Skip to main content
SpringerLink
Log in

The Logarithmic Image Processing Model: Connections with Human Brightness Perception and Contrast Estimators

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

The logarithmic image processing (LIP) model is amathematical framework based on abstract linear mathematicswhich provides a set of specific algebraic and functionaloperations that can be applied to the processing of intensityimages valued in a bounded range. The LIP model has been provedto be physically justified in the setting of transmitted lightand to be consistent with several laws and characteristics ofthe human visual system. Successful application examples havealso been reported in several image processing areas, e.g.,image enhancement, image restoration, three-dimensional imagereconstruction, edge detection and image segmentation.

The aim of this article is to show that the LIP model is atractable mathematical framework for image processing which isconsistent with several laws and characteristics of humanbrightness perception. This is a survey article in the sensethat it presents (almost) previously published results in arevised, refined and self-contained form. First, an introductionto the LIP model is exposed. Emphasis will be especially placedon the initial motivation and goal, and on the scope of themodel. Then, an introductory summary of mathematicalfundamentals of the LIP model is detailed. Next, the articleaims at surveying the connections of the LIP model with severallaws and characteristics of human brightness perception, namelythe brightness scale inversion, saturation characteristic, Weber'sand Fechner's laws, and the psychophysical contrast notion. Finally,it is shown that the LIP model is a powerful and tractable framework for handling the contrast notion. This is done througha survey of several LIP-model-based contrast estimators associated with special subparts (point, pair of points,boundary, region) of intensity images, that are justified bothfrom a physical and mathematical point of view.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Jourlin and J.C. Pinoli, “A model for logarithmic image processing,” Report No. 3, Department of Mathematics, University of Saint-Etienne, France, 1985.

    Google Scholar 

  2. J.C. Pinoli, “Contribution à la modélisation, au traitement et à l'analyse d';image,” D.Sc. Thesis, Department of Mathematics, University of Saint-Etienne, France, 1987.

    Google Scholar 

  3. M. Jourlin and J.C. Pinoli, “Logarithmic image processing,” Acta Stereol., Vol. 6, pp. 651–656, 1987.

    Google Scholar 

  4. M. Jourlin and J.C. Pinoli, “A model for logarithmic image processing,” J. Microsc., Vol. 149, pp. 21–35, 1988.

    Google Scholar 

  5. J.C. Dainty and R. Shaw, Image Science, Academic Press: London, 1974.

    Google Scholar 

  6. R.W. Ditchburn, Light, 3rd edition, Academic Press: New York, 1976.

    Google Scholar 

  7. W.G. Driscoll, Handbook of Optics, Optical Society of America, Mac Graw Hill: New York, 1978.

    Google Scholar 

  8. M. Born and E. Wolf, Principle of Optics, 2nd edition, Pergamon Press: New-York, 1980.

    Google Scholar 

  9. L.M. Hurwich and D. Jameson, The Perception of Brightness and Darkness, Allyn & Bacon: Boston, 1966.

    Google Scholar 

  10. T.N. Cornsweet, Visual Perception, Academic Press: New York, 1970.

    Google Scholar 

  11. I.E. Gordon, Theories of Visual Perception, JohnWiley & Sons: New York, 1989.

    Google Scholar 

  12. R. Watt, Understanding Vision, Academic Press: London, 1991.

    Google Scholar 

  13. A. Rosenfeld and A.C. Kak, Digital Picture Processing, 2nd edition, Academic Press: New York, 1976.

    Google Scholar 

  14. R.C. Gonzalez and P. Wintz, Digital Image Processing, 2nd edition, Addison-Wesley: Reading, Massachusetts, 1987.

    Google Scholar 

  15. A.K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall: Englewood Cliffs, 1989.

    Google Scholar 

  16. W.K. Pratt, Digital Image Processing, 2nd edition, JohnWiley: New York, 1991.

    Google Scholar 

  17. J.C. Pinoli, “A contrast definition for logarithmic images in the continuous setting,” Acta Stereol., Vol. 10, pp. 85–96, 1991.

