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The “Rubber-Mask” Technique-I, Pattern Measurement and Analysis

  • Bernard Widrow

Abstract

Template matching is a fundamental technique of pattern recognition. Although this technique is very general, its applicability has been limited because of the difficulty often encountered when fitting templates to natural data. Natural patterns are often distorted, misshapen, stretched in size, fuzzy, rotated, translated, observed at an unusual perspective, etc. Flexible templates (rubber masks) have been devised which, when fitted to natural data, can be used for measurement, data reduction, data smoothing, and classification of highly irregular waveforms and image shapes. These problems had been largely unsolved by existing template matching methods.

Specific applications to the analysis of human chromosome images, chromatographic recordings, electrocardiogram waveforms, and electroencephalogram waveforms are illustrated. The rubber-mask technique will probably be usable in a wide variety of scientific applications.

Keywords

Human Chromosome Template Match Optical Character Recognition Natural Data Pattern Measurement 
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.

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References

  1. 1.
    Matched filter issue, IRE Trans. Information Theory IT-6, 309–417 (June 1960).Google Scholar
  2. 2.
    K. STEINBUCH and U.A.W. PISKE,”Learning matrices and their applications 846–862 (1963).Google Scholar
  3. 3.
    W.H. HIGHLEYMAN, “Linear decision functions, with application to pattern recognition,” Proc. IRE 50, 1501–1514 (1962).CrossRefGoogle Scholar
  4. 4.
    J.S. KOFORD and G.F. GRONER, “The use of an adaptive threshold element to design a linear optimal pattern classifier,” IEEE Trans. Information Theory IT-12, 42–50 (1966).CrossRefGoogle Scholar
  5. 5.
    T.M. COVER and P.E. HART, “Nearest neighbor pattern classification,” IEEE Trans. Information Theory IT-13, 21–27 (1967).CrossRefGoogle Scholar
  6. 6.
    G.L. FISCHER, JR., D.K. POLLOCK, B. RADACK and M.E. STEVENS (Eds.), Optical Character Recognition. Spartan Books, Washington, D.C. (1962).Google Scholar
  7. 7.
    L.N. KANAL (Ed.), Pattern Recognition. Thompson, Washington, D.C. (1968).Google Scholar
  8. 8.
    C.N. LIU and G.L. SHELTON, Jr., “An experimental investigation of a mixed-font print recognition system,” IEEE Trans. Computers EC-15 (6), 916–925 (1966).CrossRefGoogle Scholar
  9. 9.
    Denver Conference. “A proposed standard system of nomenclature of human mitotic chromosomes,” Ann. Human Genetics 24, 319–324 (1960)CrossRefGoogle Scholar
  10. 10.
    T. CASPERSSON, L. ZECH, C. JOHANSSON and E.J. MODEST, “Identification of human chromosomes by DNA-binding fluorescent agents,” Chromosoma 30, 215–227. (1970).CrossRefGoogle Scholar
  11. 11.
    T. CASPERSSON and L. ZECH, “Chromosome identification by fluorescence.” Hospital Practice, 51–62 (September 1972).Google Scholar
  12. 12.
