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Demonstrating Invariant Encoding of Shapes Using A Matching Judgment Protocol

1 Department of Psychology, University of Southern California, Los Angeles, CA 90089, USA
2 School of Psychology, The University of Auckland, Auckland 1010, New Zealand

Many theories have been offered to explain how the visual system registers, encodes, and recognizes the shape of an object. Some of the most influential assume that border lines and edges activate neurons in primary visual cortex, and these neurons encode the orientation, curvature, and linear extent of the shape as elemental cues. The present work challenges that assumption by showing that well-spaced dots can serve as effective shape cues. The experimental tasks drew on an inventory of unknown two-dimensional shapes, each being constructed as dots that marked the outer boundary, like an outline contour. A given shape was randomly picked from the inventory and was displayed only once as a target. The target shape was quickly followed by a low-density comparison shape that was derived from the target (matching) or from a different shape (non-matching). The respondent’s task was to provide a matching judgment, i.e., deciding whether the comparison shape was the “same” or “different.” Clear evidence of non-chance decisions was found even when the matching shapes displayed only 5% of the number of dots in the target shapes. Visual encoding mechanisms allow a shape to be identified when it is displayed at various locations on the retina, or with rotation or changes in size. A number of hierarchical network (connectionist) models have been developed to accomplish this encoding step, and these models appear especially credible because they are inspired by the anatomy and physiology of the visual system. The present work demonstrates above-chance translation, rotation, and size invariance for unknown shapes that were seen only once. This is clearly at odds with connectionist models that require extensive training before a shape can be identified irrespective of location, rotation, or size.
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Keywords shape encoding; translation invariance; rotation invariance; size invariance; model matching

Citation: Ernest Greene, Michael J. Hautus. Demonstrating Invariant Encoding of Shapes Using A Matching Judgment Protocol. AIMS Neuroscience, 2017, 4(3): 120-147. doi: 10.3934/Neuroscience.2017.3.120


