Fuzzy Set Theoretic Tools for Image Analysis

Publisher Summary This chapter describes various fuzzy set theoretic tools and explores their effectiveness in representing/describing various uncertainties that might arise in an image-recognition system and the ways these can be managed in making a decision. In the chapter, some examples of uncertainties that arise often in the process of recognizing a pattern are discussed, and it describes various fuzzy set theoretic tools for measuring information on grayness ambiguity and spatial ambiguity in an image. The concepts of bound functions and spectral fuzzy sets for handling uncertainties in membership functions are also discussed in the chapter. Their applications to low-level vision operations whose outputs are crucial and responsible for the overall performance of a vision system are presented in the chapter for demonstrating the effectiveness of these tools in managing uncertainties by providing both soft and hard decisions. Their usefulness in providing the quantitative indices for autonomous operations is also explained in the chapter. The chapter also describes the issues of feature/primitive extraction, knowledge acquisition and syntactic classification, and the features of Dempster-Shafer theory and rough set theory in this context. An application of the multivalued recognition system for detecting curved structures from remotely sensed image is also described in the chapter.

[1]  Krzysztof J. Cios,et al.  A machine learning method for generation of a neural network architecture: a continuous ID3 algorithm , 1992, IEEE Trans. Neural Networks.

[2]  Sankar K. Pal,et al.  On Edge Detection of X-Ray Images Using Fuzzy Sets , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Sankar K. Pal.  Fuzzy set theoretic measures for automatic feature evaluation: II , 1992, Inf. Sci..

[4]  David J. Burr,et al.  Experiments on neural net recognition of spoken and written text , 1988, IEEE Trans. Acoust. Speech Signal Process..

[5]  King-Sun Fu,et al.  Syntactic Pattern Recognition And Applications , 1968 .

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

[7]  C. A. Murthy,et al.  Histogram thresholding by minimizing graylevel fuzziness , 1992, Inf. Sci..

[8]  Joonwhoan Lee,et al.  Fuzzy-set-based hierarchical networks for information fusion in computer vision , 1992, Neural Networks.

[9]  James C. Bezdek,et al.  An application of the c-varieties clustering algorithms to polygonal curve fitting , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Sankar K. Pal,et al.  Image segmentation using fuzzy correlation , 1992, Inf. Sci..

[11]  Terrance L. Huntsberger,et al.  Representation of Uncertainty in Computer Vision Using Fuzzy Sets , 1986, IEEE Transactions on Computers.

[12]  Hideyuki Takagi,et al.  Neural networks designed on approximate reasoning architecture and their applications , 1992, IEEE Trans. Neural Networks.

[13]  Hamid R. Berenji,et al.  A reinforcement learning--based architecture for fuzzy logic control , 1992, Int. J. Approx. Reason..

[14]  Terrance L. Huntsberger,et al.  PARALLEL SELF-ORGANIZING FEATURE MAPS FOR UNSUPERVISED PATTERN RECOGNITION , 1990 .

[15]  Sankar K. Pal,et al.  Spectral fuzzy sets and soft thresholding , 1992, Inf. Sci..

[16]  Jerzy W. Grzymala-Busse,et al.  Knowledge acquisition under uncertainty — a rough set approach , 1988, J. Intell. Robotic Syst..

[17]  Ronald R. Yager,et al.  Implementing fuzzy logic controllers using a neural network framework , 1992 .

[18]  Azriel Rosenfeld,et al.  Image enhancement and thresholding by optimization of fuzzy compactness , 1988, Pattern Recognit. Lett..

[19]  L. Darrell Whitley,et al.  Genetic algorithms and neural networks: optimizing connections and connectivity , 1990, Parallel Comput..

[20]  R.P. Lippmann,et al.  Pattern classification using neural networks , 1989, IEEE Communications Magazine.

[21]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[22]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[23]  Sankar K. Pal,et al.  Fuzzy dynamic clustering algorithm , 1990, Pattern Recognit. Lett..

[24]  Sankar K. Pal,et al.  Neural network, self-organization and object extraction , 1992, Pattern Recognit. Lett..

[25]  S. Pal,et al.  Histogram equalisation with S and π functions in detecting X-ray edges , 1981 .

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

[27]  S. Pal,et al.  Fuzzy geometry in image analysis , 1992 .

[28]  Sankar K. Pal.  A measure of edge ambiguity using fuzzy sets , 1986, Pattern Recognit. Lett..

