Biological Cybernetics

, Volume 106, Issue 3, pp 177–189 | Cite as

A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model

  • George AzzopardiEmail author
  • Nicolai Petkov
Open Access
Original Paper


Simple cells in primary visual cortex are believed to extract local contour information from a visual scene. The 2D Gabor function (GF) model has gained particular popularity as a computational model of a simple cell. However, it short-cuts the LGN, it cannot reproduce a number of properties of real simple cells, and its effectiveness in contour detection tasks has never been compared with the effectiveness of alternative models. We propose a computational model that uses as afferent inputs the responses of model LGN cells with center–surround receptive fields (RFs) and we refer to it as a Combination of Receptive Fields (CORF) model. We use shifted gratings as test stimuli and simulated reverse correlation to explore the nature of the proposed model. We study its behavior regarding the effect of contrast on its response and orientation bandwidth as well as the effect of an orthogonal mask on the response to an optimally oriented stimulus. We also evaluate and compare the performances of the CORF and GF models regarding contour detection, using two public data sets of images of natural scenes with associated contour ground truths. The RF map of the proposed CORF model, determined with simulated reverse correlation, can be divided in elongated excitatory and inhibitory regions typical of simple cells. The modulated response to shifted gratings that this model shows is also characteristic of a simple cell. Furthermore, the CORF model exhibits cross orientation suppression, contrast invariant orientation tuning and response saturation. These properties are observed in real simple cells, but are not possessed by the GF model. The proposed CORF model outperforms the GF model in contour detection with high statistical confidence (RuG data set: p < 10−4, and Berkeley data set: p < 10−4). The proposed CORF model is more realistic than the GF model and is more effective in contour detection, which is assumed to be the primary biological role of simple cells.


Aligned receptive fields Computational model Contour detection Gabor function LGN Simple cell 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