    Google Scholar 

  18. J.C. Pinoli, “Metrics, scalar product and correlation adapted to logarithmic images,” Acta Stereol., Vol. 11, pp. 157–168, 1992.

    Google Scholar 

  19. J.C. Pinoli, “Modélisation et traitement des images logarithmiques: Théorie et applications fondamentales,” Report No. 6, Department of Mathematics, University of Saint-Etienne, France, 1992. This report is an enlarged synthetis of the theoretical framework and fundamental applications of the LIP model published from 1984 to 1992. It has been reviewed as a thesis by international referees for passing in Dec. 1992 the “Habilitation à diriger des recherches” French degree.

    Google Scholar 

  20. G. Strang, Linear Algebra and its Applications, Academic Press: New York, 1976.

    Google Scholar 

  21. G. Choquet, Topology, Academic Press: New-York, 1966.

    Google Scholar 

  22. N. Dunford and J.T. Schwartz, Linear Operators, Part I, General Theory, New edition, Wiley-Interscience: New York, 1988.

    Google Scholar 

  23. W.A.J. Luxemburg and A.C. Zaanen, Riesz Spaces, North Holland: Amsterdam, 1971.

    Google Scholar 

  24. L. Kantorovitch and G. Akilov, AnalyseFonctionnelle, Editions Mir: Moscou, 1981.

    Google Scholar 

  25. R.W. Hornbeck, Numerical Methods, Quantum Publishers Inc.: New-York, 1975.

    Google Scholar 

  26. F. Mayet, J.C. Pinoli, and M. Jourlin, “Justifications physiques et applications du modèle LIP pour le traitement des images obtenues en lumière transmise,” Traitement du signal, Vol. 13, pp. 251–262, 1996.

    Google Scholar 

  27. G. Deng, “Image and signal processing using the logarithmic image processing model,” Ph.D. thesis, Department of Electronic Engineering, La Trobe University, Australia, 1993.

  28. G. Deng, L.W. Cahill, and G.R. Tobin, “A study of the logarithmic image processing model and its application to image enhancement,” IEEE Trans. Image Process.,Vol. IP-4, pp. 506–512, 1995.

    Google Scholar 

  29. G. Deng and L.W. Cahill, “Image modelling and processing using the logarithmic image processing model,” in Proc. IEEE Workshop on Visual Signal Process. Comm., Melbourne, Australia, 1993, pp. 61–64.

  30. M. Jourlin, J.C. Pinoli, and R. Zeboudj, “Contrast definition and contour detection for logarithmic images,” J. Microsc., Vol. 156, pp. 33–40, 1988.

    Google Scholar 

  31. J.C. Brailean, B.J. Sullivan, C.T. Chen, and M.L. Giger, “Evaluating the EM algorithm for image processing using a human visual fidelity criterion, in Proc. ICASSP, pp. 2957–2960, 1991.

  32. M. Jourlin and J.C. Pinoli, “Image dynamic range enhancement and stabilization in the context of the logarithmic image processing model,” Signal Process., Vol. 41, pp. 225–237, 1995.

    Google Scholar 

  33. D.A. Baylor, T.D. Lamb, and K.W. Yau, “Response of retinal rods to single photons,” J. Physiol., Vol. 288, pp. 613–634, 1979.

    Google Scholar 

  34. D.A. Baylor, B.J. Nunn, and J.L. Schnapf, “The photo-current, noise and spectral sensitivity of rods of the monkey Macaca Fascicularis,” J. Physiol., Vol. 357, pp. 575–607, 1984.

    Google Scholar 

  35. C. Bron, P. Gremillet, D. Launay, M. Jourlin, H.P. Gautschi, T. Bächi, and J. Schüpbach, “Three-dimensional electron microscopy of entire cells,” J. Microsc., Vol. 157, pp. 115–126, 1990.

    Google Scholar 

  36. P. Gremillet, M. Jourlin, C. Bron, J. Schüpbach, H.P. Gautschi, and T. Bächi, “Dedicated image analysis techniques for threedimensional reconstruction from serial sections in electron microscopy,” Mach. Vision Applic., Vol. 4, pp. 263–270, 1991.

