The café wall pattern is composed of rows of alternating light and dark tiles, and alternate rows are shifted by one fourth of a cycle. The rows of tiles are separated by narrow horizontal mortar lines whose luminance is between those of the dark and the light tiles. Although the mortar lines are physically parallel, they are perceived to be tilted, which is known as the café wall illusion. In this study, an energy-based model for encoding orientation is implemented in order to estimate the strength of the café wall illusion, and it is shown that the estimated orientation depends on the spatial frequency to which each orientation-encoding unit is tuned. The estimation of mortar line orientation from an orientationencoding unit tuned to a lower spatial frequency was greater than that from a unit tuned to a higher spatial frequency. It is assumed that the perceived mortar line orientation is the result of an integration of responses from the orientation-encoding units tuned to various spatial frequencies. This leads to the prediction that under viewing conditions in which responses from orientation-encoding units tuned to a higher spatial frequency are presumably weakened, the strength of the café wall illusion increases. In agreement with this prediction, it is shown that the café wall illusion is stronger when the café wall image is presented at the periphery or is observed under low luminance levels. On the other hand, the weighted averaging of the estimated mortar orientations across spatial frequencies overestimates the perceived orientation of the mortar lines. This suggests that the final percept of the café wall illusion could be determined by some kind of nonlinear interaction, such as an inhibitory interaction, between orientation-encoding units.
Adelson, E. H., &Bergen, J. R. (1985). Spatiotemporal energy models for the perception of motion.Journal of the Optical Society of America A,2, 284–299.
Adelson, E. H., &Bergen, J. R. (1991). The plenoptic function and the elements of early vision. In M. S. Landy & J. A. Movshon (Eds.),Computational models of visual processing (pp. 3–20). Cambridge, MA: MIT Press.
Anzai, A., Ohzawa, I., &Freeman, R. D. (1999). Neural mechanisms for processing binocular information: II. Complex cells.Journal of Neurophysiology,82, 909–924.
Barten, P. G. J. (1999).Contrast sensitivity of the human eye and its effects on image quality. Bellingham, WA: SPIE Optical Engineering Press.
Bauman, L. A., &Bonds, A. B. (1991). Inhibitory refinement of spatial frequency selectivity in single cells of the cat striate cortex.Vision Research,31, 933–944.
Bennett, P. J., &Banks, M. S. (1987). Sensitivity loss in odd- symmetric mechanisms and phase anomalies in peripheral vision.Nature,326, 873–876.
Bergen, J. R., &Landy, M. S. (1991). Computational modeling of visual texture segregation. In M. S. Landy & J. A. Movshon (Eds.),Computational models of visual processing (pp. 253–271). Cambridge, MA: MIT Press.
Blakemore, C., &Campbell, F. W. (1969). On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images.Journal of Physiology,203, 237–260.
Blakeslee, B., &McCourt, M. E. (2004). A unified theory of brightness contrast and assimilation incorporating oriented multiscale spa tial filtering and contrast normalization.Vision Research,44, 2483–2503.
Campbell, F. W., &Kulikowski, J. J. (1966). Orientation selectivity of the human visual system.Journal of Physiology,187, 437–445.
Carandini, M., Heeger, D. J., &Movshon, J. A. (1999). Linearity and gain control in V1 simple cells. In E. G. Jones & P. S. Ulinski (Eds.),Cerebral cortex: Vol. XII. Cortical model (pp. 401–443). New York: Plenum.
Daugman, J. G. (1985). Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.Journal of the Optical Society of America A,2, 1160–1169.
DeAngelis, G. C., &Anzai, A. (2004). A modern view of the classical receptive field: Linear and nonlinear spatiotemporal processing by V1 neurons. In L. M. Chalupa & J. S. Werner (Eds.),The visual neurosciences (pp. 704–719). Cambridge, MA: MIT Press.
DeAngelis, G. C., Ghose, G. M., Ohzawa, I., &Freeman, R. D. (1999). Functional micro-organization of primary visual cortex: Receptive field analysis of nearby neurons.Journal of Neuroscience,19, 4046–4064.
De Valois, K. K. (1977). Spatial frequency adaptation can enhance contrast sensitivity.Vision Research,17, 1057–1065.
De Valois, K. K., &Tootell, R. B. H. (1983). Spatial-frequency-specific inhibition in cat striate cortex cells.Journal of Physiology,291, 483–505.
De Valois, R. L., Albrecht, D. G., &Thorell, L. G. (1982). Spatial frequency selectivity of cells in macaque visual cortex.Vision Research,22, 545–559.