    M.E. DRETS and M.W. SHAW, “Specific banding patterns of human chromosomes,”Proc. Nat. Acad. Sci. U.S.A. 68 (9), 2073–2077 (1971).CrossRefGoogle Scholar
  13. 13.
    T. FLEISCHMANN, T. GUSTAFSSON, C.H. HAKANSSON and A. LEVAN, “Computer-display of the chromosomal fluorescence pattern,” Heriditas M, 325–328 (1971).Google Scholar
  14. 14.
    P.B. HAMILTON, “Ion exchange chromatography of amino acids,” Anal. Chem. 35 (13), 2055–2064 (1963).CrossRefGoogle Scholar
  15. 15.
    H.M. GLADNEY, B.F. DOWDEN and J.D. SWALEN, “Computer-assisted gas-liquid chromatography,”Anal. Chem. 41 (7) 823–828 (1969).CrossRefGoogle Scholar
  16. 16.
    C.D. SCOTT, D.D. CHILCOTE and W. WILSON PITT, Jr., “Method for resolving and measuring overlapping chromatographic peaks by use of an on-line computer with limited storage capacity,” Clin. Chem. 16 (8), 637–642 (1970).Google Scholar
  17. 17.
    H. DAVIS, P.H. DAVIS, A.L. LOOMIS, E.N. HARVEY and G. HOBART, “Electrical reactions of the human brain to auditory stimulation during sleep,” J. Neurophysiol. 500–514 (1939).Google Scholar
  18. 18.
    L.C. JOHNSON and W.E. KARPAN, “Autonomic correlates of the spontaneous K-complex,” Psychophysiology 4 (4). 444–452 (1968).CrossRefGoogle Scholar
  19. 19.
    J.F. SASSIN and L.C. JOHNSON, “Body motility during sleep and its relation to the K-complex,” Exp. Neurol. 22 (1) 133–144 (1968).CrossRefGoogle Scholar
  20. 20.
    G. BREMER, “Detection of the K-complex in electroencephalograms,” A thesis presented to the Graduate Council of the University of Florida, University of Florida (1970).Google Scholar
  21. 21.
    G.F. BREMER, J.R. SMITH and I. KARACAN, “Detection of the K-complex in electroencephalograms,” IEEE Trans. Bio-med. Engng 17. 314–323 (1970)CrossRefGoogle Scholar
  22. 22.
    J.R. SMITH and I. KARACAN, “EEG sleep stage scoring by an automatic hybrid system,” Electroenceph. Clin. Neurophysiol, 31, 231–237 (1971).CrossRefGoogle Scholar
  23. 23.
    Grant’s Clinical Electrocardiography: The Spatial Vector Approach, Second edition revised by J.R. BECKWITH, McGraw-Hill, New York (1970).Google Scholar
  24. 24.
    L.A. GEDDES and L.E. BAKER, Principles of Applied Biomedical Instrumentation. Wiley, New York (1968).Google Scholar
  25. 25.
    H.C. BURGER, Heart and Vector: Physical Basis of Electrocardiography. Philips Technical Library, Eindhoven, Netherlands (1968).Google Scholar
  26. 26.
    E. FRANK, “An accurate, clinically practical system for spatial vectorcardiography,” Circulation 13, 737–749 (1956).Google Scholar
  27. 27.
    C.S. WEAVER, J. von der GROEBEN and H.G. GLAZE, “Collecting and processing vector electrocardiograms,” Stanford Electronics Laboratories, SU-SEL-66–122 (December 1966).Google Scholar
  28. 28.
    C.S. WEAVER, J. von der GROEBEN, P.E. MANTEY, C.A. COLE, JR., J.W. FITZGERALD and R.W. LAWRENCE, “Digital filtering with applications to electrocardiogram processing,” IEEE Trans. Audio and Electroacoustics AU-16 (3), 350–391 (1968).CrossRefGoogle Scholar