    Google Scholar 

  37. P. Gremillet, “Reconstruction et visualisation de surfaces et de volumes en microscopie électronique à balayage,” Ph.D. Thesis, University of Saint-Etienne, France, 1992.

  38. P. Gremillet, M. Jourlin, and J.C. Pinoli, “LIP model-based three-dimensional reconstruction and visualisation of HIV infected entire cells,” J. Microsc., Vol. 174, pp. 31–38, 1994.

    Google Scholar 

  39. P. Gremillet, J.L. Coudert, M. Jourlin, and J.C. Pinoli, “Three-dimensional image reconstruction and visualisation of human jaws,” in Proc. IEEE Workshop on Nonlinear Images and Signals, Halkidiki, Greece, 1995, pp. 819–822.

  40. G. Deng and L.W. Cahill, “Multiscale image enhancement using the logarithmic image processing model,” Electronics Let., Vol. 29, pp. 803–804, 1993.

    Google Scholar 

  41. P. Corcuff, P. Gremillet, M. Jourlin, Y. Duvault, F. Leroy, and J.L. Leveque, “3D reconstruction of human hair by confocal microscopy,” J. Soc. Com. Chem., Vol. 44, pp. 1–12, 1993.

    Google Scholar 

  42. J.C. Brailean, D. Little, M.L. Giger, C.T. Chen, and B.J. Sullivan, “A quantitative performance evaluation of the EM algorithm applied to radiographic images,” in Proc. SPIE Biomed. Image Process II, 1991, Vol. 1450, pp. 40–46.

    Google Scholar 

  43. J.C. Brailean, D. Little, M.L. Giger, C.T. Chen, and B.J. Sullivan, “Applications of the EM algorithm to radiographic images,” Med. Phys., Vol. 19, pp. 1175–1182, 1992.

    Google Scholar 

  44. B. Roux and R.M. Faure, “Recognition and quantification of clinker phases by image analysis,” Acta Stereol., Vol. 11, pp. 149–154, 1992.

    Google Scholar 

  45. B. Roux, “Mise au point d'une méthode qui reconnait et quantifie les phases de clinker,” Ph.D. Thesis, University of Saint-Etienne, France, 1992.

    Google Scholar 

  46. H. Konik, B. Laget, and M. Calonnier, “Segmentation d'images par utilisation ar utilisation de pyramides à bases locales,” Traitement du Signal, Vol. 10, pp. 283–295, 1993.

    Google Scholar 

  47. G. Deng and L.W. Cahill, “Contrast edge detection using the logarithmic image processing model,” in Proc. Int. Conf. on Signal Process., Beijing, China, 1993, pp. 792–796.

  48. G. Deng and L.W. Cahill, “Generating sketch image for very low bit rate image communication,” in Proc. 27th Asilomar Conf. on Signal Systems and Computers, California, US, 1993, pp. 1047–1051.

  49. G. Deng and L.W. Cahill, “A novel multiscale image filtering algorithm using the contrast pyramid,” in Proc. 2nd. Conf. on Simulation and Modelling, Melbourne, Australia, 1993, pp. 57–65.

  50. G. Deng and L.W. Cahill, “A novel nonlinear filtering algorithm using the logarithmic image processing model,” in Proc. 8th. Workshop on Nonlinear Image and Signal Processing, Cannes, France, 1993, pp. 61–64.

  51. G. Deng and L.W. Cahill, “The contrast pyramid using the logarithmic image processing model,” in Proc. 2nd. Conf. on Simulation and Modelling, Melbourne, Australia, 1993, pp. 75–82.

  52. G. Deng and L.W. Cahill, “Low bit rate image coding using sketch and JBIG,” in Proc. SPIE Conf. on Electronic Imaging, San Jose: USA, 1995 (in press).

  53. J.C. Pinoli, “A general comparative study of the multiplicative homomorphic, Log-ratio and logarithmic image processing approaches,” Signal Process, Vol. 58, pp. 11–45, 1997.

