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Fusion of Image Information under Imprecision

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 12))

Abstract

We present in this paper a review of image fusion techniques paying a special attention to the management of uncertainty and imprecision. We investigate the three main numerical methods based on probabilistic reasoning, fuzzy set theory and Dempster-Shafer evidence theory. We show how it is possible to introduce imprecision at the three basic levels of modelling, combining and deciding. We underline the main advantages of each method at these three levels. We also explore some promising fields where innovative works will most certainly take place in the coming years. They concern the management of spatial information within the framework of fusion and require the development of new tools or the extension of yet established ones.

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References

  1. N.M. Andress and A. C. Nak. Evidence Accumulation and Flow Control in a Hierarchical Spatial Reasoning System. AI Magazine, pages 75–94, 1988.

    Google Scholar 

  2. A. Appriou. Formulation et traitement de l’incertain en analyse multi-senseurs. In Quatorziérne Colloque GRETS7, pages 951–954, Juan les Pins, 1993.

    Google Scholar 

  3. L. Aurdal, X. Descombes, H. Maître, I, Bloch, C. Adamsbaum, and G. Nalifa. Fully Automated Analysis of Adrenoleukodystrophy from Dual Echo MR Images: Automatic Segmentation and Quantification. In Computer Assisted Radiology CAR’95, pages 35–40, Berlin, Germany, June 1995.

    Google Scholar 

  4. J. F. Baldwin. Inference for Information Systems Containing Probabilistic and Fuzzy Uncertainties. In L. Zadeh and J. Kacprzyk, editors, Fuzzy Logic and the Management of Uncertainty, pages 353–375. J. Wiley, New York, 1992.

    Google Scholar 

  5. Y. Bar-Shalom and T. E. Fortutann. Tracking and Data. Association. Academic Press, San Diego, 1988.

    MATH  Google Scholar 

  6. J. A. Barnett. Computational Methods for a Mathematical Theory of Evidence. In Proc. of 7th LICAI, pages 868–875, Vancouver, 1981.

    Google Scholar 

  7. E. Benoit and L. Foulloy. Capteurs flous multicomposantes: applications à la reconnaissance Iles couleurs. In Les Applications des Ensembles Flous, pages 167–176, Nîmes, France, October 1993.

    Google Scholar 

  8. J. C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New-York, 1981.

    Book  MATH  Google Scholar 

  9. I. Bloch. Distances in Fuzzy Sets for Image Processing derived from Fuzzy Mathematical Morphology. In Information Processing and Management of Uncertainty in Knowledge-Based Systems, pages 1307–1312, Granada, Spain, July 1996.

    Google Scholar 

  10. I. Bloch. Fuzzy Spatial Relationships: A Few Tools for Model-based Pattern Recognition in Aerial Images. In SPIE/EUROPTO Conference on Image and Signal Processing for Remote Sensing, volume 2955, pages 111–152, Taormina, Italy, September 1996.

    Google Scholar 

  11. I. Bloch. Information Combination Operators for Data Fusion: A Comparative Review with Classification. IEEE Trans. on Systems, Man, and Cybernetics, 26 (1): 52–67, 1996.

    Google Scholar 

  12. I. Bloch. Some Aspects of Dempster-Shafer Evidence Theory for Classification of Multi-Modality Medical Images Taking Partial Volume Effect into Account. Pattern Recognition Letters, 17 (8): 905–919, 1996.

    Article  Google Scholar 

  13. I. Bloch. Using Fuzzy Mathematical Morphology in the Dempster-Shafer Framework for Image Fusion under Imprecision. In IFSA’97, Prague, 1997.

    Google Scholar 

  14. I. Bloch and H. Maître. Fusion de données en traitement d’images: modèles d’information et décisions. Traitement du. Signal, 11 (6): 435–446, 1994.

    MATH  Google Scholar 

  15. I. Bloch and H. Maître. Fuzzy Mathematical Morphologies: A Comparative Study. Pattern Recognition, 28 (9): 1341–1387, 1995.

    Article  MathSciNet  Google Scholar 

  16. I. Bloch, C. Pellot, F. Sureda, and A. Herment. 3D Reconstruction of Blood Vessels by Multi-Modality Data Fusion using Fuzzy and Markovian Modelling. In CVRMed’95, pages 392–398, Nice, France, April 1995.

    Google Scholar 

  17. B. Bouchon-Meunier and R. R. Yager. Entropy of Similarity Relations in Questionnaires and Decision Trees. In Second IEEE Int. Conf. on Fuzzy Systems, pages 1225–1230, San Francisco, California, March 1993.