  • 1. Kohler W (1938) Gestaltprobleme und Anfänge einer Gestalttheorie. Jahresbericht über der Gesellshaft Physiologie. Translated by: Ellis WD, A Source Book of Gestalt Psychology, London: Routledge & Kegan Paul: 58.
  • 2. Goldmeier E (1936/1972) Similarity in visually perceived forms. Psychol Issues 8: 1-135.
  • 3. Greene E (2007) Recognition of objects displayed with incomplete sets of discrete boundary dots. Percept Mot Skills 104: 1043-1059.
  • 4. Greene E, Visani A (2015) Recognition of letters displayed as briefly flashed dot patterns. Atten Percept Psychophys 77: 1955-1969.    
  • 5. Greene E (2016) Information persistence evaluated with low-density dot patterns. Acta Psychol 170: 215-225.
  • 6. Green DM, Swets JA (1966) Signal Detection Theory and Psychophysics. New York; Wiley.
  • 7. Hautus MJ, van Hout D, Lee HS (2009) Variants of A Not-A and 2AFC tests: Signal Detection Theory models. Food Qual Prefer 20: 222-229.    
  • 8. Macmillan NA, Creelman CD (2005) Detection Theory: A User's Guide, New Jersey: Lawrence Erlbaum.
  • 9. Hautus MJ (1995) Corrections for extreme proportions and their biasing effects on estimated values of d´. Behav Res Methods Instrum Comput 27: 46-51.    
  • 10. Miller J (1996) The sampling distribution of d'. Percept Psychophys 58: 65-72.    
  • 11. Hautus J (2012) SDT Assistant (version 1.0) [Software]. Available from http://hautus.org.
  • 12. Hautus MJ (1997) Calculating estimates of sensitivity from group data: pooled versus averaged estimators. Behav Res Methods Instrum Comput 29: 556-562.
  • 13. Hubel DH, Wiesel TN (1959) Receptive fields of single neurons in the cat's striate cortex. J Physiol 148: 574-591.
  • 14. Hubel DH, Wiesel TN (1968) Receptive fields and functional architecture of monkey striate cortex. J Physiol 195: 215-243.
  • 15. Selfridge OG (1959) Pandemonium: A Paradigm for Learning in the Mechanization of Thought Process, London; HM Stationary Office.
  • 16. Sutherland NS (1968) Outlines of a theory of visual pattern recognition in animals and man. Proc R Soc Lond B Biol Sci 171: 297-317.    
  • 17. Binford TO (1971) Visual perception by computer. Proc IEEE Conf Syst Control, Miami, FL.
  • 18. Barlow HB (1972) Single units and sensation: a neuron doctrine for perceptual psychology. Perception 1: 371-394.    
  • 19. Milner PM (1974) A model for visual shape recognition. Psychol Rev 81: 521-535.
  • 20. Palmer SE (1975) Visual perception and world knowledge: notes on a model of sensory-cognitive interaction. In: Norman DA, Rumelhart DE eds, Explorations in Cognitions, San Francisco: WH Freeman & Co.: 279-307.
  • 21. Marr D (1982) Vision: A Computational Investigation into the Human Representation and Processing of Information, New York: Freemen: 51-79.
  • 22. DeValois RL, Devalois KK (1991) Vernier acuity with stationary moving Gabors. Vision Res 31: 1619-1626.
  • 23. Panda R, Chatterji BN (1996) Gabor function: an efficient tool for digital image processing. IETE Tech Rev 13: 225-231.    
  • 24. Kohonen T, Oja E (1998) Visual feature analysis by the self-organizing maps. Neural Comput Appl 7: 273-286.
  • 25. Pettet MW, McKee SP, Grzywacz NM (1998) Constraints on long range interactions mediating contour detection. Vision Res 38: 865-879.    
  • 26. Pennefather PM, Chandna A, Kovacs I, et al. (1999) Contour detection threshold: repeatabililty and learning with 'contour cards.' Spat Vis 12: 257-266.    
  • 27. Taylor G, Hipp D, Moser A, et al. (2014) The development of contour processing: evidence from physiology and psychophysics. Front Psychol 5: e719
  • 28. Dong X, Chantlier MJ (2016) Perceptually motivated image features using contours. IEEE Trans Image Process 25: 5050-5062.
  • 29. Edelman S (1999) Representation and Recognition in Vision, MIT Press.
  • 30. Cooke T, Jakel F, Wallraven C, et al. (2007) Multimodal similarity and categorization of novel, three-dimensional objects. Neuropsychologia 45: 484-495.    
  • 31. Hayworth KJ (2012) Dynamically partitionable autoassociative networks as a solution to the neural binding problem. Front Comput Neurosci 6: e73.
  • 32. Rodriguez-Sanchez AJ, Tsotsos JK (2012) The roles of endstopped and curvature tuned computations in a hierarchical representation of 2D shape. PLoS ONE 7: e42058.    
  • 33. Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulus representation. Nature 376: 33-36.
  • 34. Hopfield JJ (1996) Transforming neural computations and representing time. Proc Nat Acad Sci 83: 15440-15444.
  • 35. Maass W (1997) Fast sigmoidal networks via spiking neurons. Neural Comput 9: 279-304.    
  • 36. McClelland JL (2013) Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review. Front Psychol 4: e503.
  • 37. Guan T, Wang Y, Duan L, et al. (2015) On-device mobile landmark recognition using binarized descriptor and multifeature fusion. ACM Trans Intell Syst Technol 7: e12.
  • 38. Wei B, Guan T, Duan L, et al. (2015) Wide area localization and tracking on camera phones for mobile segmented reality systems. Multimed Syst 21: 381-399.    
