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Fuzzy Models of Spatial Relations, Application to Spatial Reasoning

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On Fuzziness

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 298))

Abstract

Spatial relations are an important component of image content, that proved to be useful for recognition of individual objects and for image understanding. Indeed, spatial relations provide structural information about the scene, which is often more stable that individual object characteristics, can help disambiguating objects of similar appearance, and is often available as prior knowledge. A typical example is anatomy, where relations between anatomical structures are described in anatomical textbooks or dedicated web sites, and can be used to drive the interpretation of medical images. This will be illustrated on magnetic resonance images (MRI) of the brain, for segmenting and recognizing internal brain structures. This is a typical example where shape and appearance information may not be sufficient for recognition, in particular in pathological cases, while using structural knowledge is relevant and helps solving the problem. Similar examples can be found in understanding aerial and satellite images.

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References

  1. Aiello, M.: Spatial Reasoning, Theory and Practice. PhD thesis, University of Amsterdam (February 2002)

    Google Scholar 

  2. Atif, J., Hudelot, C., Bloch, I.: Abduction in description logics using formal concept analysis and mathematical morphology: application to image interpretation. In: 8th International Conference on Concept Lattices and Their Applications (CLA 2011), Nancy, Paris, pp. 405–408 (October 2011)

    Google Scholar 

  3. Atif, J., Hudelot, C., Fouquier, G., Bloch, I., Angelini, E.D.: From Generic Knowledge to Specific Reasoning for Medical Image Interpretation using Graph-based Representations. In: International Joint Conference on Artificial Intelligence, IJCAI 2007, Hyderabad, India, pp. 224–229 (January 2007)

    Google Scholar 

  4. Bloch, I.: Fuzzy Relative Position between Objects in Image Processing: a Morphological Approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(7), 657–664 (1999)

    Article  Google Scholar 

  5. Bloch, I.: On Fuzzy Distances and their Use in Image Processing under Imprecision. Pattern Recognition 32(11), 1873–1895 (1999)

    Article  Google Scholar 

  6. Bloch, I.: Modal Logics based on Mathematical Morphology for Spatial Reasoning. Journal of Applied Non Classical Logics 12(3-4), 399–424 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bloch, I.: Fuzzy Spatial Relationships for Image Processing and Interpretation: A Review. Image and Vision Computing 23(2), 89–110 (2005)

    Article  Google Scholar 

  8. Bloch, I.: Spatial Reasoning under Imprecision using Fuzzy Set Theory, Formal Logics and Mathematical Morphology. International Journal of Approximate Reasoning 41, 77–95 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bloch, I.: Duality vs. Adjunction for Fuzzy Mathematical Morphology and General Form of Fuzzy Erosions and Dilations. Fuzzy Sets and Systems 160, 1858–1867 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bloch, I., Colliot, O., Cesar, R.M.: On the Ternary Spatial Relation Between. IEEE Transactions on Systems, Man, and Cybernetics SMC-B 36(2), 312–327 (2006)

    Article  Google Scholar 

  11. Bloch, I., Géraud, T., Maître, H.: Representation and Fusion of Heterogeneous Fuzzy Information in the 3D Space for Model-Based Structural Recognition - Application to 3D Brain Imaging. Artificial Intelligence 148, 141–175 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bloch, I., Heijmans, H.J.A.M., Ronse, C.: Mathematical Morphology. In: Aiello, M., Pratt-Hartman, I., van Benthem, J. (eds.) Handbook of Spatial Logics, ch. 13, pp. 857–947. Springer. Dordrecht (2007)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Bloch, I., Maître, H., Anvari, M.: Fuzzy Adjacency between Image Objects. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(6), 615–653 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bloch, I., Ralescu, A.: Directional Relative Position between Objects in Image Processing: A Comparison between Fuzzy Approaches. Pattern Recognition 36, 1563–1582 (2003)

    Article  MATH  Google Scholar 

  16. Cesar, R.M., Bengoetxea, E., Bloch, I., Larrañaga, P.: Inexact Graph Matching for Model-Based Recognition: Evaluaton and Comparison of Optimization Algorithms. Pattern Recognition 38, 2099–2113 (2005)