    Google Scholar 

  18. N. Boujemaa, G. Stallion, J. Lemoine, and E. Petit. Fuzzy Ventricular Endocardium Detection with Gradual Focusing Decision. In 14th IEEE EMBS Conference, pages 1893–1894, Paris, France, 1992.

    Google Scholar 

  19. H. Caillol, A. Billion, and W. Pieczynski. Fuzzy Random Fields and Unsupervised Image Segmentation. IEEE Trans. an Geoscience and Remote Sensing, 31 (4): 801–810, 1993.

    Article  Google Scholar 

  20. B. Charroux. Image Analysis: Interpretation-Guided Cooperation between Segmentation Operators (in French). PhD thesis, University Paris X I, January 1996.

    Google Scholar 

  21. S. Chauvin. Evaluation of Decision Theories Applied to Data. Fusion in Satellite Imaging (in French). PhD thesis, ENST and Nantes University, December 1995.

    Google Scholar 

  22. S. Y. Chen, W. C. Lin, and C. T. Chen. Evidential Reasoning based on Dempster-Shafer Theory and its Application to Medical Image Analysis. In SPIE, volume 2032, pages 35–46, 1993.

    Google Scholar 

  23. C. C. Chu and J. N. Aggarwal. The Integration of Image Segmentation Maps using Region and Edge Information. IEEE Trans. on Pattern Analysis and Machine Intelligence, 15 (13): 1241–1252, 1993.

    Article  Google Scholar 

  24. P. Cucka and A. Rosenfeld. Evidence-based Pattern Matching Relaxation. Technical Report CAR-TR-623, (’enter of Automation Research, University of Maryland, May 1992.

    Google Scholar 

  25. B. V. Dasarathy. Fusion Strategies for Enhancing Decision Reliability in Multi-Sensor Environments. Optical Engineering, 35 (3): 603–616, March 1996.

    Article  Google Scholar 

  26. S. Dellepiane, F. Fontana. and G. A’ernazza. A Robust Non-Iterative Method for Image Labelling using Context. In IEEE [nt. Conf. on Image Processing, volume I1, pages 207–211, Austin, “lexas, November 1994.

    Google Scholar 

  27. S. Dellepiane, G. Venturi, and G. Veinazza. Model Generation and Model Matching of Real Images by a Fuzzy Approach. Pattern Recognition, 25 (2): 115–137, 1992.

    Article  Google Scholar 

  28. C. Demko, P. Loonis, and E. H. Zahzah. Isomorphism of Fuzzy Structures: a New Method for Image Classification. In 9th Scandinavian Conference on Image Analysis, pages 297–304, Uppsala, Sweden, June 1995.

    Google Scholar 

  29. T. Denoeux. A k-nearest Neighbor Classification Rule based on Dempster-Shafer Theory. IEEE Trans. on Systems. Man and Cybernetics, 25 (5): 804–813, 1995.

    Article  Google Scholar 

  30. X. Descombes, M. Moctezuma, H. Maître, and.I.-P. Ruilant. Coastline Detection by a Markovian Srgniciltaliurn in SAR lwagce. Signat processing, 55 (1): 123–132, November 1996.

    Article  MATH  Google Scholar 

  31. D. Dubois and H. Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New-York, 1980.

    MATH  Google Scholar 

  32. D. Dubois and H. Prade. A Review of Fuzzy Set Aggregation Connectives. Information Sciences, 36: 85–121, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  33. D. Dubois and H. Prade. Representation and Combination of Uncertainty with Belief Functions and Possibility Measures. Compu. Intell., 4: 244–264, 1988.

    Article  Google Scholar 

  34. D. Dubois and H. Prade. Combination of Information in the Framework of Possibility Theory. In M. Al Abidi et al., editor, Data Fusion in Robotics and Machine Intelligence. Academic Press, 1992.

    Google Scholar 

  35. R. Duda and P. Hart. Pattern Classification and Scene Analysis. Wiley, New-York, 1973.

    MATH  Google Scholar 

  36. S. J. Gee and A. M. Newman. RADIUS: Automating Image Analysis Through Model-Supported Exploitation. In Image Understanding Work shop, pages 185–196, Washington D.C., 1993.

    Google Scholar 

  37. S. Geman and D. Geman. Stochastic Relaxation, Gibbs Distribution and the Bayesian Restoration of Images. IEEE trans. on Pattern Analysis and Machine Intelligence, PAMI-6: 721–741, 1984.