[29]  Sankar K. Pal,et al.  Fuzzy tools for the management of uncertainty in pattern recognition, image analysis, vision and expert systems , 1991 .

[30]  Jirí Benes,et al.  On neural networks , 1990, Kybernetika.

[31]  Witold Pedrycz,et al.  Neurocomputations in Relational Systems , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  Sankar K. Pal,et al.  Image description and primitive extraction using fuzzy sets , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[33]  Sankar K. Pal,et al.  Image Model, Poisson Distribution and Object Extraction , 1991, Int. J. Pattern Recognit. Artif. Intell..

[34]  Takeshi Yamakawa,et al.  A design algorithm of membership functions for a fuzzy neuron using example-based learning , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[35]  Vito Di Gesù,et al.  Features selection and 'possibility theory' , 1986, Pattern Recognit..

[36]  James C. Bezdek,et al.  Fuzzy Kohonen clustering networks , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[37]  Sang Uk Lee,et al.  On the color image segmentation algorithm based on the thresholding and the fuzzy c-means techniques , 1990, Pattern Recognit..

[38]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[39]  Sankar K. Pal,et al.  Self-organization for object extraction using a multilayer neural network and fuzziness measures , 1993, IEEE Trans. Fuzzy Syst..

[40]  James C. Bezdek,et al.  Prototype classification and feature selection with fuzzy sets , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[41]  James M. Keller,et al.  Implementation of conjunctive and disjunctive fuzzy logic rules with neural networks , 1992, Int. J. Approx. Reason..

[42]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[43]  Sankar K. Pal,et al.  Object Background Classification Using Hopfield Type Neural Network , 1992, Int. J. Pattern Recognit. Artif. Intell..

[44]  K. Hirota.  Concepts of probabilistic sets , 1981 .

[45]  James M. Keller,et al.  Evidence aggregation networks for fuzzy logic inference , 1992, IEEE Trans. Neural Networks.

[46]  Sankar K. Pal,et al.  Linguistic recognition system based on approximate reasoning , 1992, Inf. Sci..

[47]  H. Zimmermann,et al.  Decisions and evaluations by hierarchical aggregation of information , 1983 .

[48]  Amita Pathak,et al.  Fuzzy Grammars in Syntactic Recognition of Skeletal Maturity from X-Rays , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[49]  Isao Hayashi,et al.  NN-driven fuzzy reasoning , 1991, Int. J. Approx. Reason..

[50]  Robert M. Kleyle,et al.  An evidential approach to problem solving when a large number of knowledge systems is available , 1990, Int. J. Intell. Syst..

[51]  Sankar K. Pal,et al.  Index of area coverage of fuzzy image subsets and object extraction , 1990, Pattern Recognit. Lett..

[52]  Sankar K. Pal,et al.  Fuzzy Medial Axis Transformation (FMAT): practical feasibility , 1992 .

[53]  Witold Pedrycz,et al.  Fuzzy sets in pattern recognition: Methodology and methods , 1990, Pattern Recognit..

[54]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[55]  Samuel D. Bedrosian,et al.  An information measure for fuzzy sets , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[56]  C. A. Murthy,et al.  Correlation between two fuzzy membership functions , 1985 .

[57]  W. Xie.  An information measure for a color space , 1990 .

[58]  C. A. Murthy,et al.  Fuzzy thresholding: mathematical framework, bound functions and weighted moving average technique , 1990, Pattern Recognit. Lett..

[59]  C. A. Murthy,et al.  DETERMINING THE SHAPE OF A PATTERN CLASS FROM SAMPLED POINTS IN R2 , 1992 .

[60]  Sankar K. Pal,et al.  A Note on the Quantitative Measure of Image Enhancement Through Fuzziness , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[61]  Michael G. Thomason,et al.  Finite fuzzy automata, regular fuzzy languages, and pattern recognition , 1973, Pattern Recognit..

[62]  Lotfi A. Zadeh,et al.  Note on fuzzy languages , 1969, Inf. Sci..

[63]  Amita Pathak,et al.  Syntactic recognition of skeletal maturity , 1984, Pattern Recognit. Lett..

[64]  R. Yager.  Fuzzy decision making including unequal objectives , 1978 .

[65]  Joonwhoan Lee,et al.  Fuzzy-connective-based hierarchical aggregation networks for decision making , 1992 .

[66]  Sankar K. Pal,et al.  Automatic selection of object enhancement operator with quantitative justification based on fuzzy set theoretic measures , 1990, Pattern Recognit. Lett..