    Google Scholar 

  54. J.S. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall: Englewood Cliffs, 1990.

    Google Scholar 

  55. A.V. Oppenheim, R.W. Schafer, and T.G. Stockham, Jr., “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE, Vol. 56, pp. 1264–1291, 1968.

    Google Scholar 

  56. T.G. Stockham, Jr., “Image processing in the context of a visual model,” Proc. IEEE, Vol. 60, pp. 828–842, 1972.

    Google Scholar 

  57. A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall: Englewood Cliffs, 1975.

    Google Scholar 

  58. H. Shvayster and S. Peleg, “Pictures as elements in a vector space,” in Proc. IEEE Conf. on Comput. Vision Pattern Recogn., Washington, pp. 442–446, 1983.

  59. E. Harouche, S. Peleg, H. Shvayster, and L.S. Davis, “Noisy image restoration by cost minimization,” Pattern Recogn. Lett., Vol. 3, pp. 65–69, 1985.

    Google Scholar 

  60. H. Shvayster and S. Peleg, “Inversion of picture operators,” Pattern Recogn. Lett., Vol. 5, pp. 46–61, 1987.

    Google Scholar 

  61. Z. Xie and T.G. Stockham, Jr., “Toward the unification of three visual laws and two visual models in brightness perception,” IEEE Trans. Syst., Man Cyber., Vol. SMC-19, pp. 379–387, 1989.

    Google Scholar 

  62. F.A. Valentine, Convex Sets, Mac Graw Hill: New-York, 1964.

    Google Scholar 

  63. H. Cartan, Cours de Calcul Différentiel, Hermann: Paris, 1979.

    Google Scholar 

  64. A.K. Halmos, Measure Theory, Van Nostrand: Princeton, 1950.

    Google Scholar 

  65. S. Mallat, “Multiresolution approximation and wavelet bases of L2,” Trans. Amer. Math. Soc., Vol. 315, pp. 69–87, 1989.

    Google Scholar 

  66. S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Patt. Anal. Mach. Intell., Vol. PAMI-11, pp. 674–693, 1989.

    Google Scholar 

  67. M.H. Pirenne, Vision and the Eye, 2nd edition, Associated Book Publishers: New York, 1967.

    Google Scholar 

  68. P. Zuidema, J.J. Koenderink, and M.A. Bouman, “A mechanistic approach to threshold behavior of the visual system,” IEEE Trans. Syst., Man Cyber., Vol. 13, pp. 923–933, 1983.

    Google Scholar 

  69. E.H. Weber, “Der tastsinn und das gemeingefühl,” in Handwörterbuch der Physiologie, E. Wagner (Ed.), Vol. 3, pp. 481–588, 1846.

  70. S.S. Stevens, Handbook of Experimental Psychology, John Wiley: New York, 1951.

    Google Scholar 

  71. H.R. Blackwell, “Contrast thresholds of the human eye,” J. Opt. Soc. Am., Vol. 36, pp. 624–643, 1946.

    Google Scholar 

  72. E.S. Lamar, S. Hecht, S. Shlaer, and D. Hendlay, “Size, shape, and contrast in detection of targets by daylight vision. I. Data and analytical description,” J. Opt. Soc. Am., Vol. 37, pp. 531–545, 1947.

    Google Scholar 

  73. G. Buchsbaum, “An analytical derivation of visual nonlinearity,” IEEE Trans. Biomed. Eng., Vol. BE-27, pp. 237–242, 1980.

    Google Scholar 

  74. L.E. Krueger, “Reconciling Fechner and Stevens: Toward an unified psychophysical law,” Behav. Brain Sci., Vol. 12, pp. 251–320, 1989.

    Google Scholar 

  75. L.E. Krueger, Continuing commentary on L.E. Krueger (1989), “Reconciling Fechner and Stevens: Toward an unified psychophysical law,” Behav. Brain Sci., Vol. 14, pp. 187–204, 1991.

    Google Scholar 

  76. G.T. Fechner, Elements of Psychophysics,Vol. 1, English translation by H.E. Adler. Holt, Rinehart & Winston: New-York, 1960.