Selected Reading: Chromosome Image and Banding Pattern Analysis

  1. 1.
    D. RUTOVITZ, “Centromere finding: Some shape descriptors for small chromosome outlines,” Machine Intelligence 5, 435–562 (1970).Google Scholar
  2. 2.
    C.J. HILDITCH, “A system of automatic chromosome analysis,” Automatic Interpretation and Classification of Images, A. GRASSELLI (ed.) Academic, New York (1969).Google Scholar
  3. 3.
    S. STONE, L. LITTLEPAGE and B. CLEGG, Second report on the chromosome scanning program at the Lawrence Radiation Laboratory, Pattern Recognition Studies S.P.I.E. Seminar Proc., vol. 18 (1969).Google Scholar
  4. 4.
    F. RUDDLE, S. SMITH, R. LEDLEY and M. BELSON, “Replication-precision study of manual and automatic chromosome analysis,” Ann. N.Y. Acad. Sci. 157 (art 1). 400–423 (1969).Google Scholar
  5. 5.
    K. PATON, “Automatic chromosome identification by the maximum likelihood method,” Ann. Human Genetics 33, 174–184 (1969).CrossRefGoogle Scholar
  6. 6.
    P. NEURATH and K. ENSLEIN, “Human chromosome analysis as computed from arm lengths measurements,” Cytogenetics 8, 337–354 (1969).Google Scholar
  7. 7.
    M. MENDELSOHN, D. HUNGERFORD, B. MAYALL, B. PERRY, T. CONWAY and J. PREWITT, “Computer-oriented analysis of human chromosomes-II.” Ann. N.Y. Acad. Sci. 157 (art 1), 376–392 (1969).CrossRefGoogle Scholar
  8. 8.
    C.J. HILDITCH and D. RUTOVITZ, “Chromosome recognition”Ann. N.Y. Acad. Sci. 157 (art 1), 339–364 (1969).CrossRefGoogle Scholar
  9. 9.
    H. FREY, “An interactive computer program for chromosome analysis,” Computers and Biomedical Research 2, 274–290 (1969).CrossRefGoogle Scholar
  10. 10.
    J.W. BUTLER, M.K. BUTLER and B. MARCZYNSKA, “Automatic analysis of 835 Mormoset Spreads,”Ann. N.Y. Acad. Sci. 157 (art 1), 424–437 (1969).CrossRefGoogle Scholar
  11. 11.
    G. GALLUS, N. MONTANARO and G. MOCCACARO, “A problem of pattern recognition in the automatic analysis of chromosomes; locating the centromere,” Computers and Biomedical Research 2, 187–197 (1968).CrossRefGoogle Scholar
  12. 12.
    Chicago Conference: Standardization in Human Cytogenetics. “Birth Defects: Original Article Series, 11:2.” The National Foundation, New York (196).Google Scholar
  13. 13.
    P. NEURATH, B. BALOUZIAN, T. WARMS, R. SERBAGI and A. FALEK, “Human chromosome analysis-an optical pattern recognition problem,” Ann. N.Y. Acad. Sci. 128. 1013–1028 (1966).CrossRefGoogle Scholar
  14. 14.
    L. PENROSE et al., “The London Conference on the normal human karyotype,” Cytogenetics 2, 264–268 (1963).CrossRefGoogle Scholar
  15. 15.
    M.A. BENDER and M.A. KASTENBAUM, “Statistical analysis of the normal human karyotype,” Am. J. Human Genetics 21 (4), 322–351 (1969).Google Scholar
  16. 16.
    C.W. GILBERT and S. MULDAL, “Measurement and computer system for karyotyping human and other cells,” Nature N.B. 230, 203–207 (April 1971).Google Scholar
  17. 17.
    A. KLINGER, A. KOCHMAN and N. ALEXANDRIDIS, “Computer analysis of chromosome patterns: Feature encoding for flexible decision making,” IEEE Trans. Computers C-20 (9), 1014–1022 (1971).CrossRefGoogle Scholar
  18. 18.
    M. MENDELSOHN et al., “Computer oriented analysis of human chromosomes I-photometric analysis of DNA content,” Cytogenetics 5, 223–242 (1966).CrossRefGoogle Scholar
