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Kernel smoothing classification of multiattribute data in the belief function framework: Application to multichannel image segmentation

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Abstract

Bayesian approaches turn out to be inefficient when decision making involves many uncertain, imprecise or unreliable sources of information. The same problem occurs in multiattribute data classification where each attribute can be perceived as a source of information. The theory of belief functions has been extensively used to overcome this issue. Moreover, Markov field approaches involving this theory have shown their interest in image modeling and processing. The aim of this paper is to propose a new approach for multichannel (typically remote sensing) image segmentation through hidden Markov fields, which better manage non Gaussian noise forms, by adopting Weighted Parzen-Rosenblatt Dempster-Shafer likelihood model. More explicitly, observations are modeled through belief functions constructed through a kernel smoothing- based scheme rather than using plain Gaussian densities as in the typical hidden Markov fields. The interest of the proposed approach is shown through experiments conducted on sampled and real multichannel remote sensing images.

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References

  1. An L, Li M, Boudaren MEY, Pieczynski W (2018) Unsupervised segmentation of hidden markov fields corrupted by correlated non-gaussian noise. Int J Approx Reason 102:41–59

    Article  MathSciNet  Google Scholar 

  2. Bendjebbour A, Delignon Y, Fouque L, Samson V, Pieczynski W (2001) Multisensor image segmentation using dempster-shafer fusion in markov fields context. IEEE Trans Geosci Remote Sens 39(8):1789–1798

    Article  Google Scholar 

  3. Besag J (1974) Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B (Methodological), 192–236

  4. Boudaren MEY, An L, Pieczynski W (2016) Dempster–shafer fusion of evidential pairwise markov fields. Int J Approx Reason 74:13–29

    Article  MathSciNet  Google Scholar 

  5. Boudaren MEY, Monfrini E, Pieczynski W (2012) Unsupervised segmentation of random discrete data hidden with switching noise distributions. IEEE Signal Process Lett 19(10):619–622

    Article  Google Scholar 

  6. Bowman AW, Azzalini A (1997) Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations, vol 18. OUP Oxford

  7. Cao X, Xu L, Meng D, Zhao Q, Xu Z (2017) Integration of 3-dimensional discrete wavelet transform and markov random field for hyperspectral image classification. Neurocomputing 226:90–100

    Article  Google Scholar 

  8. Chang CC, Lin CJ (2011) Libsvm: a library for support vector machines. ACM Trans Intell Syst Technol (TIST) 2(3):27

    Google Scholar 

  9. Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inform Theor 13(1):21–27

    Article  Google Scholar 

  10. Delmas JP (1997) An equivalence of the EM and ICE algorithm for exponential family. IEEE Trans Signal Process 45(10):2613–2615

    Article  Google Scholar 

  11. Denoeux T (1995) A k-nearest neighbor classification rule based on dempster-shafer theory. IEEE Trans Syst Man Cybern 25(5):804–813

    Article  Google Scholar 

  12. Derin H, Elliot H (1987) Modelling and segmentation of noisy and textured images using Gibbs random fields. Pattern Analysis and Machine Intelligence IEEE Transactions on 9(1):39–55

    Article  Google Scholar 

  13. Dezert J, Smarandache F (2006) Proportional conflict redistribution rules for information fusion. Advances and Applications of DSmT for Information Fusion-Collected Works 2:3–68

    Google Scholar 

  14. Ding J, Chang CW (2016) An adaptive hidden markov model-based gesture recognition approach using kinect to simplify large-scale video data processing for humanoid robot imitation. Multimed Tools Appl 75(23):15537–15551

    Article  Google Scholar 

  15. Dubois D (2007) Uncertainty theories: a unified view. In: IEEE Cybernetic systems conference, dublin, ireland, invited paper, pp 4–9

  16. Dubois DJ (1980) Fuzzy sets and systems: theory and applications, vol 144. Academic Press

  17. Duin R, Juszczak P, Paclik P, Pekalska E, De Ridder D, Tax D, Verzakov S (2000) A matlab toolbox for pattern recognition. PRTools Version 3:109–111

