Abstract

Perceptual filling-in is the phenomenon where visual information is perceived although information is not physically present. For instance, the blind spot, which corresponds to the retinal location where there are no photoreceptor cells to capture the visual signals, is filled-in by the surrounding visual signals. The neural mechanism for such immediate filling-in of surfaces is unclear. By means of computational modeling, we show that surround inhibition produces rebound or after-discharge spiking in neurons that otherwise do not receive sensory information. The behavior of rebound spiking mimics the immediate surface filling-in illusion observed at the blind spot and also reproduces the filling-in of an empty object after a background flash, like in the color dove illusion. In conclusion, we propose rebound spiking as a possible neural mechanism for surface filling-in.

INTRODUCTION

The blind spot is the region in the visual field that corresponds to the optic disk where the optic nerve leaves the retina. At this location, there are no light-detecting photoreceptor cells to capture the visual events, and consequently this part of the visual field is not perceived. Yet we do not see a hole in our visual scene when we look with one eye because the location of the blind spot is filled-in by the surrounding visual information (see Figure 1A). This is shown by neurophysiological reports that describe neural responses related to filling-in at the blind spot in the early visual cortex (Matsumoto & Komatsu, 2005; Komatsu, Kinoshita, & Murakami, 2000, 2002; Fiorani, Rosa, Gattas, & Rocha-Miranda, 1992), which are consistent with neural descriptions of other forms of surface filling-in early visual cortex (Huang & Paradiso, 2008; MacEvoy, Kim, & Paradiso, 1998; De Weerd, Gattass, Desimone, & Ungerleider, 1995).

Figure 1. 

Perceptual filling-in and model architecture. (A) A surface (input) is perceived although at some retinal parts there are no sensory receptors. The blind spot region is filled-in by the surrounding visual information so that cortical neurons whose receptive field locations correspond to the blind spot region respond to the surface stimulus. (B) The model consists of two neural layers, which are unidirectional connected. All layers receive point-to-point (retinotopic) excitatory input (black arrow). The first neural layer receives sensory input. Neurons in the second layer also receive inhibitory input from all preceding neurons (gray shading).

Figure 1. 

Perceptual filling-in and model architecture. (A) A surface (input) is perceived although at some retinal parts there are no sensory receptors. The blind spot region is filled-in by the surrounding visual information so that cortical neurons whose receptive field locations correspond to the blind spot region respond to the surface stimulus. (B) The model consists of two neural layers, which are unidirectional connected. All layers receive point-to-point (retinotopic) excitatory input (black arrow). The first neural layer receives sensory input. Neurons in the second layer also receive inhibitory input from all preceding neurons (gray shading).

The neural mechanisms for filling-in of are still a matter of debate. Two different theories have been put forward to explain the filling-in completion phenomenon. One theory postulates that spreading of neural activity in early visual areas is the basis for filling-in of visual information (Pessoa, Thompson, & Noe, 1998; Ramachandran & Gregory, 1991). This theory is based on the assumption that cells at contrast borders spread their activity to surrounding cells. In such a case, filling-in is accomplished by the dense network of horizontal connections that exist in the visual cortex. Horizontal connections have slow conduction velocities (0.1–0.2 m/sec; Angelucci & Bressloff, 2006) and may explain slow surface filling-in processes but they are probably too slow to explain the rather immediate surface filling-in at the blind spot (see Komatsu, 2006). The other hypothesis, the cognitive or symbolic filling-in theory, postulates that blind regions are ignored and object representation is realized at high cortical level on the basis of contrast information from lower areas (Pessoa et al., 1998). Feedback projections from these higher areas have large axonal termination fields in the early visual areas and may so provide sensory information to neurons in the lower areas located at the blind spot region. However, it has been shown that feedback has a role in modulating stimulus-evoked responses and does not activate otherwise silent neurons (Ekstrom, Roelfsema, Arsenault, Bonmassar, & Vanduffel, 2008). This indicates that cortical neurons at the blind spot region need to be activated, presumably by feed-forward connections.

How can retinal signals be effective in activating cells in early cortical areas that do not receive feed-forward excitatory projections? The excitatory retinal information is accompanied by inhibitory signals. Besides the global influence, inhibition is robust, fast, and prominent in retina, LGN, and visual cortex (Alitto & Usrey, 2008; Solomon, Lee, & Sun, 2006; Blitz & Regehr, 2005). It is well known that strong inhibition may cause rebound excitation at the end of the hyperpolarized period. Rebound or paradoxical excitation is a biophysical feature of neurons in which, following a period of strong hyperpolarization below the resting membrane potential, the membrane potential briefly rebounds to a more depolarized level resulting in firing spikes. Rebound spiking is thus triggered by inhibition and not by direct sensory activation. After-discharges may also be evoked by rebounds through inhibitory networks (Macknik & Martinez-Conde, 2004; Macknik & Livingstone, 1998). Here we prefer to use the term rebound spikes instead of after-discharges (Adrian & Matthews, 1927) because in our study, neurons become active (rebound) after the end of suppression rather than continue firing spikes after removal of the receptive field stimulus.