  • 39. Pan H, Guan T, Luo Y, et al. (2016) Dense 3D reconstruction combining depth and RGB information. Neurocomputing 175: 644-651.
  • 40. Ullman S (1976) Filling-in the gaps: the shape of subjective contours and a model for their generation. Biol Cybern 25: 1-6.
  • 41. Sha'ashua A, Ullman S (1988) Structural saliency: the detection of globally salient structures using a locally connected network. In: Proc 2nd Intern Conf Comput Vision, Clearwater FL: 321-327.
  • 42. Kellman PJ, Shipley TF (1991) A theory of visual interpolation in object rperception. Cogn Psychol 23: 141-221.    
  • 43. Shipley TF, Kellman PJ (1992) Strength of visual interpolation depends on the ratio of physically specified to total edge length. Percept Psychophys 52: 97-106.
  • 44. Cormen TH, Leherson CE, Rivest RL, et al. (2001) Single-source shortest paths and all pairs shortest paths. In: Introduction to Algorithms, MIT Press & McGraw-Hill: 580-642.
  • 45. Field DJ, Hayes A, Hess RF (1993) Contour integration by the human visual system: evidence for a local "association field." Vision Res 33: 173-193.
  • 46. Kwon TK, Agrawal K, Li Y, et al. (2016) Spatially-global integration of closed, fragmented contours by finding the shortest-path in a log-polar representation. Vision Res 126: 143-163.
  • 47. Sceniak MP, Hawken MJ, Shapley R (2001) Visual spatial characterization of Macaque V1 neurons. J Neurophysiol 85: 1873-1887.
  • 48. Bowers JS (2009) On the biological plausibility of grandmother cells: implications for neural network theories in psychology and neuroscience. Psychol Rev 116: 220-251.
  • 49. Greene E (2008) Additional evidence that contour attributes are not essential cues for object recognition. Behav Brain Funct 4: e26.
  • 50. Greene E (2016) How do we know whether three dots form an equilateral triangle? JSM Brain Sci 1: 1002.
  • 51. Lichtsteiner P, Posch C, Delbruck T (2008) A 128x128 120 dB 15 µs latency asynchronous temporal contrast vision sensor. IEEE J Solid-State Circuits 43: 566-576.    
  • 52. Robinson DA (1964) The mechanisms of human saccadic eye movement. J Physiol 174: 245-264.
  • 53. Zimmermann E, Lappe M (2016) Visual space constructed by saccadic motor maps. Front Human Neurosci 10: e225.
  • 54. McSorlely E, McCloy R, Williams L (2016) The concurrent programming of saccades. PLoS ONE 11: e0168724.    
  • 55. Bhutani N, Sengupta S, Basu D, et al. (2017) Parallel activation of prospective motor plans during visually-guided sequential saccades. Neurosci 45: 631-642.
  • 56. Feldman JA, Ballard DH (1982) Connectionist models and their properties. Cogn Sci 6: 205-254.    
  • 57. Fukushima K (1980) Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biol Cybern 36: 193-202.    
  • 58. Rolls ET (1992) Neurophysiological mechanisms underlying face processing within and beyond the temporal cortical visual areas. Phil Trans R Soc 335: 11-21.    
  • 59. Wallis G, Rolls ET (1997) Invariant face and object recognition in the visual system. Prog Neurobiol 51: 167-194.
  • 60. Riesenhuber M, Poggio T (2000) Models of object recognition. Nature Neurosci (S3): 1199-1204.
  • 61. Pasupathy A, Connor CE (2001) Shape representation in area V4: position-specific tuning for boundary conformation. J Neurophysiol 86: 2505-2519.
  • 62. Suzuki N, Hashimoto N, Kashimori Y, et al. (2004) A neural model of predictive recognition in form pathway of visual cortex. BioSystems 76: 33-42.    
  • 63. Pinto N, Cox DD, DeCarlo JJ (2008) Why is real-world visual object recognition hard? PLoS Comput Biol 4: e27.    
  • 64. Hancock PJB, Walton L, Mitchell G, et al. (2008) Segregation by onset asynchrony. J Vision 8: 1-21.
  • 65. Karplus I, Goren M, Algorn D (1982) A preliminary experimental analysis of predator face recognition by Chromis caenuleus (Pisces, Pomacentridae). Z Tierpsychol 58: 53-65.
  • 66. Siebeck UE, Parker AN, Sprenger D, et al. (2010) A species of reef fish that uses untraviolet patterns for covert face recognition. Curr Biol 20: 407-410.
  • 67. Karplus I, Katzenstein R, Goren M (2006) Predator recognition and social facilitation of predator avoidance in coral reef fish Dascyllus marginatus juveniles. Mar Ecol Prog Ser 319: 215-223.
  • 68. Siebeck UE, Litherland L, Wallis GM (2009) Shape learning and discrimination in reef fish. J Exp Biol 212: 2113-2119.
  • 69. Newport C, Wallis G, Reshitnyk Y, et al. (2016) Discrimination of human faces by archerfish (Toxotes catareus). Sci Rep 6: e27523.    
  • 70. Greschner M, Field GD, Li PH, et al. (2014) A polyaxonal amacrine cell population in the primate retina. J Neurosci 34: 3597-3606.    
  • 71. Greschner M, Heitman AK, Field GD, et al. (2016) Identification of a retinal circuit for recurrent suppression using indirect electrical imaging. Curr Biol 26: 1935-1942.    
  • 72. Greene E (2007) Retinal encoding of ultrabrief shape recognition cues. PLoS One 2: e871.
  • 73. Greene E (2016) Retinal encoding of shape boundaries. JSM Anat Physiol 1: 1002.


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Copyright Info: 2017, Ernest Greene, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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