    Google Scholar 

  18. Elouedi Z, Lefèvre E, Mercier D (2010) Discountings of a belief function using a confusion matrix. In: 2010 22Nd IEEE international conference on tools with artificial intelligence, vol 1. IEEE, pp 287–294

  19. Elouedi Z, Mellouli K, Smets P (2004) Assessing sensor reliability for multisensor data fusion within the transferable belief model. IEEE Trans Syst Man Cybern Part B (Cybern) 34(1):782–787

    Article  Google Scholar 

  20. Fedrizzi M, Kacprzyk J, Yager RR et al (1994) Advances in the dempster–Shafer theory of evidence

  21. Fisher RA (1936) The use of multiple measurements in taxonomic problems. Annals of Human Genetics 7(2):179–188

    Google Scholar 

  22. Freund Y, Mason L (1999) The alternating decision tree learning algorithm. In: Icml, vol 99, pp 124–133

  23. Ghamisi P, Benediktsson JA, Ulfarsson MO (2014) Spectral–spatial classification of hyperspectral images based on hidden Markov random fields. IEEE Trans Geosci Remote Sens 52(5):2565–2574

    Article  Google Scholar 

  24. Guo H, Shi W, Deng Y (2006) Evaluating sensor reliability in classification problems based on evidence theory. IEEE Trans Syst Man Cybern Part B (Cybern) 36(5):970–981

    Article  Google Scholar 

  25. Hamache A, Boudaren MEY, Boukersoul H, Debicha I, Sadouk H, Zibani R, Habbouchi A, Merouani O (2018) Uncertainty-aware parzen-rosenblatt classifier for multiattribute data. In: International conference on belief functions. Springer, pp 103–111

  26. Hu BG (2014) What are the differences between bayesian classifiers and mutual-information classifiers? IEEE Trans Neural Netw Learn Syst 25 (2):249–264

    Article  Google Scholar 

  27. Hu X, Yang K, Fei L, Wang K (2019) Acnet: Attention based network to exploit complementary features for rgbd semantic segmentation. In: 2019 IEEE International conference on image processing (ICIP). IEEE, pp 1440–1444

  28. Ising E (1925) Report on the theory of ferromagnetism. Zeitschrift fur physik 31:253–258

    Article  Google Scholar 

  29. Khaleghi B, Khamis A, Karray FO, Razavi SN (2013) Multisensor data fusion: a review of the state-of-the-art. Inform Fusion 14(1):28–44

    Article  Google Scholar 

  30. Lama RK, Choi MR, Kwon GR (2016) Image interpolation for high-resolution display based on the complex dual-tree wavelet transform and hidden markov model. Multimed Tools Appl 75(23):16487–16498

    Article  Google Scholar 

  31. Le Hegarat-Mascle S, Bloch I, Vidal-Madjar D (1997) Application of dempster-shafer evidence theory to unsupervised classification in multisource remote sensing. IEEE Trans Geosci Remote Sens 35(4):1018–1031

    Article  Google Scholar 

  32. Lichman M (2015) Uci machine learning repository, 2013. http://archive.ics.uci.edu/ml114

  33. Liu YT, Pal NR, Marathe AR, Lin CT (2018) Weighted fuzzy dempster–shafer framework for multimodal information integration. IEEE Trans Fuzzy Syst 26(1):338–352

    Article  Google Scholar 

  34. Mercier D, Lefèvre É, Delmotte F (2012) Belief functions contextual discounting and canonical decompositions. Int J Approx Reason 53 (2):146–158

    Article  MathSciNet  Google Scholar 

  35. Mor B, Garhwal S, Kumar A (2020) A systematic review of hidden markov models and their applications. Archives of Comput Methods Eng, 1–20

  36. Murphy CK (2000) Combining belief functions when evidence conflicts. Dec Support Syst 29(1):1–9

    Article  Google Scholar 

  37. Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33(3):1065–1076

    Article  MathSciNet  Google Scholar 

  38. Pieczynski W, Benboudjema D (2006) Multisensor triplet markov fields and theory of evidence. Image Vis Comput 24(1):61–69