    Google Scholar 

  38. T. Géraud, J.-F. Mangin, I. Bloch, and H. Maître. Segmenting Internal Structures in 3D MR Images of the Brain by Markovian Relaxation on a Watershed Based Adjacency Graph. In ICIP-95,pages 548–551, Washington DC, October 1995

    Google Scholar 

  39. J. Gordon and E. H. Shortliffe. A Method for Managing Evidential Reasoning in a Hierarchical Hypothesis Space. Artificial Intelligence, 26: 323–357, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  40. J. Guan and D. A. Bell. Evidence Theory and its Applications. North-Holland, Amsterdam, 1991.

    MATH  Google Scholar 

  41. L. O. Hall, T. L. Machrzak, and M. S. Silbiger. Obtaining Fuzzy Classification Rules in Segmentation. In IPIVIU, pages 619–621, Paris, France, 1994.

    Google Scholar 

  42. T. L. Huntsberger, C. Rangarajan, and S. Javaramamurthy. Representation of Uncertainty in Computer Vision using Fuzzy Sets. IEEE Trans. on Computers, C-35(2): 145–156, 1986.

    Google Scholar 

  43. H. H. S. Ip and.J. M. C. Ng. Human Face Recognition using Dempster-Shafer Theory. In ICIP, volume II, pages 292–295, Austin, Texas, 1994.

    Google Scholar 

  44. M. C. Jaulent and A. Yang. Application of Fuzzy Pattern Matching to the Flexible Interrogation of a Digital Angiographies Database. In IPMU, pages 904–909, Paris, France, 1994.

    Google Scholar 

  45. E. T. Jaynes. Information Theory and Statistical Mechanics. Physical Review, 106 (4): 620–630, 1957.

    Article  MathSciNet  MATH  Google Scholar 

  46. A. Kandel, M. Schneider, and G. Langholz. Autonomous Fuzzy Intelligent Systems for Image Processing. In IPMU, pages 613–618, Paris, France, 1994.

    Google Scholar 

  47. H. B. Nang and E. L. Walker. Characterizing and Controlling Approximation in Hierarchical Perceptual Grouping. Fuzzy Sets and Sytems, 65: 187–223, 1994.

    Article  Google Scholar 

  48. R. Krishnapuram and J. M. Keller. Fuzzy Set Theoretic Approach to Computer Vision: an Overview. In IEEE Int. Conf. on Fuzzy Systems, pages 135–142, San Diego, CA, 1992.

    Google Scholar 

  49. R. Krishnapuram, J. M. Keller and Y. Ma. Quantitative Analysis of Properties and Spatial Relations of Fuzzy Image Regions. IEEE Transactions on Fuzzy Systems, 1 (:3): 222–233, 1993.

    Article  Google Scholar 

  50. S. Kullback. Information Theory and Statistics. Wiley, New York, 1959.

    MATH  Google Scholar 

  51. R. H. Lee and R. Leahy. Multi-Spectral Classification of MR Images Using Sensor Fusion Approaches. In SPIE Medical Imaging IV: Image Processing, volume 1233, pages 149–157, 1990.

    Google Scholar 

  52. T. Lee,.1. A. Richards, and P. H. Swain. Probabilistic and Evidential Approaches for Multisource Data Analysis. IEEE Transactions on Geoscience and Remote Sensing, GE-25(3): 283–293, 1987.

    Google Scholar 

  53. H. Leung. Neural Networks Data Association with Application to Multiple-Target Tracking. Optical Engineering, 35 (3): 693–700, March 1996.

    Article  Google Scholar 

  54. I. D. Lowrance, T. M. Strat, L. P. Wesley, T. D. Garvey, E. H. Ruspini, and D. E. Wilkins. The Theory, Implementation and Practice of Evidential Reasoning. SRI project. 5701 final report, SRI, Palo Alto, June 1991.

    Google Scholar 

  55. A. De Luca and S. Termini. A Definition of Non-Probabilistic Entropy in the Setting of Fuzzy Set Theory. Information and Control, 20: 301–312, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  56. H. Maître. Image Fusion and Decision in a Context of Multisource Images. In 9th Scandinavian Conference on Image Analysis, volume 1. pages 139–153, Uppsala, Sweden. June 1995.

    Google Scholar 

  57. H. Maître- Entropy, Information and Image. In H. Maître and J. Zinn-Justin, editors, Progress in Picture Processing, Les Houches Session LVIII, pages 881–1115. Springer Verlag, 1996.

    Google Scholar 

  58. G. M. T. Man and J. C. H. Poon. A new Similarity Measurement Method for Fuzzy-Attribute Graph Matching and its Application to Handwritten Character Recognition. In Int. Carnahan Conf. on Security Technology, pages 46–49, Lexington, NY, October 1992.

