Fuzzy Set Methods in Computer Vision

  • James M. Keller
  • Raghu Krishnapuram
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 165)


Computer vision is the study of theories and algorithms involving the sensing and transmission of images; preprocessing of digital images for noise removal, smoothing, or sharpening of contrast; segmentation of images to isolate objects and regions; description and recognition of the segmented regions; and finally interpretation of the scene. We normally think of images in the visible spectrum, either monochrome or color, but in fact, images can be produced by a wide range of sensing modalities including X-rays, neutrons, ultrasound, pressure sensing, laser range finding, infrared, and ultraviolet, to name a few.


Membership Function Fuzzy Subset Fuzzy Measure Possibility Distribution Aggregation Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.M. Prewitt, “Object enhancement and extraction”, inPicture Processing and PsychopictoricsB.S. Lipkin and A. Rosenfield (Eds.), Academic Press, New York, 1970, pp. 75–149.Google Scholar
  2. 2.
    S.K. Pal, and RA. King. “Image enhancement using smoothing with fuzzy sets,”IEEE Transactions on System. Man and CyberneticsVol. SMC-11, 1981, pp. 494–501.Google Scholar
  3. 3.
    S.K. Pal, and RA. King. “Histogram equalization withSand x functions in detecting x-ray edges”Electronics LettersVol. 17, 1981, pp. 302–304.CrossRefGoogle Scholar
  4. 4.
    S.K. Pal, and R.A. King. “On edge detection of x-ray images using fuzzy sets,”IEEE Transactions on Pattern Analysis and Machine IntelligenceVol. PAMI5, 1983, pp. 69–77.CrossRefGoogle Scholar
  5. 5.
    J. Keller, H. Qiu, and H. Tahani, “The fuzzy integral in image segmentation,”Proceedings. NAFIPS-86New Orleans, June 1986, pp. 324–338.Google Scholar
  6. 6.
    R. Sankar, “Improvements in image enhancement using fuzzy sets”Proceedings NAFIPS-86New Orleans, June 2–4, 1986, pp. 502–515.Google Scholar
  7. 7.
    LA. Zadeh, “Calculus of fuzzy restrictions”in Fuzzy Sets and Their Applications to Cognitive and Decision ProcessesL. A. Zadeh, K. S. Fu, K. Tanaka, and M. Shimura, Eds., Academic Press, London, 1975, pp. 1–26.Google Scholar
  8. 8.
    Y. Nakagowa, and A. Rosenfeld, “A note on the use of local min and max operators in digital picture processing,”IEEE Transactions on System. Man and CyberneticsVol. SMC-8, 1978, pp. 632–635.Google Scholar
  9. 9.
    M.M. Gupta, G.K. Knopf, and P.N. Mikiforuk, “Edge Perception Using Fuzzy Logic”in Fuzzy Computing: Theory Hardware and ApplicationsNorth Holland, 1988.Google Scholar
  10. 10.
    Huntsberger, and M. Desclazi, “Color edge detection”Pattern Recognition Letters3, 1985, 205.CrossRefGoogle Scholar
  11. 11.
    S.K. Pal and A. Rosenfeld, “Image enhances and thresholding by optimization of fuzzy compactness”Pattern Recognition Lettersvol. 7, 1988, pp. 77–86.zbMATHCrossRefGoogle Scholar
  12. 12.
    R. Krishnapuram and J. Lee, “Fuzzy-Compensative-Connective-Based Hier-archical Networks and their Application to Computer Vision” under review.Google Scholar
  13. 13.
    Lee, “Fuzzy-Set-Theory-Based Aggregation Networks for Information Fusion and Decision Making”, Ph.D. Thesis, University of Missouri - Columbia.Google Scholar
  14. 14.
    Tahani, “The generalized fuzzy integral in computer vision,” Ph.D. dissertation, University of Missouri - Columbia, 1990.Google Scholar
  15. 15.
    J.C. Dunn, A fuzzy relative of the Isodata process and its use in detecting compact well-separated clustersJournal Cybemet31(3), 1974, pp. 32–57.MathSciNetGoogle Scholar
  16. 16.
    C. BezdekPattern Recognition with Fuzzy Objective Function AlgorithmsPlenum Press, New York, 1981.zbMATHCrossRefGoogle Scholar
  17. 17.
    T. Huntsberger, C. Jacobs, and R. Cannon, “Iterative fuzzy image segmentation,”Pattern Recognitionvol. 18, 1985, pp. 131–138.CrossRefGoogle Scholar
  18. 18.
