Invariances in Pattern Recognition

  • Herbert J. Reitboeck


Humans and animals can recognize objects independent of object position in the visual field, largely independent of viewing angle and distance, and even independent of considerable variations in object shape. For object classification in the visual system, a comparison of sensory information with data in memory is required. Due to the large number of possible retinal pictures that can represent members of the same object class and even one individual object, such comparison is only feasible if an efficient object description can be generated that is object specific and invariant to changes in “non-essential” parameters. Of particular interest for models of invariance operations in the CNS are shift-invariant transforms. Shift-invariance is a primary invariance and other invariances can be derived from it. Size- and rotation-invariance, e.g., can be realized via a shift-invariance mechanism in combination with a logarithmic polar coordinate transform. With some approximations, the mapping of visual space to area 17 in the visual cortex of primates can be described by a logarithmic polar coordinate transform. Models of size-invariant processing in the CNS based on this mapping function have been proposed. In this paper, concepts for the generation of shift-, size-, and rotation-invariant pattern representations in the visual system are discussed, and a critical evaluation of their advantages, drawbacks, and neurophysiological implications will be given. Particularly, the paper will focus on two basic problems: (a) Neural networks are not well suited to perform exact arithmetic operations, as required in many models. A shift-invariant transform will be described that puts minimal demands on the neural transfer function. (b) Invariance operations generally require that the object has been separated from the background. Our model of region labeling via correlated neural activities preserves individual object contributions in composite pattern transforms, and is thus able to cope with the problem of figure/ground separation.


Visual System Spatial Frequency Visual Cortex Basilar Membrane Visual Space 
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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  1. Albrecht DG, De Valois RL, Thorell LG (1981) Visual cortical neurons: are bars or gratings the optimal stimuli? Science 207: 88–90CrossRefGoogle Scholar
  2. Allmann JH, Kaas JH (1971) Representation of the visual field in striate and adjoining cortex of the owl monkey (Aotus trivirgatus). Brain Res 35: 89–106CrossRefGoogle Scholar
  3. Altes RA (1978) The Fourier-Mellin transform and mammalian hearing. JAcoust Soc Amer 63: 174–183CrossRefGoogle Scholar
  4. Altmann J, Reitboeck HJ (1984) A fast correlation method for scale-and translation-invariant patterns recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI6: 46–57Google Scholar
  5. Blakemore C, Campbell FW (1969) On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. JPhysiol203: 237–260Google Scholar
  6. Bracewell R (1965) The Fourier transform and its applications. McGraw-Hill Book Comp, New York Burkhardt H, Mueller X (1980) On invariant sets of a certain class of fast translation-invariant transforms. IEEE Trans ASSP 28: 517–523Google Scholar
  7. Campbell FW, Robson JG (1968) Application of Fourier analysis to the visiblity of gratings. JPhysio1197: 551–566Google Scholar
  8. Campbell FW, Cooper FG, Enroth-Cugell C (1969) The spatial selectivity of the visual cells of the cat. J Physiol 203: 223–235PubMedGoogle Scholar
  9. Campbell FW, Howell ER, Robson JG (1971) The appearance of gratings with and without the fundamental Fourier component. JPhysioI217: 17–18Google Scholar
  10. Casasent D, Psaltis D (1976) Scale invariant optical correlation using Mellin transforms. Opt Commun 17: 59–63CrossRefGoogle Scholar
  11. Casasent D, Psaltis D (1977) New optical transforms for pattern recognition. Proc IEEE 65: 77–84 Cavanagh P (1981) Size invariance: reply to Schwartz. Perception 10: 469–474Google Scholar
  12. Cavanagh P (1982) Functional size invariance is not provided by the cortical magnification factor. Vision Res 22: 1409–1412PubMedCrossRefGoogle Scholar
  13. Cavanagh P (1985) Local log polar frequency analysis in the striate cortex as a basis for size and orientation invariance. In: Rose D, Dobson VG (eds) Models of the visual cortex John Wiley, Chichester, pp 85–95Google Scholar
  14. Cowey A (1964) Projection of the retina onto striate and prestriate cortex in the squirrel monkey (Saimiri sciureus). JNeurophysiol27: 366–393Google Scholar