    Google Scholar 

  77. G.T. Fechner, Elemente der Psychophysik, Vols. 1 and 2, Breitkopf & Hartel: Leipzig, 1860.

    Google Scholar 

  78. M.G.F. Fuortes, “Initiation of impulses in visual cells of Limulus,” J. Physiol., Vol. 148, pp. 14–28, 1959.

    Google Scholar 

  79. H. DeVries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica, Vol. X, pp. 553–564, 1943.

    Google Scholar 

  80. A. Rose, “The sensitivity performance of the human eye on an absolute scale,” J. Opt. Soc. Am., Vol. 38, pp. 196–208, 1948.

    Google Scholar 

  81. A. Rose, Vision: Human and Electronic, Plenum Press: New York, 1973.

    Google Scholar 

  82. Y.Y. Zeevi and S.S. Mangoubi, “Noise suppression in photoreceptors and its relevance to incremental intensity,” J. Opt. Soc. Am., Vol. 68, pp. 1772–1776, 1978.

    Google Scholar 

  83. S.S. Stevens, “On the psychophysical law,” Psychol. Rev., Vol. 64, pp. 153–181, 1957.

    Google Scholar 

  84. S.S. Stevens and E.H. Galenter, “Ratio scales and category scales for a dozen perceptual continua,” J. Exp. Psychol., Vol. 54, pp. 377–411, 1957.

    Google Scholar 

  85. S.S. Stevens, “Concerning the psychophysical power law,” Quat. J. Exp. Psychol., Vol. 16, pp. 383–385, 1964.

    Google Scholar 

  86. K.I. Naka and W.A.H. Rushton, “S-potentials from luminosity units in the retina of fish (cyprinidae),” J. Physiol., Vol. 185, pp. 587–599, 1966.

    Google Scholar 

  87. R.A. Normann and F.S. Werblin, “Control of retinal sensitivity. I. Light and dark adaptation of vertebrate rods and cones,” J. Gen. Physiol., Vol. 63, pp. 37–61, 1974.

    Google Scholar 

  88. D.C. Hood, M.A. Finkelstein, and E. Buckingham, “Psychophysical tests of models of the response-intensity function,” Vis. Res., Vol. 19, pp. 401–406, 1979.

    Google Scholar 

  89. M. Treisman, “Sensory scaling and the psychophysical law,” Quat. J. Exp. Psychol., Vol. 16, pp. 11–22, 1964.

    Google Scholar 

  90. E.C. Poulton, “The new psychophysics: six models for magnitude estimation,” Psychol. Bull., Vol. 69, pp. 1–19, 1968.

    Google Scholar 

  91. E.C. Poulton, “Why unbiased numerical magnitude judgments of the loudness of noise are linear in decibels: A rejoinder to the Teghtsoonians,” Percept. Psychophysics, Vol. 40, pp. 131–134, 1986.

    Google Scholar 

  92. E.C. Poulton, “Quantifying Judgements,” in Oxford Companions to the Mind, R.L. Gregory and O.L. Zangwill (Eds.), Oxford University Press, pp. 667–670, 1987.

  93. R.L. Gregory, “Questions of quanta and qualia: Does sensation make sense of matter or does matter make sense of sensation? Part 1,” Percept., Vol. 17, pp. 699–702, 1988.

    Google Scholar 

  94. G. Ekman, “Weber's law and related functions,” J. Psychol., Vol. 47, pp. 343–352, 1959.

    Google Scholar 

  95. G. Ekman, “Is the power law a special case of Fechner's law?,” Percept. Motor Skills, Vol. 19, p. 730, 1964.

    Google Scholar 

  96. S.S. Stevens, “The surprising simplicity of sensory metrics,” Amer. Psychol., Vol. 17, pp. 29–39, 1962.

    Google Scholar 

  97. R. Teghtsoonian, “On the exponents in Stevens' law and the constant in Ekman's law,” Psychol. Review, Vol. 78, pp. 72–80, 1971.

    Google Scholar 

  98. T.O. Kvalseth, “Is Fechner's logarithmic law a special case of Stevens' power law?,” Percept. Motor Skills, Vol. 52, pp. 617–618, 1981.