    R. Cannon, J. Dave and J. Bezdek, “Efficient implementation of the fuzzy c-means clustering algorithm,”IEEE Transactions on Pattern Analysis Machine IntelligenceVol. 8, No. 2, 1986, pp. 248–255.zbMATHCrossRefGoogle Scholar
  19. 19.
    S. Horowitz and T. Pavlidis, “Picture segmentations by a directed split and merge procedure”Proceedings of the Second International Journal Conference Pattern Recognition1974, pp. 424–433.Google Scholar
  20. 20.
    T. Huntsberger., “Representation of uncertainty in low level vision”IEEE Transactions on ComputersVol. 235, No. 2, 145, 1986, p. 145.CrossRefGoogle Scholar
  21. 21.
    R. Cannon, J. Dave, J.C. Bezdek, and M. Trivedi, “Segmentation of a thematic mapper image using the fuzzy c-means clustering algorithm,”IEEE Transactions on Geographical Science and Remote SensingVol. 24, No. 3, 1986, pp. 400–408.CrossRefGoogle Scholar
  22. 22.
    J. Keller and C. Carpenter, “Image Segmentation in the Presence of Uncertainty,”International Journal of Intelligent Systemsvol. 5, 1990, pp. 193–208.zbMATHCrossRefGoogle Scholar
  23. 23.
    A. Rosenfeld, Fuzzy digitaltopology Information and Control40, 1979, pp. 76–87.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    A. Rosenfeld, “On connectivity properties of gray scale pictures”Pattern Recognition16, 1983, pp. 47–50.CrossRefGoogle Scholar
  25. 25.
    A. Rosenfeld, “The fuzzy geometry of image subsets”Pattern Recognition Letters2, 1984, pp. 311–317.CrossRefGoogle Scholar
  26. 26.
    D. Dubois and M.C. Jaulent, “Shape understanding via fuzzy models”2nd IFAC/IFIP/IFORS/IEA Conference on analysis. design and evaluation of man-machine systems1985, pp. 302–307.Google Scholar
  27. 27.
    D. Dubois and M.C. Jaulent, “A general approach to parameter evaluations in fuzzy digital pictures”Pattern Recognition Lettersto appear.Google Scholar
  28. 28.
    S. Peleg and A. Rosenfeld, A mini-max medial axis transformationIEEE Transactions on Pattern Analysis and Machine IntelligenceVol. PAMI-3, 1981, pp. 208–210.CrossRefGoogle Scholar
  29. 29.
    C.R. Dyer and A. Rosenfeld, “Thinning operations on grayscale pictures,”IEEE Transactions on Pattern Analysis and Machine IntelligenceVol. PAMI1, 1979, pp. 88–89.Google Scholar
  30. 30.
    A. Rosenfeld and A.C. KakDigital Picture ProcessingVol. 2, Academic Press, N.Y., 1982.Google Scholar
  31. 31.
    L. Liao, “Image segmentation and enhancement by optimizing geometric parameters”, M.S. Thesis, University of Missouri-Columbia, 1990.Google Scholar
  32. 32.
    I. Gath and A.B. Geva, “Unsupervised Optimal Fuzzy Clustering”IEEE Transactions on Pattern Analysis Mac ineligencevol. PAMI-11, no. 7, pp. 773–781, July 1989.Google Scholar
  33. 33.
    J. Keller and Y. Seo, “Local fractal geometric features for image segmentation”, to appearInternational Journal of Imaging Systems and Technology1990.Google Scholar
  34. 34.
    R. Krishnapuram and A. Munshi, “Cluster-Based Segmentation of Range Images Using Differential-Geometric Features”, submitted to under review.Google Scholar
  35. 35.
    R. Krishnapuram and J. Lee “Fuzzy-Connective-Based Hierarchical Aggregation Networks for Decision Making”Fuzzy Sets and Systemsto appear.Google Scholar
  36. 36.
    R. Krishnapuram and J. Lee “Determining the Structure of Uncertainty Management Networks”, to appear in theProceedings of the SPIE Conference on Robotics and Computer VisionPhiladelphia, November 1989.Google Scholar
  37. 37.
    H. Qiu and J. Keller, “Multispectral segmentation using fuzzy techniques,”Proceedings NAFIPS-87Purdue University, May 1987, pp. 374–387.Google Scholar
  38. 38.
    H. Tahani and J. Keller, “Information fusion in computer vision using the fuzzy integral”IEEE Transactions on System. Man and Cyberneticsvol. 20, no. 3, 1990, pp. 733–741.CrossRefGoogle Scholar
  39. 39.