  15. Daniel PM, Whitteridge D (1961) The representation of the visual field on the cerebral cortex in monkeys. JPhysio1159: 203–221Google Scholar
  16. Daugman, JG (1985) Representational issues and local filter models of two-dimensional spatial visual encoding. In: Rose D, Dobson VG (eds) Models of the visual cortex. John Wiley, Chichester, pp 96–107Google Scholar
  17. DeValois RL, Albrecht DG, Thorell LG (1978) Cortical cells: bar and edge detectors, or spatial frequency filters? In: Cool SJ, Smith EL (eds) Frontiers of visual science. Springer-Verlag, New York, pp 544–556Google Scholar
  18. DeValois KK, DeValois RL, Yund EY (1979) Responses of striate cortex cells to grating and checkerboard patterns. JPhysiol291: 483–505Google Scholar
  19. DeValois RL, Albrecht DG, Thorell LG (1982) Spatial frequency selectivity of cells in macaque visual cortex. Vision Res 22: 545–559CrossRefGoogle Scholar
  20. Dow BM, Snyder AZ, Vautin RG, Bauer R (1981) Magnification factor and receptive field size in foveal striate cortex of monkey. Dip Brain Res44: 213–228Google Scholar
  21. Eckhorn R, Reitboeck HJ (1988) Assessment of cooperative firing in groups of neurons: special concepts for multiunit recordings from the visual system. In: Basar E (ed) Dynamics of sensory and cognitive processing Springer-Verlag, Berlin Heidelberg New York, pp 219–227Google Scholar
  22. Eckhorn R, Bauer R, Reitboeck HJ (1988) Discontinuities in visual cortex and possible functional implications: relating cortical structure and function with multi-electrode/correlation techniques. In: Basar E (ed) Springer series in brain dynamics, Vol 2 (in press)Google Scholar
  23. Elliott DF, Rao KR (1982) Fast transforms: algorithms, analyses, applications. Academic Press, New York Enroth-Cugell C, Robson JG (1966) The contrast sensitivity of retinal ganglion cells of the cat. J Physiol 187: 517–552Google Scholar
  24. Epstein LI (1984) An attempt to explain the differences between the upper and lower halves of the striate cortical map of the cat’s field of view. Biol Cybern 49: 175–177PubMedCrossRefGoogle Scholar
  25. Fu KS (1974) Syntactic methods in pattern recognition. Academic Press, LondonGoogle Scholar
  26. Fu KS, Rosenfeld A (1976) Pattern recognition and image processing. IEEE Trans Comput C 25: 1336–1345Google Scholar
  27. Gray CM, Singer W (1987) Stimulus-dependent neuronal oscillations in the cat visual cortex area 17. Neurosci 22: 1301Google Scholar
  28. Harmuth HF (1972) Transmission of information by othogonal functions. Springer-Verlag, Berlin Heidelberg New YorkCrossRefGoogle Scholar
  29. Hu MK (1962) Visual pattern recognition by moment invarants. IRE Trans Inform Theo ‘II-8: 179–187 Huang GC, Russell FD, Chen WH (1975) Pattern recognition by Mellin transform. EIA/AIPR Symposium, Univ of MarylandGoogle Scholar
  30. Hughes HC, Sprague JM (1986) Cortical mechanisms for local and global analysis of visual space in the cat. Pap Brain Res 61: 332–354Google Scholar
  31. Johannesma P, Aertsen A, van den Boogaard H, Eggermont J, Epping W (1986) From synchrony to harmony: ideas on the function of neural assemblies and on the interpretation of neural synchrony. In: Palm G, Aertsen A (eds) Brain theory. Springer-Verlag, Berlin Heidelberg New York, pp 25–47CrossRefGoogle Scholar
  32. Kulikowski JJ, Bishop PO (1981) Fourier analysis and spatial representation in the visual cortex. Experientia 37: 160–163PubMedCrossRefGoogle Scholar
  33. Kulikowski JJ, Kranda K (1986) Image analysis performed by the visual system: feature versus Fourier analyis and adaptable filtering. Pettigrew JD (ed) Visual neuroscience. Cambridge Univ Press, Cambridge Mass, pp 381–404Google Scholar
  34. Kunt M (1975) On computation of the Hadamard transform and the R-transform in ordered form. IEEE Comput Trans C-24: 1120–1121Google Scholar
  35. Macleod IDG, Rosenfeld A (1974) The visibility of gratings: spatial frequency channels or bar detecting units? Vision Res 14: 909–915PubMedCrossRefGoogle Scholar
  36. MacKay D (1981) Strife over visual cortical function. Nature 289: 117–118PubMedCrossRefGoogle Scholar
  37. Maffei L (1978) Spatial frequency channels: neural mechanisms. In: Held R, Leibowitz HW, Teuber HL (eds) Handbook of sensory physiology, Vol 8. Springer-Verlag, Berlin Heidelberg New York, pp 3966Google Scholar
  38. Maffei L, Fiorentini A (1973) The visual cortex as a spatial frequency analyzer. Vision Res 13: 1255–1267PubMedCrossRefGoogle Scholar
  39. Malsburg C v d (1981) The correlation theory of brain function. Dept of Neurobiology Internal Report 812, MPI Biophysical Chemistry GöttingenGoogle Scholar