De Valois, R. L., &De Valois, K. K. (1988).Spatial vision. New York: Oxford University Press.
De Valois, R. L., Morgan, H., &Snodderly, D. M. (1974). Psychophysical studies of monkey vision: 3. Spatial luminance contrast sensitivity tests of macaque and human observers.Vision Research,14, 75–81.
Earle, D. C., &Maskell, S. J. (1993). Fraser cords and reversal of the café wall illusion.Perception,22, 383–390.
Emerson, R. C., Bergen, J. R., &Adelson, E. H. (1992). Directionally selective complex cells and the computation of motion energy in cat visual cortex.Vision Research,32, 203–218.
Field, D. J., &Tolhurst, D. J. (1986). The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex.Proceedings of the Royal Society of London: Series B,228, 379–400.
Fraser, J. (1908). A new illusion of visual direction.British Journal of Psychology,2, 307–320.
Freeman, W. T., &Adelson, E. H. (1991). The design and use of steerable filters.IEEE Transactions on Pattern Analysis & Machine Intelligence,13, 891–906.
Georgeson, M. A., &Meese, T. S. (1997). Perception of stationary plaids: The role of spatial filters in edge analysis.Vision Research,37, 3255–3271.
Georgeson, M. A., &Sullivan, G. D. (1975). Contrast constancy: Deblurring in human vision by spatial frequency channels.Journal of Physiology,252, 627–656.
Gorea, A., &Papathomas, T. V. (1991). Texture segregation by chromatic and achromatic visual pathways: An analogy with motion processing.Journal of the Optical Society of America A,8, 386–393.
Gray, C. M., König, P., Engel, A. K., &Singer, W. (1989). Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties.Nature,338, 334–337.
Gregory, R. L. (1968). Visual illusions.Scientific American,219, 66–76.
Gregory, R. L. (1972). [Editorial].Perception,1, 492.
Gregory, R. L., &Heard, P. F. (1979). Border locking and the café wall illusion.Perception,8, 365–380.
Haig, N. D. (1989). A new visual illusion, and its mechanism.Perception,18, 333–345.
Heeger, D. J. (1992). Normalization of cell responses in cat striate cortex.Visual Neuroscience,9, 181–197.
Hood, D. C., &Finkelstein, M. A. (1986). Visual sensitivity. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.),Handbook of perception and human performance (Vol. 1, pp. 1–66). New York: Wiley.
Hubel, D. H., &Wiesel, T. (1962). Receptive fields, binocular interaction, and functional architecture in the cat’s visual cortex.Journal of Physiology,160, 106–154.
Kelly, D. H. (1984). Retinal inhomogeneity: I. Spatiotemporal contrast sensitivity.Journal of the Optical Society of America A,1, 107–113.
Kruizinga, P., &Petkov, N. (1999). Nonlinear operator for oriented texture.IEEE Transactions on Image Processing,8, 1395–1407.
Levitt, H. (1971). Transformed up—down methods in psychoacoustics.Journal of the Acoustical Society of America,49, 467–477.
Lulich, D. P., &Stevens, K. A. (1989). Differential contributions of circular and elongated spatial filters to the café wall illusion.Biological Cybernetics,61, 427–435.
Malik, J., &Perona, P. (1990). Preattentive texture discrimination with early vision mechanisms.Journal of the Optical Society of America A,7, 923–932.
Marr, D. (1982).Vision: A Computational investigation into the human representation and processing of visual information. San Francisco: Freeman.
Marr, D., &Hildreth, E. (1980). Theory of edge detection.Proceedings of the Royal Society of London: Series B,207, 187–217.
Morgan,M. J., &Casco, C. (1990). Spatial filtering and spatial primitives in early vision: An explanation of the Zöllner—Judd class of geometrical illusion.Proceedings of the Royal Society of London: Series B,242, 1–10.
Morgan, M. J., &Hotopf, H. N. (1989). Perceived diagonals in grids and lattices.Vision Research,29, 1005–1015.
Morgan, M. J., &Moulden, B. (1986). The Münsterberg figure and twisted cords.Vision Research,26, 1793–1800.
Morrone, M. C., &Burr, D. C. (1988). Feature detection in human vision: A phase dependent energy model.Proceedings of the Royal Society of London: Series B,235, 221–245.
Münsterberg, H. (1897). Die verschobene Schachbrettfigur.Zeitschrift für Psychologie,5, 185–188.