[67]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[68]  Frederick E. Petry,et al.  Scene recognition using genetic algorithms with semantic nets , 1990, Pattern Recognit. Lett..

[69]  Stephen I. Gallant,et al.  Connectionist expert systems , 1988, CACM.

[70]  Hamid R. Berenji,et al.  Learning and tuning fuzzy logic controllers through reinforcements , 1992, IEEE Trans. Neural Networks.

[71]  L. A. Zadeh,et al.  Making computers think like people [fuzzy set theory] , 1984, IEEE Spectrum.

[72]  Sankar K. Pal,et al.  Fuzzy models for pattern recognition : methods that search for structures in data , 1992 .

[73]  Azriel Rosenfeld,et al.  A fuzzy medial axis transformation based on fuzzy disks , 1991, Pattern Recognit. Lett..

[74]  James M. Keller,et al.  Neural network implementation of fuzzy logic , 1992 .

[75]  Sankar K. Pal,et al.  Some properties of the exponential entropy , 1992, Inf. Sci..

[76]  Basabi Chakraborty,et al.  Fuzzy Set Theoretic Measure for Automatic Feature Evaluation , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[77]  James M. Keller,et al.  A fuzzy logic rule‐based automatic target recognizer , 1991, Int. J. Intell. Syst..

[78]  Ernest Czogaa,et al.  A generalized concept of a fuzzy probabilistic controller , 1983 .

[79]  Sankar K. Pal,et al.  Recognition of bones from X-rays of the hand† , 1985 .

[80]  James M. Keller,et al.  Backpropagation neural networks for fuzzy logic , 1992, Inf. Sci..

[81]  Azriel Rosenfeld,et al.  A Min-Max Medial Axis Transformation , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[82]  Sankar K. Pal,et al.  Pattern recognition techniques in analyzing the effect of thiourea on brain neurosecretory cells , 1990, Pattern Recognit. Lett..

[83]  Constantin V. Negoita,et al.  On Fuzzy Systems , 1978 .

[84]  Nikhil R. Pal,et al.  Some new information measures for fuzzy sets , 1993, Inf. Sci..

[85]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[86]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[87]  Witold Pedrycz,et al.  Fuzzy neural networks with reference neurons as pattern classifiers , 1992, IEEE Trans. Neural Networks.

[88]  Sankar K. Pal.  Fuzzy skeletonization of an image , 1989, Pattern Recognit. Lett..

[89]  Masaharu Mizumoto,et al.  Some Properties of Fuzzy Sets of Type 2 , 1976, Inf. Control..

[90]  Ezzatollah Salari,et al.  The ridge-seeking method for obtaining the skeleton of digital images , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[91]  Giorgio Levi,et al.  A Grey-Weighted Skeleton , 1970, Inf. Control..

[92]  Sankar K. Pal,et al.  Higher order fuzzy entropy and hybrid entropy of a set , 1992, Inf. Sci..

[93]  Behrooz Kamgar-Parsi,et al.  On problem solving with Hopfield neural networks , 1990, International 1989 Joint Conference on Neural Networks.

[94]  James M. Keller,et al.  Incorporating Fuzzy Membership Functions into the Perceptron Algorithm , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[95]  Robert N. Lea,et al.  Fuzzy logic in autonomous orbital operations , 1992, Int. J. Approx. Reason..

[96]  Paul J. Werbos,et al.  Neurocontrol and fuzzy logic: Connections and designs , 1992, Int. J. Approx. Reason..

[97]  Sankar K. Pal,et al.  Entropy-coded hybrid differential pulse-code modulation , 1983 .

[98]  Edward T. Lee,et al.  Fuzzy Neural Networks , 1975 .

[99]  Sankar K. Pal,et al.  Entropy: a new definition and its applications , 1991, IEEE Trans. Syst. Man Cybern..

[100]  Sankar K. Pal,et al.  Multilayer perceptron, fuzzy sets, and classification , 1992, IEEE Trans. Neural Networks.

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

[102]  Z. Pawlak.  Rough sets and fuzzy sets , 1985 .

[103]  Amita Pathak,et al.  A generalised learning algorithm based on guard zones , 1986, Pattern Recognit. Lett..

[104]  Stefan Bornholdt,et al.  General asymmetric neural networks and structure design by genetic algorithms: a learning rule for temporal patterns , 1992, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[105]  Shouhong Wang,et al.  Fuzzy set representation of neural network classification boundaries , 1991, IEEE Trans. Syst. Man Cybern..