Fuzzy spatial relationships for image processing and interpretation: a review

In spatial reasoning, relationships between spatial entities play a major role. In image interpretation, computer vision and structural recognition, the management of imperfect information and of imprecision constitutes a key point. This calls for the framework of fuzzy sets, which exhibits nice features to represent spatial imprecision at different levels, imprecision in knowledge and knowledge representation, and which provides powerful tools for fusion, decision-making and reasoning. In this paper, we review the main fuzzy approaches for defining spatial relationships including topological (set relationships, adjacency) and metrical relations (distances, directional relative position).

[1]  Isabelle Bloch,et al.  Spatial representation of spatial relationship knowledge , 2000, KR.

[2]  L. Kohout,et al.  FUZZY POWER SETS AND FUZZY IMPLICATION OPERATORS , 1980 .

[3]  Gian Antonio Mian,et al.  Normalized weighted Levensthein distance and triangle inequality in the context of similarity discrimination of bilevel images , 1996, Pattern Recognit. Lett..

[4]  Ronald R. Yager,et al.  Entropy measures under similarity relations , 1992 .

[5]  Nikhil R. Pal,et al.  Fuzzy divergence, probability measure of fuzzy events and image thresholding , 1992, Pattern Recognit. Lett..

[6]  Bernadette Bouchon-Meunier,et al.  Towards general measures of comparison of objects , 1996, Fuzzy Sets Syst..

[7]  John Freeman,et al.  The modelling of spatial relations , 1975 .

[8]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Marie-Christine Jaulent,et al.  A general approach to parameter evaluation in fuzzy digital pictures , 1987, Pattern Recognit. Lett..

[10]  Isabelle Bloch,et al.  Modal Logics Based on Mathematical Morphology for Qualitative Spatial Reasoning , 2002, J. Appl. Non Class. Logics.

[11]  Raimondo Schettini,et al.  Fuzzy reasoning approach to similarity evaluation in image analysis , 1993, Int. J. Intell. Syst..

[12]  A. Tversky Features of Similarity , 1977 .

[13]  Azriel Rosenfeld,et al.  On a metric distance between fuzzy sets , 1996, Pattern Recognit. Lett..

[14]  E. Walker Fuzzy relations for feature-model correspondence in 3D object recognition , 1996, Proceedings of North American Fuzzy Information Processing.

[15]  Azriel Rosenfeld,et al.  Distances between fuzzy sets , 1985, Pattern Recognit. Lett..

[16]  J. A. Goguen,et al.  The logic of inexact concepts , 1969, Synthese.

[17]  Benjamin Kuipers,et al.  Modeling Spatial Knowledge , 1978, IJCAI.

[18]  Ramesh C. Jain,et al.  Similarity measures for image databases , 1995, Electronic Imaging.

[19]  Peter Braß On the nonexistence of Hausdorff-like metrics for fuzzy sets , 2002, Pattern Recognit. Lett..

[20]  H. Prade,et al.  FUZZY PATTERN MATCHING , 1982 .

[21]  Valerie Cross,et al.  A mathematical relationship between set-theoretic and metric compatibility measures , 1995, Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society.

[22]  James M. Keller,et al.  Quantitative analysis of properties and spatial relations of fuzzy image regions , 1993, IEEE Trans. Fuzzy Syst..

[23]  A. Ralescu,et al.  Spatial organization in 2D images , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[24]  Hagit Hel-Or,et al.  Symmetry as a Continuous Feature , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Shyi-Ming Chen,et al.  A comparison of similarity measures of fuzzy values , 1995 .

[26]  Azriel Rosenfeld,et al.  The fuzzy geometry of image subsets , 1984, Pattern Recognit. Lett..

[27]  Isabelle Bloch,et al.  On fuzzy distances and their use in image processing under imprecision , 1999, Pattern Recognit..

[28]  K. Sridharan,et al.  Fuzzy distances for proximity characterization under uncertainty , 1999, Fuzzy Sets Syst..

[29]  Robert Lowen,et al.  Distances between fuzzy sets representing grey level images , 1998, Fuzzy Sets Syst..

[30]  Roberto Marcondes Cesar Junior,et al.  Inexact graph matching using stochastic optimization techniques for facial feature recognition , 2002, Object recognition supported by user interaction for service robots.

[31]  Wen-June Wang,et al.  New similarity measures on fuzzy sets and on elements , 1997, Fuzzy Sets Syst..

[32]  B. Kosko Fuzziness vs. probability , 1990 .

[33]  Isabelle Bloch,et al.  Directional relative position between objects in image processing: a comparison between fuzzy approaches , 2003, Pattern Recognit..

[34]  C. Pappis,et al.  A comparative assessment of measures of similarity of fuzzy values , 1993 .

[35]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[36]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[37]  Isabelle Bloch,et al.  Fuzzy Adjacency between Image Objects , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[38]  Anca L. Ralescu,et al.  Spatial organization in 2D segmented images: representation and recognition of primitive spatial relations , 1994, CVPR 1994.