  19. 19.
    S.R. PATIL, S. MERRICK and H.A. LUBS, “Identification of each human chromosome with a modified giemsa strain,” Science 173, 821–822 (1971).CrossRefGoogle Scholar
  20. 20.
    W. SCHNEDL, “Banding patterns of human chromosomes,” Nature N.B. 233, 93–94 (15 September 1971).Google Scholar
  21. 21.
    T. CASPERSSON, L. ZECH, C. JOHANSSON and E.J. MODEST, “Identification of human chromosomes by DNA-binding fluorescing agents,” Chromosoma 30, 215 (1970).CrossRefGoogle Scholar
  22. 22.
    T. CASPERSSON, L. ZECH, and C. JOHANSSON, “Analysis of the human metaphase chromosome set by aid of DNA-binding fluorescent agents,” Expl. Cell Res. 62, 490 (1970).CrossRefGoogle Scholar
  23. 23.
    A. MOLLER, H. NILSSON, T. CASPERSSON and G. LOMAKKA, “Identification of human chromosome regions by aid of computerized pattern analysis,” Expl. Cell Res. 70, 475 (1972).CrossRefGoogle Scholar
  24. 24.
    T. CASPERSSON, G. GAHRTON, J. LINDSTEN and L. ZECH, “identification of the Philadelphia chromosome as a number 22 by quinacrine mustard fluorescence analysis,” Expl. Cell Res. 13, 238 (1970).CrossRefGoogle Scholar
  25. 25.
    T. CASPERSSON, G. LOMAKKA and L. ZECH, “The 24 fluorescence patterns of the human metaphase chromosomes-distinguishingcharacters arid variability,” Hereditas 67, 89 (1972).CrossRefGoogle Scholar
  26. 26.
    T. CASPERSSON, G. LOMAKKA and A. MOLLER, “Computerized chromosome identification by aid of the quinacrine mustard fluorescence technique,” Hereditas 67, 103 (1971)CrossRefGoogle Scholar
  27. 27.
    H.J. EVANS, K.E. BUCKTON and A. T. SUMNER, “Cytological mapping of human chromosomes: Results obtained with quinacrine fluorescence and the acetic-saline-giemsa techniques,” Chromosoma 35, 310–325 (1971).CrossRefGoogle Scholar
  28. 28.
    W. SCHNEDL, “Analysis of the human karyotype using a reassociation technique,” Chromosoma 34, 448–454 (1971).CrossRefGoogle Scholar
  29. 29.
    G. MANOLOV, Y. MANOLOVA and A. LEVAN, “The fluorescence pattern of the human karyotype,”Hereditas 69, 273–286 (1971).CrossRefGoogle Scholar
  30. 30.
    W. UNAKUL, R.T. JOHNSON, P.N. RAO and T.C. HSU, “Giemsa banding of interphase HeLa chromosomes,” J. Cell Biol. 55, 264a (1972).Google Scholar
  31. 31.
    J.G. GALL and M. L. PARDUE, “Nucleic acid hybridization in cytological preparations,” Methods in Enzymology, Nucleic Acids Part, D.L. GROSSMAN and K. MOLDAVE (Eds.) Vol. 21, pp. 470–480 (1971).CrossRefGoogle Scholar
  32. 32.
    F.E. ARRIGHI and T.C. HSU, “Localization of heterochromatin in human chromosomes,” Cytogenetics 10, 81–86 (1971).CrossRefGoogle Scholar
  33. 33.
    B. DUTRILLAUX and J. LEJEUNE, C.R. Acad. Sci., Paris 272, 2638–2640 (1971).Google Scholar
  34. 34.
    M.E. DRETS and M.W. SHAW, “Specific banding patterns of human chromosomes,” Proc. Nat. Acad. Sci. U.S.A. 68 (9), 2073–2077 (1971).CrossRefGoogle Scholar
  35. 35.
    M. SEABRIGHT, “A rapid banding technique for human chromosomes Lancet 2, 971–972 (1971).Google Scholar
  36. 36.
    Section of Cell Biology, M.D. Anderson Hospital and Tumor Institute, Mammalian Chromosomes Newsl. 13, 21–47 (1972).Google Scholar