  1. Albrecht DG, De Valois RL, Thorell LG (1980) Visual cortical-neurons—are bars or gratings the optimal stimuli. Science 207(4426): 88–90PubMedCrossRefGoogle Scholar
  2. Andrews BW, Pollen DA (1979) Relationship between spatial-frequency selectivity and receptive-field profile of simple cells. J Physiol 287: 163–176PubMedGoogle Scholar
  3. Azzopardi G, Petkov N (2012) Trainable COSFIRE filters for keypoint detection and pattern recognition. IEEE Trans Pattern Anal Mach Intell (to appear)Google Scholar
  4. Canny J (1986) A computational approach to edge-detection. IEEE Trans Pattern Anal Mach Intell 8(6): 679–698PubMedCrossRefGoogle Scholar
  5. Chung S, Ferster D (1998) Strength and orientation tuning of the thalamic input to simple cells revealed by electrically evoked cortical suppression. Neuron 20(6): 1177–1189PubMedCrossRefGoogle Scholar
  6. Croner LJ, Kaplan E (1995) Receptive-fields of P-ganglion and M-ganglion cells across the primate retina. Vis Res 35(1): 7–24PubMedCrossRefGoogle Scholar
  7. Daugman JG (1985) Uncertainty relation for resolution in space, spatial-frequency, and orientation optimized by two-dimensional visual cortical filters. J Opt Soc Am A 2(7): 1160–1169PubMedCrossRefGoogle Scholar
  8. de Boer R, Kuyper P (1968) Triggered correlation. IEEE Trans Bio-med Eng 15(3): 169–179CrossRefGoogle Scholar
  9. De Valois RL, Albrecht DG, Thorell LG (1978) Cortical cells: bar and edge detectors, or spatial frequency filters? In: Cool SJ, Smith I E L (eds) Frontiers in visual science, Springer-Verlag, Berlin, West Germany pp 544–556Google Scholar
  10. De Valois KK, De Valois RL, Yund EW (1979) Responses of striate cortex cells to grating and checkerboard patterns. J Physiol 291: 483–505PubMedGoogle Scholar
  11. De Valois RL, Yund EW, Hepler N (1982) The orientation and direction selectivity of cells in macaque visual-cortex. Vis Res 22(5): 531–544PubMedCrossRefGoogle Scholar
  12. DeAngelis GC, Ohzawa I, Freeman RD (1995) Receptive-field dynamics in the central visual pathways. Trends Neurosci 18(10): 451–458PubMedCrossRefGoogle Scholar
  13. DuBuf JMH (1993) Responses of simple cells—events, interferences, and ambiguities. Biol Cybernet 68(4): 321–333CrossRefGoogle Scholar
  14. Ferster D, Chung S, Wheat H (1996) Orientation selectivity of thalamic input to simple cells of cat visual cortex. Nature 380(6571): 249–252PubMedCrossRefGoogle Scholar
  15. Finn IM, Priebe NJ, Ferster D (2007) The emergence of contrast-invariant orientation tuning in simple cells of cat visual cortex. Neuron 54(1): 137–152PubMedCrossRefGoogle Scholar
  16. Gabor D (1946) Theory of communication. J Inst Electr Eng 93: 429–457Google Scholar
  17. Glezer VD, Tsherbach TA, Gauselman VE, Bondarko VM (1980) Linear and non-linear properties of simple and complex receptive-fields in area-17 of the cat visual-cortex—a model of the field. Biological Cybernetics 37(4): 195–208PubMedCrossRefGoogle Scholar
  18. Grigorescu C, Petkov N, Westenberg MA (2004) Contour and boundary detection improved by surround suppression of texture edges. Image Vis Comput 22(8): 609–622CrossRefGoogle Scholar
  19. Grigorescu C, Petkov N, Westenberg MA (2003) Contour detection based on nonclassical receptive field inhibition. IEEE Trans Image Process 12(7): 729–739PubMedCrossRefGoogle Scholar
  20. Heitger F (1995) Feature detection using suppression and enhancement. Communication Technology Laboratory, Swiss Federal Institute of Technology, Lausanne, Technical Report TR-163Google Scholar
  21. Hubel DH (1982) Exploration of the primary visual-cortex, 1955–78. Nature 299(5883): 515–524PubMedCrossRefGoogle Scholar
  22. Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in cats visual cortex. J Physiol 160(1):106–154PubMedGoogle Scholar
  23. Hubel DH, Wiesel TN (1974) Sequence regularity and geometry of orientation columns in monkey striate cortex. J Comp Neurol 158(3): 267–294PubMedCrossRefGoogle Scholar
  24. Irvin GE, Casagrande VA, Norton TT (1993) Center surround relationships of magnocellular, parvocellular, and koniocellular relay cells in primate lateral geniculate nucleus. Vis Neurosci 10(2): 363–373PubMedCrossRefGoogle Scholar
  25. Jones JP, Palmer LA (1987) An evaluation of the two-dimensional gabor filter model of simple receptive-fields in cat striate cortex. J Neurophysiol 58(6): 1233–1258PubMedGoogle Scholar
  26. Kovesi P (1999) Image features from phase congruency. Videre 1(3)Google Scholar