    Google Scholar 

  99. T.O. Kvalseth, “Fechner's psychophysical law as a special case of Stevens' three-parameter power law,” Percept. Motor Skills, Vol. 75, pp. 1205–1206, 1992.

    Google Scholar 

  100. W.J. McGill and J.P. Goldberg, “A study of the near-miss involving Weber's law and pure intensity discrimination,” Percept. Psychophysics, Vol. 4, pp. 105–109, 1968.

    Google Scholar 

  101. V. Graf, J.C. Baird, and G. Glesman, “An empirical test of two psychophysical models,” Acta Psychol., Vol. 38, pp. 59–72, 1974.

    Google Scholar 

  102. R.J.W. Mansfield, “Visual adaptation: Retinal transduction, brightness and sensitivity,” Vis. Res., Vol. 16, pp. 679–690, 1976.

    Google Scholar 

  103. D.C. Hood and M.A. Finkelstein, “Comparison of changes in sensitivity and sensation: Implications for the responseintensity function of the human photopic system,” J. Exp. Psychol.: Human Percept. Perf., Vol. 5, pp. 391–405, 1979.

    Google Scholar 

  104. D.J. Weiss, “The impossible dream of Fechner and Stevens,” Percept., Vol. 10, pp. 431–434, 1981.

    Google Scholar 

  105. A. Rosenfeld, “Connectivity in digital pictures,” J. Ass. Comp. Mach., Vol. 17, pp. 146–160, 1970.

    Google Scholar 

  106. J.C. Alexander and A.I. Thaler, “The boundary count of digital pictures,” J. Ass. Comp. Mach., Vol. 18, pp. 105–112, 1971.

  107. G. Tourlakis and J. Mylopoulos, “Some results in computational topology,” J. Ass. Comp. Mach., Vol. 20, pp. 439–455, 1973.

    Google Scholar 

  108. A. Rosenfeld, “Digital topology,” Amer. Math. Monthly, Vol. 86, pp. 621–630, 1979.

    Google Scholar 

  109. T. Pavlidis, Algorithms for Graphics and Image Processing, Computer Science Press: Rockville, MD, 1982.

    Google Scholar 

  110. V.A. Kovalevsky, “Finite topology as applied to image analysis,” Comp. Vision, Graph. Image Process., Vol. 46, pp. 141–161, 1989.

    Google Scholar 

  111. T.Y. Kong and A. Rosenfeld, “Digital topology: Introduction and survey,” Comp. Vision, Graph. Image Process., Vol. 48, pp. 357–393, 1989.

    Google Scholar 

  112. T.Y. Kong and R. Kopperman, “A topological approach to digital topology,” Amer. Math. Monthly, Vol. 98, pp. 901–917, 1991.

    Google Scholar 

  113. E. Peli, “Contrast in complex images,” J. Opt. Soc. Am., Vol. 7, pp. 2032–2040, 1990.

    Google Scholar 

  114. J.J. Stoker, Differential Geometry, New edition, Wiley-Interscience: New York, 1989.

    Google Scholar 

  115. H. Federer, Geometric Measure Theory, Springer Verlag: Berlin, 1969.

    Google Scholar 

  116. G. Deng and J.C. Pinoli, “Differentiation-based edge detection using the logarithmic image processing model,” accepted by J. Math. Imaging Vision.

Download references

Author information

Authors and Affiliations

  1. Pechiney, Centre de Recherches, Parc Economique Centr'Alp, BP 27, F38340, Voreppe, France

    Jean-Charles Pinoli

  2. Laboratoire Image, Signal et Acoustique, CNRS EP 92, Ecole Supérieure de Chimie, Physique et Electronique, 31 Place Bellecour, F69288, Lyon Cedex2, France

    Jean-Charles Pinoli

Authors
  1. Jean-Charles Pinoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pinoli, JC. The Logarithmic Image Processing Model: Connections with Human Brightness Perception and Contrast Estimators. Journal of Mathematical Imaging and Vision 7, 341–358 (1997). https://doi.org/10.1023/A:1008259212169

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008259212169

Search

Navigation