Analysis of Spectrograms and Chromatograms

  1. 1.
    D.G. LUENBERGER, “Resolution of mass spectrometer data,” Stanford Electronic Laboratories, Stanford, Calif., Tech. Report. SEL-64–129 (TR 6451–1) (November 1964)Google Scholar
  2. 2.
    L.R. SYNDER, “A rapid approach to selecting the best experimental conditions for high-speed liquid column chromatography”, Part 1, J. Chromatog. Sci. 10, 200–212 (1972).Google Scholar

Computer Analysis of EKG Waveforms

  1. 1.
    R. HELM, “An accurate lead system for spatial vectorcardiography,” Am. Heart J1. 53, 415 (1957).CrossRefGoogle Scholar
  2. 2.
    H.R. Warner, A.F. Toronto, L.G. Veasey and R. Stephenson, “A mathenaticla approch to medical diagnosis, application to congenital heart disease, “.J.A.M.A. 3, no. 177, 177–183 (1961)CrossRefGoogle Scholar
  3. 3.
    C. A. STEINBERG, S. ABRAHAM and C.A. CACERES, “Pattern recognition in the clinical electrocardiogram,” IRE Trans. Biomedical Electronics BME-9, 23–30 (1962).CrossRefGoogle Scholar
  4. 4.
    L. STARK, M. OKAJIMA and G.H. WHIPPLE, “Computer pattern recognition techniques; electrocardiographic diagnosis,”Commun. ACM 5, 527–532 (10 October 1962).CrossRefGoogle Scholar
  5. 5.
    H.V. PIPBERGER, “Use of computers in interpretation of eletrocardiograms,”Circulation Res. 11, 555 (1962).Google Scholar
  6. 6.
    T.Y. YOUNG and W.H. HUGGINS, “Computer analysis of electrocardiograms using a linear regression technique,” IEEE Trans. Bio-medical Engineering BME-11, 60–67 (July 1964).CrossRefGoogle Scholar
  7. 7.
    D.F. SPECHT, “Vectorcardiographic diagnosis using the polynominal discriminant method of pattern recognition,” IEEE Trans. Bio-medical Engineering BME-14 (2), 90–95 (1967).CrossRefGoogle Scholar
  8. 8.
    J.P. BROWN, D.B. FRANCIS, T.W. CALVERT and R.L. LONGINI, “Compensating the VCG for anatomic variations of individuals,” Proc Annual Conf. on Engineering in Biology and Medicine, Boston, Mass. (November 1967).Google Scholar
  9. 9.
    J.P. BROWN, T.W. CALVERT, R.L. LONGINI and E.W. HECKERT,”Normalizing the VCG to facilitate diagnosis,”Proc. Annual Conf. on Engineering in Biology and Medicine, Houston Texas (1968).Google Scholar
  10. 10.
    A.A. LANGER, R.L. LONGINI and E.W. HECKERT, “Body compensator system for VCGs,”Proc. 8th Int. Conf. on Medical and Biological Engineering, Chicago, Illinois (1969).Google Scholar
  11. 11.
    R. GAMBOA, J.D. KLINGEMAN and H.V. PIPBERGER, “Computer diagnosis of biventricular hypertrophy from orthogonal electrocardiograms,”Circulation 39, 72–82 (January 1969).Google Scholar
  12. 12.
    D.B. GESELOWITZ and O. H. SCHMITT, “Electrocardiography,” Biomedical Engineering, H.P. SCHWANN (ed) McGraw-Hill, New York (1969).Google Scholar
  13. 13.
    J. von der GROEBEN, J.G. TOOLE and C.S. WEAVER, “Vectorcardiographic analysis with the aid of a small digital computer,” Actuelle Probleme der Vektorkardiographie, R. WENGER (ed.) GEORG THIEME, Stuttgart (1968).Google Scholar
  14. 14.
    W.P. HOLSINGER, K.M. KEMPUER and M.H. MILLER, “A QRS preprocessor based on digital differentiation,” IEEE Trans. Biomedical Engineering BME-18 (3), 212–217 (May 1971).CrossRefGoogle Scholar
  15. 15.
    D.B. GESELOWITZ, “Use of the multipole expansion to extract significant features of the surface electrocardiogram,” IEEE Trans. Computers C-20 (9), 1086–1089 (September 1971).CrossRefGoogle Scholar
  16. 16.
    R. PLONSEY, “Capability and limitations of electrocardiography and magnetocardiography,” IEEE Trans. Bio-medical Engineering BME-19 (3), 239–244 (May 1972)CrossRefGoogle Scholar

Other Work with Flexible Templates and Parametrized Descriptions of Patterns

  1. 1.
    R.G. Casey and G. Purdy, “Moment normalization of handprinted character,” IBM Research, Yorktown Heights New York: RC2666 (14 October 1969).Google Scholar
  2. 2.
    H.J. BREMERMANN, “Pattern recognition by means of deformable prototypes,” a talk presented at the 1971 Workshop on Pattern Recognition, Anaheim, Calif., October 27, 1971; abstracted on p. 547, IEEE Trans. Systems, Man and Cybernetics SMC-2 (4), (September 1972).Google Scholar
  3. 3.
    C.T. ZAHN and R.Z. ROSKIES, “Fourier descriptors for plane closed curves,” IEEE Trans. Computers C-21, 269–281 (1972).CrossRefGoogle Scholar
  4. 4.
    T. CASPERSSON and L. ZECH, “Chromosome identification by fluorescence,” Hospital Practice 7 (9), 51–62 (1972).Google Scholar