    Google Scholar 

  59. J.-F. Mangin, J. Regis, I. Bloch, V. Frouin, Y. Samson, and J. Lopez-Krahe. A Markovian Random Field based Random Graph Modelling the Human Cortical Topography. In CVRMed’95, pages 177–183, Nice, France, April 1995.

    Google Scholar 

  60. L. Mascarilla. Rule Extraction based on Neural Networks for Satellite Image interpretation. In SPIE Image and Signal Processing for Remote Sensing, volume 2315, pages 657–668, Rome, Italy, 1994.

    Google Scholar 

  61. S. Mascle, I. Bloch, and D. Vidal-Madjar. Unsupervised Multisource Remote Sensing Classification using Dempster-Shafer-Evidence Theory. In SPIE/EUROPTO Conference on Image and Signal Processing for Remote Sensing, volume 2579, Paris, France, September 1995.

    Google Scholar 

  62. D. McKeown, W. A. Harvey, and J. McDermott. Rule-Based Interpretation of Aerial Imagery. IEEE Trans. on Pattern Analysis and Machine Intelligence, 7 (5): 570–585 1985.

    Article  Google Scholar 

  63. M. Ménard, E. H. Zahzah, and A. Shahin. Mass Function Assessment: Case of Multiple Hypotheses for the Evidential Approach. In Enropto Conf. on Image and Signal Processing for Remote Sensing, Taormina, Italy, September 1996.

    Google Scholar 

  64. H. Moissinac, H. Maître, and I. Bloch. Markov Random Fields and Graphs for Uncertainty Management and Symbolic Data Fusion in a Urban Scene Interpretation. In SPIE/EUROPTO Conference on Image and Signal Processing for Remote Sensing, Paris, France, September 1995.

    Google Scholar 

  65. R. E. Neapolitan. A Survey of Uncertain and Approximate Inference. In L. Zadeh and J. Kaprzyk, editors, Fuzzy Logic for the Management of Uncertainty, pages 55–82. J. Wiley, New York, 1992.

    Google Scholar 

  66. H. Ogawa. A Fuzzy Relaxation Technique for Partial Shape Matching. Pattern Recognition Letters, 15: 349–355, 1994.

    Article  Google Scholar 

  67. S. E. Pal. Fuzzy Set. Theoretic Measures for Automatic Feature Evaluation. Information Science, 64: 165–179, 1992.

    Article  MATH  Google Scholar 

  68. J. Pearl. Fusion, Propagation, and Structuring in Belief Networks. Artificial Intelligence, 29: 241–288, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  69. W. Pedrycz. Fuzzy Sets in Pattern Recognition: Methodology and Methods. Pattern Recognition, 23 (1/2): 121–146, 1990.

    Article  Google Scholar 

  70. E. Piat. Fusion de croyances clans le cadre combiné de la logique des propositions et de la théorie des probabilités, application à la reconstruction de scène en robotique mobile. PhD thesis, Université de Technologie de Compiègne, 1996.

    Google Scholar 

  71. A. Ralescu and R. Hartani. Modeling the Perception of Facial Expressions from Face Photographs. In 10th Fuzzy System. Symposium,pages 405–408, Ozaka, Japan, June 1994

    Google Scholar 

  72. H. S. Ranganath and L. C. Chipman. Fuzzy Relaxation Approach for Inexact Scene Matching. Image and Vision Computing, 10 (9): 631–640, 1992.

    Article  Google Scholar 

  73. N. S. V. Rao and S. S. lyengar. Distributed Decision Fusion under Unknown Distributions. Optical Engineering, 35 (3): 617–624, March 1996.

    Article  Google Scholar 

  74. J. B. Romine and E. W. Kamen. Modeling and Fusion of Radar and Imaging Sensor Data for Target Tracking. Optical Engineering, 35 (3): 659–673, March 1996.

    Article  Google Scholar 

  75. A. Rosenfeld. Fuzzy Digital Topology. Information and Control, 40: 76–87, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  76. A. Rosenfeld. The Fuzzy Geometry of Image Subsets. Pattern Recognition Letters, 2: 311–317, 1984.

    Article  Google Scholar 

  77. A. Rosenfeld, R. Hummel, and S. Zucker. Scene Labeling by Relaxation Operations. IEEE Transactions on Systems, Man and Cybernetics, 6: 420–433, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  78. F. Russo and G. Ramponi. An Image Enhancement Technique based on the FIRE Operator. In IEEE Int. Conf. on Image Processing, volume I, pages 155–158, Washington DC, 1995.