Nachmias, J., Sansbury, R., Vassilev, A., &Weber, A. (1973). Adaptation to square-wave gratings: In search of the elusive third harmonic.Vision Research,13, 1335–1342.
Nestares, O., &Heeger, D. J. (1997). Modeling the apparent frequencyspecific suppression in simple cell responses.Vision Research,37, 1535–1543.
Ohzawa, I., DeAngelis, G. C., &Freeman, R. D. (1990). Stereoscopic depth discrimination in the visual cortex: Neurons ideally suited as disparity detectors.Science,249, 1037–1041.
Peli, E. (2002). Feature detection algorithm based on a visual system model.Proceedings of the IEEE,90, 78–93.
Petkov, N., &Kruizinga, P. (1997). Computational models of visual neurons specialized in the detection of periodic and aperiodic oriented visual stimuli: Bar and grating cells.Biological Cybernetics,76, 83–96.
Phillips, G. C., &Wilson, H. R. (1984). Orientation bandwidths of spatial mechanisms measured by masking.Journal of the Optical Society of America A,1, 226–232.
Pollen, D. A., &Ronner, S. F. (1983). Visual cortical neurons as localized spatial frequency filters.IEEE Transactions on Systems, Man, & Cybernetics,13, 907–916.
Robson, J. G., &Graham, N. (1981). Probability summation and regional variation in contrast sensitivity across the visual field.Vision Research,21, 409–418.
Rock, I. (1986). The description and analysis of object and event perception. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.),Handbook of perception and human performance (Vol. 2, pp. 33–71). New York: Wiley.
Rovamo, J., Virsu, V., &Näsänen, R. (1978). Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision.Nature,271, 54–56.
Savage, G. L., &Banks, M. S. (1992). Scotopic visual efficiency: Constraints by optics, receptor properties and rod pooling.Vision Research,32, 645–656.
Stabell, B., &Stabell, U. (1981). Absolute spectral sensitivity at different eccentricities.Journal of the Optical Society of America,71, 836–840.
Stuart, G. W., &Bossomaier, T. R. J. (1992). Cooperative representation of visual borders.Perception,21, 185–194.
Takeuchi, T. (1997). The motion analogue of the café wall illusion.Perception,26, 569–584.
Tanner, P. P., Jolicoeur, P., Cowan, W. B., Booth, K., &Fishman, F. D. (1989). Antialiasing: A technique for smoothing jagged lines on a computer graphics image—an implementation on the Amiga.Behavior Research Methods, Instruments, & Computers,21, 59–66.
Tolhurst, D. J. (1972). Adaptation to square-wave gratings: Inhibition between spatial frequency channels in the human visual system.Journal of Physiology,226, 231–248.
Tyler, C. W., &Nakayama, K. (1984). Size interactions in the perception of orientation. In L. Spillman & B. R. Woten (Eds.),Sensory experience and perception (pp. 529–546). Hillsdale, NJ: Erlbaum.
van Nes, F. L., Koenderink, J. J., Nas, H., &Bouman, M. A. (1967). Spatiotemporal modulation transfer in the human eye.Journal of the Optical Society of America,57, 1082–1088.
Watson, A. B., &Ahumada, A. (1985). Model of human visual motion sensing.Journal of the Optical Society of America A,2, 322–341.
Watt, R. J. (1990).Visual processing: Computational, psychophysical and cognitive research. London: Psychology Press.
Watt, R. J., &Morgan, M. J. (1985). A theory of the primitive spatial code in human vision.Vision Research,37, 127–142.
Wilson, H. R., Ferrera, V. P., &Yo, C. (1992). A psychophysically motivated model for two-dimensional motion perception.Visual Neuroscience,9, 79–97.
Wilson, H. R., &Giese, S. (1977). Threshold visibility of frequency gradient patterns.Vision Research,17, 1177–1190.
Wilson, H. R., McFarlane, D. K., &Phillips, G. C. (1983). Spatial frequency tuning of orientation selective units estimated by oblique masking.Vision Research,23, 873–882.
Wilson, H. R., &Wilkinson, F. (2004). Spatial channels in vision and spatial pooling. In L. M. Chalupa & J. S. Werner (Eds.),The visual neurosciences (pp. 1060–1068). Cambridge, MA: MIT Press.
Rights and permissions
About this article
Cite this article
Takeuchi, T. The effect of eccentricity and the adapting level on the café wall illusion. Perception & Psychophysics 67, 1113–1127 (2005). https://doi.org/10.3758/BF03193545
- Spatial Frequency
- Gabor Filter
- Wall Image
- Average Luminance
- Orientation Energy