  40. McCollough C (1965) Color adaptation of edge-detectors in the human visual system. Science 149: 1115–1116PubMedCrossRefGoogle Scholar
  41. Mishkin M, Ungerleider LG (1982) Contribution of striate inputs to the visuospatial functions of parietopreoccipital cortex in monkeys. Behav Brain Res6: 57–77Google Scholar
  42. Rao KR, Ahmed N (1980) A Class of discrete orthogonal transforms. Comp and Electr Eng (USA) Co 7: 79–87CrossRefGoogle Scholar
  43. Rao KR (1985) Discrete transforms and their applications. Van Nostrand Reinhold Comp, New York Reichardt W, Poggio T (1979) Figure-ground discrimination by relative movement in the visual system of the fly. Part I: Experimental results. Biol Cybern 35: 81–100Google Scholar
  44. Reichardt W, Poggio T, Hausen K (1983) Figure-ground discrimination by relative movement in the visual system of the fly. Part II: Towards the neural circuitry. Biol Cybern 46: 1–30CrossRefGoogle Scholar
  45. Reitboeck HJ (1982) in Altmann L (1982) Psychophysische Untersuchungen zur Rolle derSynchronität bei der Mustererkennung mit Hilfe einer mikroprozessorgesteuerten LED-Matrix MS Thesis, Univ of MarburgGoogle Scholar
  46. Reitboeck HJ (1983) A Multi-electrode matrix for studies of temporal signal correlations within neural assemblies. In: Basar E, Flohr H, Haken H, Mandell AJ (eds) Synergetics of the brain. Springer-Verlag, Berlin Heidelberg New York, pp 174–181CrossRefGoogle Scholar
  47. Reitboeck HJ, Altmann J (1984) A model for size-and rotation-invariant pattern processing in the visual system. Biol Cybem 51: 113–121CrossRefGoogle Scholar
  48. Reitboeck HJ, Brody TP (1969) A transformation with invariance under cyclic permutation for applications in pattern recognition. Inf Control 15: 130–154CrossRefGoogle Scholar
  49. Reitboeck HJ, Eckhorn R, Pabst M (1987a) A model of figure/ground separation based on correlated neural activity in the visual system. In: Haken H (ed) Synergetics of the brain. Springer-Verlag, Berlin Heidelberg New York, pp 44–54Google Scholar
  50. Reitboeck HJ, Eckhorn R, Pabst M (1987b) Texture description in the time domain. In: Cotterill RMJ (ed) Computer simulation in brain science. Cambridge Univ Press, Cambridge MassGoogle Scholar
  51. Schiller PH, Finlay BL, Volman SF (1976) Quantitative studies of single-cell properties in monkey striate cortex. JNeurophysio139: 1288–1351Google Scholar
  52. Schwartz EL (1981) Cortical anatomy, size invariance, and spatial frequency analysis. Perception 10: 455–468PubMedCrossRefGoogle Scholar
  53. Schwartz EL (1983) Cortical mapping and perceptual invariance: a reply to Cavanagh. Vision Res 23: 831–835PubMedCrossRefGoogle Scholar
  54. Schwartz EL (1985) Local and global functional architecture in primate striate cortex: outline of a spatial mapping doctrine for perception. In: Rose D, Dobson VG (eds) Models of the visual cortex John Wiley, Chichester, pp 146–156Google Scholar
  55. Sprague JM, Leby J, DiBerardino A, Berlucchi G (1977) Visual cortical areas mediating form discrimination in the cat. J Comp Neural 172: 441–488CrossRefGoogle Scholar
  56. Stromeyer CF (1972) Edge-contingent color after effects: spatial frequency specificity. Vision Res 12: 717–733PubMedCrossRefGoogle Scholar
  57. Teague MR (1980) Image analysis via the general theory of moments. J Opt SocAmer70: 920–930Google Scholar
  58. Ulman LJ (1970) Computation of the Hadamard transform and the R-transform in ordered form. IEEE Comput Trans C-19:359–360Google Scholar
  59. Wagh MD (1975) R-Transform amplitude bounds and transform volume. J Inst Electronics and Telecom Engrs 21: 501–502Google Scholar
  60. Wagh MD, Kanetkar SV (1975a) A multiplexing theorem and generalization of R-transform. Intern J Comput C-24: 1120–1121Google Scholar
  61. Wagh MD, Kanetkar SV (1975b) A multiplexing theorem and generalization of R-transform. Intern J Comput Math 5: 163–171CrossRefGoogle Scholar
  62. Wagh MD, Kanetkar SV (1977) A class of translation invariant transforms. IEEE Trans on Acoustics, Speech and Signal Processing, ASSP-25: 203–205Google Scholar
  63. West G, Reitboeck HJ (1979) Zur ähnlichkeitsinvarianten Mustererkennung mittels der Fourier-MellinTransformation. Elektron Informationsverarb und Kybernetik 15: 507–512Google Scholar
  64. Wilson JTL, Singer W (1981) Simultaneous visual events show a long-range spatial interaction. Perception and Psych ophys 30: 107–113CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Herbert J. Reitboeck
    • 1
  1. 1.Angewandte Physik und BiophysikPhilipps-Universität MarburgMarburgFR Germany

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