    Google Scholar 

  79. F. Salzenstein and W. Pieczynski. Unsupervised Bayesian Segmentation using Hidden Fuzzy Markov Fields. In IEEE Int. Conf. on Acoustics. Speech and Signal Procesing, Detroit., Michigan, 1995.

    Google Scholar 

  80. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, 1976.

    Google Scholar 

  81. J. C. Simon. From Pixels to Features. V-X, North Holland, Amsterdam, 1989.

    Google Scholar 

  82. P. Smets. Medical Diagnosis: Fuzzy Sets and Degree of Belief. In Colloque International sur la Théorie et les Applications des Sous-Ensembles Flous, Marseille, September 1978.

    Google Scholar 

  83. P. Smets. The Combination of Evidence in the Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-12(5): 447–458, 1990.

    Google Scholar 

  84. P. Smets. Belief Functions: The Disjunctive Rule of Combination and the Generalized Bayesian Theorem. International Journal of Approximate. Reasoning, 9: 1–35, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  85. P. Surets. The Transferable Belief Model for Uncertainty Representation. Technical Report TR/IRIDIA/95–23, IRIDIA, Université Libre de Bruxelles, Bruxelles, Belgium, 1995.

    Google Scholar 

  86. Léa Sombé. Raisonnements sur des informations incomplètes en intelligence artificielle. Teknea, Marseille, 1989.

    Google Scholar 

  87. H. E. Stephanou and S. Y. Lu. Measuring Consensus Effectiveness by a Generalized Entropy Criterion. In First Conference on Artificial Intelligence Applications, pages 518–523, Denver, December 1984.

    Google Scholar 

  88. T. M. Strat. Decision Analysis using Belief Functions. Technical Note 472, SRI, September 1989.

    Google Scholar 

  89. D. Y. Suh, R. M. Mersereau, R. L. Eisner, and R. I. Pettigrew. Automatic Boundary Detection on Cardiac Magnetic Resonance Image Sequences for Four Dimensional Visualization of the Left Ventricle. In First Conference on Visualization in Biomedical Computing, pages 149–156, Atlanta GE, 1990.

    Google Scholar 

  90. H. Tahani and J. M. Keller. Information Fusion in Computer Vision Using the Fuzzy Integral. IEEE Transactions on System, Man and Cybernetics, 20 (3): 733–741, 1990.

    Article  Google Scholar 

  91. S. C. A. Thomopoulos. Sensor Integration and Data Fusion. Journal of Robotics Systems, 7 (3): 337–372, 1990.

    Article  Google Scholar 

  92. F. Tupin, H. Maître, J-F. Mangin, J-M. Nicolas, and E. Pechersky. Linear Feature Detection on SAR Images: Application to the Road Network. Technical report, Ecole Nationale Supérieure des Télécommunications (96D006), May 1996.

    Google Scholar 

  93. J. van Cleynenbreugel, S. A. Osinga, F. Fierens, P. Suetens, and A. Oosterlinck. Road Extraction from Multi-temporal Satellite Images by an Evidential Reasoning Approach. Pattern Recognition Letters, 12: 371–380, 1991.

    Article  Google Scholar 

  94. A. Winter, H. Maître, N. Caribou, and E. Legrand. Object. Detection Using a Multiscale Probability Model. In IEEE Int. Conf. on Image Processing ICIP’96, volume I, pages 269–272, Lausanne, September 1996.

    Google Scholar 

  95. R. R. Yager. Connectives and Quantifiers in Fuzzy Sets. Fuzzy Sets and Systems. 40: 39–75, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  96. B. Van. Semiconormed Possibility Integrals and Multi-Feature Pattern Classification. Pattern Recognition, 26 (12): 1855–1862, 1993.

    Article  MathSciNet  Google Scholar 

  97. L. A. Zadeh. Fuzzy Sets. Information and Control, 8: 338–353, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  98. L. A. Zadeh. Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1: 3–28, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  99. E. Zahzah. Contribution n la représentation des connaissances et 6 leur utilisation pour l’interprétation automatique des images satellites. Thèse de doctorat, Université Paul Sabatier, Toulouse, 1992.

    Google Scholar 

  100. R. Zwick, E. Carlstein, and D. V. Budescu. Measures of Similarity Among Fuzzy Concepts: A Comparative Analysis. International Journal of Approximate Reasoning, 1: 221–242, 1987.

    Article  MathSciNet  Google Scholar 

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Bloch, I., Maître, H. (1998). Fusion of Image Information under Imprecision. In: Bouchon-Meunier, B. (eds) Aggregation and Fusion of Imperfect Information. Studies in Fuzziness and Soft Computing, vol 12. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1889-5_11

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  • DOI: https://doi.org/10.1007/978-3-7908-1889-5_11

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