[39]  A. Kaufman,et al.  Introduction to the Theory of Fuzzy Subsets. , 1977 .

[40]  J.C.H. Poon,et al.  A fuzzy-attributed graph approach to handwritten character recognition , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[41]  D. Dubois,et al.  Fuzzy sets in approximate reasoning. I, Inference with possibility distributions , 1991 .

[42]  Peter E. Maher A similarity measure for conceptual graphs , 1993, Int. J. Intell. Syst..

[43]  Mongi A. Abidi,et al.  Data fusion in robotics and machine intelligence , 1992 .

[44]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions , 1999 .

[45]  László T. Kóczy On the description of relative position of fuzzy patterns , 1988, Pattern Recognit. Lett..

[46]  B. Baets,et al.  A comparative study of similarity measures , 1995 .

[47]  Azriel Rosenfeld,et al.  Degree of adjacency or surroundedness , 1984, Pattern Recognit..

[48]  E. Dougherty,et al.  Fuzzification of set inclusion: theory and applications , 1993 .

[49]  Jiu-lun Fan Note on Hausdorff-like metrics for fuzzy sets , 1998, Pattern Recognit. Lett..

[50]  Thierry Denoeux,et al.  Multidimensional scaling of fuzzy dissimilarity data , 2002, Fuzzy Sets Syst..

[51]  James M. Keller,et al.  Comparison of spatial relation definitions in computer vision , 1995, Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society.

[52]  Laurent Wendling,et al.  A New Way to Represent the Relative Position between Areal Objects , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[53]  El-hadi Zahzah,et al.  Image understanding using fuzzy isomorphism of fuzzy structures , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[54]  Giangiacomo Gerla,et al.  Extension Principles for Fuzzy Set Theory , 1998, Inf. Sci..

[55]  Cnrs Ura,et al.  FUZZY RELATIVE POSITION BETWEEN OBJECTS IN IMAGES: A MORPHOLOGICAL APPROACH , 1996 .

[56]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

[57]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[58]  Isabelle Bloch,et al.  Inexact graph matching by means of estimation of distribution algorithms , 2002, Pattern Recognit..

[59]  Didier Dubois,et al.  On the combination of uncertain or imprecise pieces of information in rule-based systems-A discussion in the framework of possibility theory , 1988, Int. J. Approx. Reason..

[60]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[61]  B. Bouchon-Meunier,et al.  Entropy of similarity relations in questionnaires and decision trees , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[62]  Supun Samarasekera,et al.  Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation , 1996, CVGIP Graph. Model. Image Process..

[63]  A. Bonaert Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[64]  Roberto Marcondes Cesar Junior,et al.  Approximate reflectional symmetries of fuzzy objects with an application in model-based object recognition , 2004, Fuzzy Sets Syst..

[65]  Alexander V. Tuzikov,et al.  Characterization of approximate plane symmetries for 3D fuzzy objects , 2002 .

[66]  Vijay K. Rohatgi,et al.  Advances in Fuzzy Set Theory and Applications , 1980 .

[67]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[68]  Isabelle Bloch,et al.  Fuzzy morphisms between graphs , 2002, Fuzzy Sets Syst..

[69]  Isabelle Bloch,et al.  Fuzzy Relative Position Between Objects in Image Processing: New Definition and Properties Based on a Morphological Approach , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[70]  Isabelle Bloch,et al.  Fuzzy Spatial Relationships from Mathematical Morphology for Model-Based Pattern Recognition and Spatial Reasoning , 2003, DGCI.

[71]  R. Willmott Two fuzzier implication operators in the theory of fuzzy power sets , 1980 .

[72]  Rami Zwick,et al.  Measures of similarity among fuzzy concepts: A comparative analysis , 1987, Int. J. Approx. Reason..

[73]  Isabelle Bloch,et al.  Fuzzy mathematical morphologies: A comparative study , 1995, Pattern Recognit..

[74]  Isabelle Bloch,et al.  Representation and fusion of heterogeneous fuzzy information in the 3D space for model-based structural recognition--Application to 3D brain imaging , 2003, Artif. Intell..

[75]  Laurence Boxer,et al.  On Hausdorff-like metrics for fuzzy sets , 1997, Pattern Recognit. Lett..

[76]  Benjamin Kuipers,et al.  Navigation and Mapping in Large Scale Space , 1988, AI Mag..

[77]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[78]  Isabelle Bloch,et al.  On Fuzzy Spatial Distances , 2003 .

[79]  H. Carter Fuzzy Sets and Systems — Theory and Applications , 1982 .

[80]  Virginia R. Young,et al.  Fuzzy subsethood , 1996, Fuzzy Sets Syst..

[81]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 2: logical approaches , 1991 .

[82]  Isabelle Bloch,et al.  Fuzzy Relative Position Between Objects in Image Processing: A Morphological Approach , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[83]  D. Dubois,et al.  Weighted fuzzy pattern matching , 1988 .