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Representing three-dimensional objects by sets of activities of receptive fields

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Idealized models of receptive fields (RFs) can be used as building blocks for the creation of powerful distributed computation systems. The present report concentrates on investigating the utility of collections of RFs in representing three-dimensional objects under changing viewing conditions. The main requirement in this task is that the pattern of activity of RFs vary as little as possible when the object and the camera move relative to each other. I propose a method for representing objects by RF activities, based on the observation that, in the case of rotation around a fixed axis, differences of activities of RFs that are properly situated with respect to that axis remain invariant. Results of computational experiments suggest that a representation scheme based on this algorithm for the choice of stable pairs of RFs would perform consistently better than a scheme involving random sets of RFs. The proposed scheme may be useful under object or camera rotation, both for ideal lambertian objects, and for real-world objects such as human faces.

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  1. Aloimonos JY, Shulman D (1989) Integration of visual modules: an extension of the Marr paradigm. Academic Press, Boston

  2. Aloimonos JY, Weiss I, Bandopadhay A (1988) Active vision. Int J Comput Vision 2:333–356

  3. Amari S (1968) Invariant structures of signal and feature spaces in pattern recognition problems. RAAG Mem 4:553–566

  4. Amari S (1978) Feature spaces which admit and detect invariant signal transformations. In: Proc 4th Intl Conf on Pattern Recognition, Tokyo, pp 452–456

  5. Amari S, Maruyama M (1987) A theory on the determination of 3D motion and 3D structure from features. Spatial Vision 2:151–168

  6. Bishop PO, Coombs JS, Henry GH (1973) Receptive fields of simple cells in the cat striate cortex. J Physiol (Lond) 231:31–60

  7. Blinn JF (1988), Models of light reflection for computer-synthesized pictures. In: Richards W (eds) Natural computation. MIT Press, Cambridge, Mass, pp 214–223

  8. Bülthoff HH, Edelman S (1992) Psychophysical support for a 2-D view interpolation theory of object recognition. Proc Natl Acad Sci USA 89:60–64

  9. Dawis S, Shapley R, Kaplan E, Tranchina D (1984) The receptive field organization of X-cells in the cat: spatiotemporal coupling and asymmetry. Vision Res 24:549–564

  10. Edelman S (1992) Class similarity and viewpoint invariance in the recognition of 3D objects. CS-TR 92-17, Weizmann Institute of Science

  11. Edelman S, Reisfeld D, Yeshurun Y (1992) Learning to recognize faces from examples. In Sandini G (eds) Proceedings of the 2nd European Conference on Computer Vision. (Lecture notes in computer science, vol 588) Springer, Berlin Heidelberg New York, pp 787–791

  12. Harris CS (1980) Insight or out of sight? Two examples of perceptual plasticity in the human adult. In: Harris CS (eds) Visual Coding and Adaptability. Erlbaum, Hillsdale, NJ, pp 95–149

  13. Harris CS, Gibson AR (1968) Is orientation-specific color adaptation in human vision due to edge detectors, afterimages, or “dipoles”? Science 162:1506–1507

  14. Hubel DH, Wiesel TN (1959) Receptive fields of single neurons in the cat's striate cortex. J Physiol (Lond) 148:574–591

  15. Hurlbert A, Poggio T (1988) Synthesizing a color algorithm from examples. Science 239:482–485

  16. Intrator N (1992) Feature extraction using an unsupervised neural network. Neural Computation 4:98–107

  17. Intrator N, Cooper LN (1992) Objective function formulation of the BCM theory of visual cortical plasticity: statistical connections, stability conditions. Neural Networks 5:3–17

  18. Kanatani K (1990) Group-theoretical methods in image understanding. Springer, Berlin Heidelberg New York

  19. Katz LC, Callaway EM (1992) Development of local circuits in mammalian visual cortex. Annu Rev Neurosci 15:31–56

  20. Koenderink JJ, Doorn AJ van (1986) Optic flow. Vision Res 26:161–180

  21. Kuffler SW (1953) Discharge patterns and functional organization of mammalian retina. J Neurophysiol 16:37–68

  22. Malach R, Amir Y, Bartfeld E, Grinvald A (1992) Biocytin injections, guided by optical imaging, reveal relationships between functional architecture and intrinsic connections in monkey visual cortex. Soc Neurosci Abstr 18:364

  23. Mallot HA, Seelen W von, Giannakopoulos F (1990) Neural mapping and space-variant image processing. Neural Networks 3:16–25

  24. McCollough C (1965) Color adaptation of edge detectors in the human visual system. Science 149:1115–1116

  25. Moses Y, Edelman S, Ullman S (1993) Generalization across illumination and orientation changes in inverted and upright faces. CS-TR 93-14, Weizmann Institute of Science

  26. Mundy JL, Zisserman A (eds) (1992) Geometric invariance in computer vision. MIT Press, Cambridge, Mass

  27. Nishihara HK, Poggio T (1984) Stereo vision for robotics. In: Brady JM, Paul R (eds) Robotics research: the first international symposium. MIT Press, Cambridge, Mass, pp 489–505

  28. Poggio T (1990) A theory of how the brain might work. Cold Spring Harb Symp Quant Biol 55:899–910

  29. Poggio T, Edelman S (1990) A network that learns to recognize three-dimensional objects. Nature 343:263–266

  30. Poggio T, Girosi F (1990) Regularization algorithms for learning that are equivalent to multilayer networks. Science 247:978–982

  31. Poggio T, Fahle M Edelman S (1992) Fast perceptual learning in visual hyperacuity. Science 256:1018–1021

  32. Poggio T, Yang W, Torre V (1989) Optical flow: computational properties and net-works, biological and analog. In: Durbin R, Miall C, Mitchison G (eds) The computing neuron. Addison-Wesley, New York, pp 355–370

  33. Polat U, Sagi D (1992) Lateral interactions between spatial filters: excitation and inhibition affected by spatial configuration. Perception 21 [Suppl 2]:92

  34. Snippe HP, Koenderink JJ (1992) Discrimination thresholds for channel-coded systems. Biol Cybern 66:543–551

  35. Spitzer H, Hochstein S (1988) Complex-cell receptive field models. Prog Neurobiol 31:285–309

  36. Torrance KE, Sparrow EM (1966) Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces. J Opt Soc Am 56:916–925

  37. Ullman S (1979) The interpretation of visual motion. MIT Press, Cambridge, Mass

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Edelman, S. Representing three-dimensional objects by sets of activities of receptive fields. Biol. Cybern. 70, 37–45 (1993).

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  • Building Block
  • Representation Scheme
  • Receptive Field
  • Present Report
  • Computational Experiment