General Bio-Medical Pattern Recognition

  1. 1.
    R.S. LEDLEY and L.S. ROTOLO, “Application of pattern recognition to biomedical problems,” Automatic Interpretation and Classification of Images, A. GRASSELLI (ed.), pp. 323–362, Academic Press, New York (1969).Google Scholar
  2. 2.
    C.J. HILDITCH, “A system of automatic chromosome analysis,” IMI 363–390, (1969).Google Scholar
  3. 3.
    M. PFEILER, “Image transmission and image processing in radiology,” Ibid 399–416 (1969).Google Scholar
  4. 4.
    R.S. LEDLEY, “Automatic pattern recognition for clinical medicine,” Proc. IEEE 57 (11). 2017–2035 (1969).CrossRefGoogle Scholar
  5. 5.
    E.E. GOSE, “Introduction to biological and mechanical pattern recognition,” Methodologies of Pattern Recognition, S. WATANABE (ed.) pp. 203–253. Academic Press, New York (1969).Google Scholar
  6. 6.
    E.E. GOSE, J.W. BACUS and L.V. ACKERMAN, “A comparison of some computer-measured and human-measured pattern recognition properties,” J. Cybernetics 1 (4), 68–74 (1971).CrossRefGoogle Scholar
  7. 7.
    J.W. BACUS and E.E. GOSE, “Leukocyte pattern recognition,” IEEE Trans. Systems, Man, and Cybernetics SMC-2 (4) 513–525 (1972).Google Scholar
  8. 8.
    R. LEDLEY, F. RUDDLE, J. WILSON, M. BELSON and J. ALBARRAN, “The case of touching and overlapping chromosomes” Pictorial Pattern Recognition, G. CHENG et al. (eds.) pp. 87–97. Thompson (1968).Google Scholar
  9. 9.
    R. LEDLEY, “Automatic pattern recognition for clinical medicine,” Proc. IEEE 57, 2017–2035 (1969).CrossRefGoogle Scholar
  10. 10.
    K. PATON, “An automatic method for finding metaphase spreads,” Pictorial Pattern Recognition, G. CHENG et al. (eds.) pp. 135–146 Thompson (1968).Google Scholar
  11. 11.
    R. LEDLEY, M. LEGATOR and J. WILSON, “Automatic determination of mitotic index,” Pictorial Pattern Recognition, G. CHENG et al. (eds.) pp. 99–103. Thompson (1968).Google Scholar
  12. 12.
    J.W. BUTLER, M.K. BUTLER and A. STROUD, “Automatic classification of chromosomes-11, and Automatic classification of chromosomes-111,”Data Acquisition and Processing in Biology and Medicine, K. ENSLEIN (ed.) pp. 45–57 and pp. 21–37. Pergamon, Oxford (1965 and 1968).Google Scholar
  13. 13.
    R. LEDLEY, “FIDAC: Film input to digital automatic computer and associated syntax directed pattern recognition programming system,” Optical and Electro-Optical Information Processing, J. TIPPETT et al. (eds.) Chapter 33, pp. 591–612. MIT Press (1965).Google Scholar
  14. 14.
    R. LEDLEY, “High speed automatic analysis of biomedical pictures,”Science 146, 216–223 (9 October 1964).CrossRefGoogle Scholar
  15. 15.
    K. ENSLEIN and P.W. NEURATH, “Augmented stepwise discriminent analysis applied to two classification problems in the biomedical field,” Computers and Biomedical Research 2, 568–581 (1969).CrossRefGoogle Scholar
  16. 16.
    D. RUTOVITZ, “Pattern recognition,” Royal Statistical Society 12a, 504–530, series A (1966).Google Scholar
  17. 17.
    R. STEFANELLI and A. ROSENFELD, “Some parallel thinning algorithms for digital pictures,” J. ACM 18 (2) 255–264 (1971).CrossRefGoogle Scholar
  18. 18.
    J. HILDITCH and D. RUTOVITZ, “Chromosome recognition,” Ann. N.Y. Acad. Sci. 157, 339–364 (1969).CrossRefGoogle Scholar
  19. 19.
    M. INGRAM, P.E. NORGREN and K. PRESTON, JR., “Automatic differentiation of white blood cells,” Image Processing in Biological Sciences, P.M. RAMSEY (ed.) Univ. Calif. Press, Berkeley, Calif. (1968).Google Scholar
  20. 20.
    M. INGRAM and K. PRESTON, JR., “Automatic analysis of blood cells,” Scient. Am. 223, 72–82 (1970).CrossRefGoogle Scholar
  21. 21.
    M.L. MENDELSOHN, B.H. MAYALL, J.M.S. PREWITT, R.C. BOSTROM and W.G. HOLCOMB, “Digital transformations and computer analysis of microscopic images,” Advances in Optical and Electron Microscopy, V.E. COSLETT (ed.) pp. 77–150. Academic, New York (1968).Google Scholar
  22. 22.
    J.M.S. PREWITT and M.L. MENDELSOHN, “A general approach to image analysis by parameter extraction,” Proc. Computers in Radiology, Chicago (1966).Google Scholar
  23. 23.
    “The analysis of cell images,”Ann. N.Y. Acad. Sci. 128, 1035–1053 (1966).Google Scholar
  24. 24.
    T. GOLAB, R.S. LEDLEY and L.S. ROTOLO, “FIDAC-Film input to digital computer,” Pattern Recognition 3, 123 (1971).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • Bernard Widrow
    • 1
  1. 1.Department of Electrical EngineeringStanford Electronics LaboratoriesStanfordUSA

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