    H.J. Zimmermann and P. Zysno “Decisions and evaluations by hierarchical aggregation of information”Fuzzy Sets and Systemsvol.10, no.3, 1983 pp. 243–260.zbMATHCrossRefGoogle Scholar
  40. 40.
    Y. OhtaKnowledge-Based Interpretation of Outdoor National ScenesPitman Advanced Publishing, Boston, 1985.Google Scholar
  41. 41.
    R. Dave, “Use of the adaptive fuzzy clustering algorithm to detect lines in digital images”Proceedings of the Intelligent Robots and Computer Vision VIIIvol. 1192, no. 2, 1989, pp. 600–611.Google Scholar
  42. 42.
    C.-P. Freg, “Algorithms to detect linear and planar clusters and their applications”, MS Project Report, University of Missouri-Columbia, May 1990.Google Scholar
  43. 43.
    J. Bezdek, C. Cordy, R. Gunderson and J. Watson, “Detection and characterization of cluster substructure”SIAM Journal Applied MathematicsVol. 40, 1981, pp. 339–372.zbMATHCrossRefGoogle Scholar
  44. 44.
    M. Windham, “Geometrical fuzzy clustering algorithms”Fuzzy Sets and Systemsvol. 10, 1983, pp. 271–279.MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    R. Dave, “Fuzzy Shell-Clustering and applications to circle detection in digital images”International Journal of General Systems1990.Google Scholar
  46. 46.
    M. Sugeno, “Fuzzy measures and fuzzy integrals: A survey”in Fuzzy Automatic and Decision ProcessesNorth Holland, Amsterdam, 1977, pp. 89–102.Google Scholar
  47. 47.
    J. Wootton, J. Keller, C. Carpenter, and G. Hobson, “A multiple hypothesis rule-based automatic target recognizes”, inPattem RecognitionLecture Notes in Computer Science, Vol. 301, J. Kittler (ed.), Springer-Verlag, 1988, pp. 315–324.CrossRefGoogle Scholar
  48. 48.
    G. ShaferA Mathematical Theory of EvidencePrinceton University Press, Princeton, 1976.zbMATHGoogle Scholar
  49. 49.
    J. Keller, G. Hobson, J. Wootton, A. Nafarieh, and K. Luetkemeyer, “Fuzzy confidence measures in midlevel vision,”IEEE Transactions on System Man and CyberneticsVol. SMC-17, No. 4, 1987, pp. 676–683.CrossRefGoogle Scholar
  50. 50.
    J. Keller and D. Jeffreys, “Linguistic computations in computer vision”Proceedings NAFIPS-90Vol. 2, Toronto, 1990, pp. 432–435.Google Scholar
  51. 51.
    J. Keller, H. Shah, and F. Wong, “Fuzzy Computations in risk and decision analysis”Civil Engineering Systemsvol. 2, 1985, pp. 201–208.CrossRefGoogle Scholar
  52. 52.
    J. Keller, M. Gray, and J. Givens, “A fuzzy k-nearest neighbor algorithm,”IEEE Transactions on System. Man and Cyberneticsvol. 15, 1985, pp. 580–585.CrossRefGoogle Scholar
  53. 53.
    J. Keller, D. Subhanghasen, K. Unldesbay, and N. Unklesbay, “An approximate reasoning technique for recogntion in color images of beef steaks”International Journal General Systemsto appear, 1990.CrossRefGoogle Scholar
  54. 54.
    A. Nafarieh and J. Keller, “A fuzzy logic rule-based automatic target recognizes”International Journal of Intelligent Systemsto appear, 1990.Google Scholar
  55. 55.
    L. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning”Information SciencesPart 1, Vol. 8, pp. 199–249; Part 2, Vol. 8, pp. 301–357; Part 3, Vol. 9, pp. 43–80, 1975.Google Scholar
  56. 56.
    J. Keller and H. Tahani, “Backpropagation neural networks for fuzzy logic”Information Sciencesto appear 1990.Google Scholar
  57. 57.
    J. Keller and R. Yager, “Fuzzy logic inference neural networks”Proceedings of the SPIE Symposium on Intelligent Robots and Computer Vision VIII1989, pp. 582–591.Google Scholar
  58. 58.
    J. Keller and H. Tahani, “Implementation of conjunctive and disjunctive fuzzy logic rules with neural networks”International Journal of Approximate Reasoningto appear.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • James M. Keller
    • 1
  • Raghu Krishnapuram
    • 1
  1. 1.Electrical and Computer EngineeringUniversity of Missouri-ColumbiaColumbiaUSA

Personalised recommendations