The Hermann grid illusion revisited
Peter H Schiller, Christina E Carvey
Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; e-mail: firstname.lastname@example.org Received 12 October 2004, in revised form 12 January 2005; published online 23 September 2005 Abstract. The Hermann grid illusion consists of smudges perceived at the intersections of a white grid presented on a black background. In 1960 the effect was first explained by a theory advanced by Baumgartner suggesting the illusory effect is due to differences in the discharge characteristics of retinal ganglion cells when their receptive fields fall along the intersections versus when they fall along non-intersecting regions of the grid. Since then, others have claimed that this theory might not be adequate, suggesting that a model based on cortical mechanisms is necessary [Lingelbach et al, 1985 Perception 14(1) A7; Spillmann, 1994 Perception 23 691 ^ 708; Geier et al, 2004 Perception 33 Supplement, 53; Westheimer, 2004 Vision Research 44 2457 ^ 2465]. We present in this paper the following evidence to show that the retinal ganglion cell theory is untenable: (i) varying the makeup of the grid in a manner that does not materially affect the putative differential responses of the ganglion cells can reduce or eliminate the illusory effect; (ii) varying the grid such as to affect the putative differential responses of the ganglion cells does not eliminate the illusory effect; and (iii) the actual spatial layout of the retinal ganglion cell receptive fields is other than that assumed by the theory. To account for the Hermann grid illusion we propose an alternative theory according to which the illusory effect is brought about by the manner in which S1 type simple cells (as defined by Schiller et al, 1976 Journal of Neurophysiology 39 1320 ^ 1333) in primary visual cortex respond to the grid. This theory adequately handles many of the facts delineated in this paper.
1 Introduction The Hermann grid illusion (1870) in its best-known form consists of intersecting vertical and horizontal white bars superimposed on a black background, thereby forming an array of evenly spaced black squares. At the intersection of the bars, ghostly gray smudges are perceived comprising the illusion. The grid in this form is displayed in figure 1a. The smudges are seen everywhere except at the center of gaze. In figure 1b, the grid is displayed in reverse contrast; in this case white smudges are perceived at the intersections. Over the years, the Hermann grid illusion has received considerable attention (for examples see Hering 1920; Baumgartner 1960; Spillmann and Levine 1971; Spillmann 1994; Ninio and Stevens 2000; De Lafuente and Ruiz 2004). Interest in the illusion was heightened when a clever hypothesis was advanced to explain the perception of the phantasmal smudges (Baumgartner 1960). We shall refer to this hypothesis as the retinal ganglion cell theory. As cited in several publications, the theory is laid out in figures 1c and 1d (Wolfe 1984; Sekuler and Blake 1994; Spillmann 1994). The explanation suggested is based on the findings made by neurophysiologists demonstrating that retinal ganglion cells have antagonistic center/surround organization (Kuffler 1953; Werblin and Dowling 1969; Schiller 1996). Consequently, when the grid consists of black squares and white bars, an ON-center retinal ganglion cell responds much more vigorously to a small bright spot placed into its receptive field center than to a large bright spot that activates both the center and the surround of the receptive field. The argument advanced was that smaller responses are elicited in the ON-center retinal ganglion cells whose receptive field centers fall into the intersections of the white bars than in cells whose receptive fields fall along non-intersecting regions of the bars.