol Syst 1(2):97–110Google Scholar
  22. Huang LK, Wang MJJ (1995) Image thresholding by minimizing the measures of fuzziness. Pattern Recognit 28(1):41–51Google Scholar
  23. Hulianytskyi LF, Riasna II (2016) Automatic classification method based on a fuzzy similarity relation. Cybern Syst Anal 52(1):30–37zbMATHGoogle Scholar
  24. Jung D, Choi JW, Park WJ (2011) Quantitative comparison of similarity measure and entropy for fuzzy sets. J Cent South Univ Technol 18(6):2045–2049Google Scholar
  25. Klir GJ, Yuan B (1996) Fuzzy sets and fuzzy logic:  theory and applications. Prentice Hall, Upper Saddle River, NJzbMATHGoogle Scholar
  26. Kosko B (1992) Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  27. Kosko B (1990) Fuzziness vs. probability. Int J Gen Syst 17:211–240zbMATHGoogle Scholar
  28. Kosko B (1986) Fuzzy entropy and conditioning. Inf Sci 40:165–174MathSciNetzbMATHGoogle Scholar
  29. Lan R, Fan JL, Liu Y (2016) Image thresholding by maximizing the similarity degree based on intuitionistic fuzzy sets. Quant Log Soft Comput Adv Intell Syst Comput 510:631–640Google Scholar
  30. Leedham G, Yan C, Takru K et al (2003) Thresholding algorithms for text/background segmentation in difficult document images. In: Seventh international conference on document analysis and recognition (ICDAR), pp 859–864Google Scholar
  31. Leng G, Zeng XJ, Keane JA (2012) An improved approach of self-organising fuzzy neural network based on similarity measures. Evol Syst 3(1):19–30Google Scholar
  32. Lukka P (2011) Feature selection using fuzzy entropy measures with similarity classifer. Expert Syst Appl 38(4):4600–4607Google Scholar
  33. Mansoori EG, Shafiee KS (2016) On fuzzy feature selection in designing fuzzy classifiers for high-dimensional data. Evol Syst 7(4):255–265Google Scholar
  34. Mardia KV, Hainsworth TJ (1988) A spatial thresholding method for image segmentation. IEEE Trans Pattern Anal Mach Intell 10:919–927Google Scholar
  35. Niblack W (1986) An introduction to digital image processing. Prentice-Hall International, Englewood CliffsGoogle Scholar
  36. Oh W, Lindquist B (1999) Image thresholding by indicator kriging. Pattern Anal Mach Intell IEEE Trans 21(7):590–602Google Scholar
  37. Otsu N (1975) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66Google Scholar
  38. Palanisamy C, Selvan S (2009) Efficient subspace clustering for higher dimensional data using fuzzy entropy. J Syst Sci Syst Eng 18(1):95–110zbMATHGoogle Scholar
  39. Parker JR (1991) Gray level thresholding in badly illuminated images. IEEE Trans Pattern Anal Mach Intell 13(8):813–819Google Scholar
  40. Prasad M, Divakar T, Rao B (2011) Unsupervised image thresholding using fuzzy measures. Int J Comput Appl 27(2):32–41Google Scholar
  41. Sauvola J, Pietikainen M (2000) Adaptive document image binarization. Pattern Recognit 33(2):225–236Google Scholar
  42. Sauvola J, Seppanen T, Haapakoski S et al (1997) Adaptive document binarization. In: Proceedings of 4th international conference on document analysis and recognition, Ulm Germany, pp 147–152Google Scholar
  43. Scozzafava R, Vantaggi B (2009) Fuzzy inclusion and similarity through coherent conditional probability. Fuzzy Sets Syst 160:292–305MathSciNetzbMATHGoogle Scholar
  44. Sezgin M, Sankur B (2001) Comparison of thresholding methods for non-destructive testing applications, IEEE ICIP’2001. In: International Conference Image Processing, pp 764–767Google Scholar
  45. Sezgin M, Sankur B (2004)  Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13:146Google Scholar
  46. Singh TR, Roy S, Singh OI et al (2011) A new local adaptive thresholding technique in binarization. Int J Comput Sci Issues 8(6):271–277Google Scholar
  47. Singh OI, Sinam T, James O et al (2012) Local contrast and mean based thresholding technique in image binarization. Int J Comput Appl 51(6):4–10Google Scholar
  48. Sussner P, Valle ME (2008) Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality. J Math Imaging Vis 32(2):139–159MathSciNetGoogle Scholar
  49. Trier OD, Taxt T (1995) Evaluation of binarization methods for document images. IEEE Trans Pattern Anal Mach Intell 17:312–315Google Scholar
  50. White JM, Rohrer GD (1983) Image thresholding for optical character recognition and other applications requiring character image extraction. IBM J Res Dev 27(4):400–411Google Scholar
  51. Xiaoyi J (2003) Adaptive local thresholding by verification—based multithreshold probing with application to vessel detection in retinal images. In: IEEE transactions on pattern analysis and machine intelligence Vol. 25. Computer Society, pp 131–137Google Scholar
  52. Yanowitz SD, Bruckstein AM (1989) A new method for image segmentation*. Comput Vis Graph Image Process 46(1):82–95Google Scholar
  53. Young RV (1996) Fuzzy subsethood. Fuzzy Sets Syst 77:371–384MathSciNetzbMATHGoogle Scholar
  54. Zhang H, Yang S (2016) Inclusion measure for typical hesitant fuzzy sets, the relative similarity measure and fuzzy entropy. Soft Comput 20(4):1277–1287MathSciNetzbMATHGoogle Scholar
  55. Zhang YJ (1996) A survey on evaluation methods for image segmentation. Pattern Recognit 29:1335–1346Google Scholar
  56. Zhou R, Yang Z, Yu M (2015) A portfolio optimization model based on information entropy and fuzzy time series. Fuzzy Optim Decis Mak 14(4):381–397MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Democritus University of Thrace, Department of Civil Engineering, Section of Mathematics, Informatics and General CoursesXanthiGreece

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