  27. Kulikowski JJ, Bishop PO (1981) Fourier-analysis and spatial representation in the visual-cortex. Experientia 37(2): 160–163PubMedCrossRefGoogle Scholar
  28. Macleod IDG, Rosenfeld A (1974) Visibility of gratings—spatial frequency channels or bar-detecting units. Vis Res 14(10): 909–915PubMedCrossRefGoogle Scholar
  29. Maffei L, Morrone C, Pirchio M, Sandini G (1979) Responses of visual cortical-cells to periodic and non-periodic stimuli. J Physiol 296: 27–47PubMedGoogle Scholar
  30. Marcelja S (1980) Mathematical-description of the responses of simple cortical-cells. J Opt Soc Am 70(11): 1297–1300PubMedCrossRefGoogle Scholar
  31. Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th international conference computer vision, vol 2, pp 416–423Google Scholar
  32. Martin DR, Fowlkes CC, Malik J (2004) Learning to detect natural image boundaries using local brightness, color, and texture cues. IEEE Trans Pattern Anal Mach Intell 26(5): 530–549PubMedCrossRefGoogle Scholar
  33. Mehrotra R, Namuduri KR, Ranganathan N (1992) Gabor filter-based edge-detection. Pattern Recogn 25(12): 1479–1494CrossRefGoogle Scholar
  34. Morrone MC, Burr DC (1988) Feature detection in human-vision—a phase-dependent energy-model. Proc R Soc Lond B 235(1280): 221–245PubMedCrossRefGoogle Scholar
  35. Morrone MC, Owens RA (1987) Feature detection from local energy. Pattern Recogn Lett 6(5): 303–313CrossRefGoogle Scholar
  36. Movshon JA, Thompson ID, Tolhurst DJ (1978a) Receptive-field organization of complex cells in cats striate cortex. J Physiol 283: 79–99PubMedGoogle Scholar
  37. Petkov N (1995) Biologically motivated computationally intensive approaches to image pattern-recognition. Future Gener Comput Syst 11(4–5): 451–465CrossRefGoogle Scholar
  38. Priebe NJ, Ferster D (2006) Mechanisms underlying cross-orientation suppression in cat visual cortex. Nat Neurosci 9(4): 552–561PubMedCrossRefGoogle Scholar
  39. Reid RC, Alonso JM (1995) Specificity of monosynaptic connections from thalamus to visual-cortex. Nature 378(6554): 281–284PubMedCrossRefGoogle Scholar
  40. Ringach D, Shapley R (2004) Reverse correlation in neurophysiology. Cogn Sci 28(2): 147–166CrossRefGoogle Scholar
  41. Rodieck RW (1965) Quantitative analysis of cat retinal ganglion cell response to visual stimuli. Vision Res 5(11): 583–601PubMedCrossRefGoogle Scholar
  42. Rosenthaler L, Heitger F, Kubler O, von der Heydt R (1992) Detection of general edges and keypoints. In: Sandini G (ed) Proceedings of the European Conference Computer Vision (ECCV92), pp 78–86Google Scholar
  43. Sclar G, Freeman R (1982) Orientation selectivity in the cats striate cortex is invariant with stimulus contrast. Exp Brain Res 46(3): 457–461PubMedCrossRefGoogle Scholar
  44. Sclar G, Maunsell JHR, Lennie P (1990) Coding of image-contrast in central visual pathways of the macaque moneky. Vision Res 30(1): 1–10PubMedCrossRefGoogle Scholar
  45. Shin MC, Goldgof D, Bowyer KW (1998) An objective comparison methodology of edge detection algorithms using a structure from motion task. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1998 (Cat. No.98CB36231), pp 190–195Google Scholar
  46. Sonka M, Hlavac V, Boyle R (1999) Image processing, analysis, and machine vision. Brooks/Cole, Pacific GroveGoogle Scholar
  47. Stork DG, Wilson HR (1990) Do gabor functions provide appropriate descriptions of visual cortical receptive-fields. J Opt Soc Am A 7(8): 1362–1373PubMedCrossRefGoogle Scholar
  48. Tyler CW (1978) Selectivity for spatial-frequency and bar width in cat visual-cortex. Vision Res 18(1): 121–122PubMedCrossRefGoogle Scholar
  49. VonDer Heydt R (1987) Approaches to visual cortical function. Rev Physiol Biochem Pharmacol 108: 69–150CrossRefGoogle Scholar
  50. Xu XM, Ichida JM, Allison JD, Boyd JD, Bonds AB, Casagrande V (2001) A comparison of koniocellular, magnocellular and parvocellular receptive field properties in the lateral geniculate nucleus of the owl monkey (Aotus trivirgatus). J Physiol 531(1): 203–218PubMedCrossRefGoogle Scholar
  51. Xu XM, Bonds AB, Casagrande VA (2002) Modeling receptive-field structure of koniocellular, magnocellular, and parvocellular LGN cells in the owl monkey (Aotus trivigatus). Visual Neurosci 19(6): 703–711CrossRefGoogle Scholar
  52. Zhang YJ (1996) A survey on evaluation methods for image segmentation. Pattern Recogn 29(8): 1335–1346CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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