    Article  Google Scholar 

  17. Colliot, O., Camara, O., Bloch, I.: Integration of Fuzzy Spatial Relations in Deformable Models - Application to Brain MRI Segmentation. Pattern Recognition 39, 1401–1414 (2006)

    Article  Google Scholar 

  18. Colliot, O., Tuzikov, A.V., Cesar, R.M., Bloch, I.: Approximate Reflectional Symmetries of Fuzzy Objects with an Application in Model-Based Object Recognition. Fuzzy Sets and Systems 147, 141–163 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dubois, D., Prade, H., Testemale, C.: Weighted Fuzzy Pattern Matching. Fuzzy Sets and Systems 28, 313–331 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  20. Fouquier, G., Atif, J., Bloch, I.: Sequential model-based segmentation and recognition of image structures driven by visual features and spatial relations. Computer Vision and Image Understanding 116(1), 146–165 (2012)

    Article  Google Scholar 

  21. Freeman, J.: The Modelling of Spatial Relations. Computer Graphics and Image Processing 4(2), 156–171 (1975)

    Article  Google Scholar 

  22. Heijmans, H.J.A.M., Ronse, C.: The Algebraic Basis of Mathematical Morphology – Part I: Dilations and Erosions. Computer Vision, Graphics and Image Processing 50, 245–295 (1990)

    Article  MATH  Google Scholar 

  23. Hudelot, C., Atif, J., Bloch, I.: Fuzzy Spatial Relation Ontology for Image Interpretation. Fuzzy Sets and Systems 159, 1929–1951 (2008)

    Article  MathSciNet  Google Scholar 

  24. Hudelot, C., Atif, J., Bloch, I.: A Spatial Relation Ontology Using Mathematical Morphology and Description Logics for Spatial Reasoning. In: ECAI 2008 Workshop on Spatial and Temporal Reasoning, Patras, Greece, pp. 21–25 (July 2008)

    Google Scholar 

  25. Kuipers, B.J., Levitt, T.S.: Navigation and Mapping in Large-Scale Space. AI Magazine 9(2), 25–43 (1988)

    Google Scholar 

  26. Moreno, A., Takemura, C.M., Colliot, O., Camara, O., Bloch, I.: Using Anatomical Knowledge Expressed as Fuzzy Constraints to Segment the Heart in CT images. Pattern Recognition 41, 2525–2540 (2008)

    Article  Google Scholar 

  27. Mike, N., Kerre, E.E.: Classical and Fuzzy Approaches towards Mathematical Morphology. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, ch. 1. STUDFUZZ, pp. 3–57. Physica-Verlag, Heidelberg (2000)

    Google Scholar 

  28. Nempont, O., Atif, J., Angelini, E.D., Bloch, I.: Structure Segmentation and Recognition in Images Guided by Structural Constraint Propagation. In: European Conference on Artificial Intelligence ECAI, Patras, Greece, pp. 621–625 (July 2008)

    Google Scholar 

  29. Nempont, O., Atif, J., Angelini, E.D., Bloch, I.: A New Fuzzy Connectivity Measure for Fuzzy Sets and Associated Fuzzy Attribute Openings. Journal of Mathematical Imaging and Vision 34, 107–136 (2009)

    Article  MathSciNet  Google Scholar 

  30. Perchant, A., Bloch, I.: Fuzzy Morphisms between Graphs. Fuzzy Sets and Systems 128(2), 149–168 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ronse, C., Heijmans, H.J.A.M.: The Algebraic Basis of Mathematical Morphology – Part II: Openings and Closings. Computer Vision, Graphics and Image Processing 54, 74–97 (1991)

    MATH  Google Scholar 

  32. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, New-York (1982)

    MATH  Google Scholar 

  33. Takemura, C.M., Cesar, R.M., Bloch, I.: Modeling and measuring the spatial relation “along”: regions, contours and fuzzy sets. Pattern Recognition 45, 757–766 (2011)

    Article  Google Scholar 

  34. Vanegas, M.C.: Spatial relations and spatial reasoning for the interpretation of earth observation images using a structural model. PhD thesis, Télécom ParisTech (January 2011)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Bloch, I. (2013). Fuzzy Models of Spatial Relations, Application to Spatial Reasoning. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35641-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-35641-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35640-7

  • Online ISBN: 978-3-642-35641-4

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