    Article  Google Scholar 

  39. Potts RB (1952) Some generalized order-disorder transformations. In: Mathematical proceedings of the cambridge philosophical society, vol 48. Cambridge University Press, pp 106–109

  40. Rosenblatt M (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 832–837

  41. Salzenstein F, Boudraa AO (2001) Unsupervised multisensor data fusion approach. In: Signal processing and its applications, sixth international, symposium on. 2001, vol 1. IEEE, pp 152–155

  42. Sebbak F, Benhammadi F, Mataoui M, Bouznad S, Amirat Y (2014) An alternative combination rule for evidential reasoning. In: Information fusion (FUSION), 2014 17th international conference on. IEEE, pp 1–8

  43. Shafer G (1976) A mathematical theory of evidence, vol 1. Princeton University Press, Princeton

    Book  Google Scholar 

  44. Shafer G (2016) The problem of dependent evidence. Int J Approx Reason 79:41–44

    Article  MathSciNet  Google Scholar 

  45. Shafer G, Logan R (1987) Implementing Dempster’s rule for hierarchical evidence. Artif Intell 33(3):271–298

    Article  MathSciNet  Google Scholar 

  46. Singh A, Sethi G, Kalra G (2020) Spatially adaptive image denoising via enhanced noise detection method for grayscale and color images. IEEE Access 8:112985–113002

    Article  Google Scholar 

  47. Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66(2):191–234

    Article  MathSciNet  Google Scholar 

  48. Smolka B, Kusnik D (2020) On the application of the reachability distance in the suppression of mixed gaussian and impulsive noise in color images. Multimed Tools Appl 79(43):32857–32879

    Article  Google Scholar 

  49. Veenman CJ, Reinders MJ (2005) The nearest subclass classifier: a compromise between the nearest mean and nearest neighbor classifier. IEEE Trans Pattern Anal Machine Intell 27(9):1417–1429

    Article  Google Scholar 

  50. Walley P (1991) Statistical reasoning with imprecise probabilities, vol 42. Peter Walley

  51. Wand MP, Jones MC (1994) Kernel smoothing. Crc Press

  52. Wi H, Eibe F, Mining D (2011) Practical machine learning tools and techniques. United State, Morgan Kauffman

    Google Scholar 

  53. Xu P, Davoine F, Zha H, Denoeux T (2016) Evidential calibration of binary svm classifiers. Int J Approx Reason 72:55–70

    Article  MathSciNet  Google Scholar 

  54. Xu P, Deng Y, Su X, Mahadevan S (2013) A new method to determine basic probability assignment from training data. Knowl-Based Syst 46:69–80

    Article  Google Scholar 

  55. Zadeh LA (1979) On the validity of Dempster’s rule of combination of evidence, Electronics Research Laboratory, College of Engineering. University of California, Berkeley

    Google Scholar 

  56. Zadeh LA (1996) Fuzzy sets. In: Fuzzy sets, fuzzy logic, and fuzzy systems: Selected papers by lotfi a zadeh. World Scientific, pp 394–432

  57. Zadeh LA (2002) Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J Stat Plann Inf 105(1):233–264

    Article  MathSciNet  Google Scholar 

  58. Zimmermann HJ (2011) Fuzzy set theory—and its applications. Springer Science & Business Media, Berlin

    Google Scholar 

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Authors and Affiliations

  1. Ecole Militaire Polytechnique, PO Box 17, Bordj El Bahri, 16111, Algiers, Algeria

    Ali Hamache & Mohamed El Yazid Boudaren

  2. SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, 9 rue Charles Fourier, 91000, Evry, France

    Wojciech Pieczynski

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  1. Ali Hamache
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  2. Mohamed El Yazid Boudaren
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  3. Wojciech Pieczynski
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Correspondence to Ali Hamache.

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Hamache, A., Boudaren, M.E.Y. & Pieczynski, W. Kernel smoothing classification of multiattribute data in the belief function framework: Application to multichannel image segmentation. Multimed Tools Appl 81, 29587–29608 (2022). https://doi.org/10.1007/s11042-022-12086-w

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