In the visual system, rebound spiking is observed in the retina (Margolis & Detwiler, 2007; Mitra & Miller, 2007a, 2007b), LGN (Bright, Aller, & Brickley, 2007; Zhu & Lo, 1996; Mastronarde, 1987), and visual cortex (Moliadze, Zhao, Eysel, & Funke, 2003). In the retina amacrine cells may inhibit ganglion cells over a large region causing rebound spiking in these cells (see Mitra & Miller, 2007a), and in the LGN, reticular cells may evoke rebound burst in relay cells (Destexhe & Sejnowski, 2002). Hence, strong, global inhibition, and rebound spiking are prominent in early visual structures. Therefore, although it has been argued that rebound activity may not represent visual information (Buzsaki, 2006), we consider the possibility that rebound activity induced by widespread suppression can be an alternative explanation for surface filling-in.

To test this idea, we used computer simulations of a neural network model composed of biologically plausible spiking neurons (Izhikevich, 2003) that permit to investigate such dynamic network behavior. Our results show that inhibition produced rebound spiking in neurons corresponding to the blind spot after surface stimulation. Surrounding cells also responded to the surface stimulus, although they received the same inhibitory input as the cells at the blind spot. The strength and onset latency of the rebound responses were similar to the ones of the stimulus evoked response, which agrees with complete and immediate perceptual filling-in of the blind spot (Komatsu, 2006; Ramachandran & Gregory, 1991). Finally, our model can explain the immediate filling-in of an empty object at the normal visual field location at the end of a background color flash, as happens in the color dove illusion. So we propose rebound spiking as an alternative neural mechanism for some types of surface filling-in.

METHODS

Model Architecture and Inputs

The model is composed of two layers, each containing two arrays of 64 × 64 units of neurons of the Izhikevich type (Izhikevich, 2003; Figure 1B). Each layer corresponds to a visual region. We consider neurons in the first layer as retinal ganglion cells, which transform continuous or graded input into spike activity. In this layer, the region of the optic nerve corresponding to the blind spot was modeled by a center region (16 × 16) void of neuronal cells. For the color dove illusion, the center part represented the location of the empty object and contained neurons like in the normal visual field. The second layer may correspond to the LGN or V1. Neurons in the first layer receive surface input, which is an array of 64 × 64 pixels. The pixel values of the input array are 1 and correspond to the preference of a single visual feature, like direction of motion or color. For the color dove illusion, the pixel values were set to 0 for the background and object region.

Feed-forward Connections

The excitatory feed-forward projections from the input layer to the first neural layer and from the first to the second neural layer are retinotopic (point-to-point connections), where pixel/neuron Nij in the one layer solely connects to neuron Nij in the next layer (Figure 1B). Thus, the excitatory part of a neuron's receptive field has size one. Neurons in the first neural layer do not receive inhibitory signals from the surface stimulus input. Neurons in the second layer receive inhibition from all neurons located in the preceding layer. Thus, inhibition is global. Inhibition is achieved by assigning negative weights to the connections. Neither intralaminar connections, that is, horizontal connections between neurons within a layer, nor feedback connections, that is, connections from the second neural layer to the first neural layer, are included in the network architecture.

Neuronal Cell Type

Hodgkin–Huxley models are too slow for network operations, and integrate-and-fire models are unrealistically simple and incapable of producing rich spiking and bursting dynamics exhibited by cortical neurons. We opted to use the spiking neurons of Izhikevich (2003). These neurons combine the biologically plausibility of Hodgkin–Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons and are capable of producing rich firing patterns exhibited by real biological neurons.

Model Dynamics

Cell dynamics is described by the “simple” spiking model of Izhikevich (2003) (Equations 1 and 2)
formula
supplemented with the after-spike reset rule
formula
The v, u, I, and t are dimensionless versions of membrane voltage, recovery variable, current intensity, and time. Further, a is a time scale, b measures the recovery sensitivity, c is the reset value for v, and d is the height of the reset jump for u. A capacitance factor C was chosen to be 1 and therefore omitted (Izhikevich, 2003). For all our simulations, a = 0.02, b = 0.25, c = −55, d = 0.05, and vsp, = 30. When dimensions are reintroduced, voltages are read in millivolts and time in milliseconds. These values correspond to the phasic bursting type of the Izhikevich neuron (Izhikevich, 2003). We choose the neurons to be phasic bursting because of the importance of bursts in sensory processing (Swadlow & Gusev, 2001). Spike bursts report the beginning of the stimulation and can transmit the saliency of the input because the effect of a burst on the postsynaptic neuron is stronger than the effect of a single spike, and bursts are needed to overcome the synaptic transmission failure and reduce neuronal noise.
As initial conditions at t0 = 0, we set
formula
for all the positions in our arrays (because we deal with two-dimensional objects, Equations 1 and 2 are actually meant for vvij, uuij, IIij, i,j = 1,…, N, and Equation 3 is in fact applied to vij, uij, and ∀ij. We used the Euler or Izhikevich method with Δt = 0.20 msec. The input current I in Equation 1 is the result of summing different matrix contributions of the form
formula
where “exc” stands for “excitatory,” “inh” for “inhibitory,” and i,j are spatial indices. Further, for neural layers,
formula
F is either the two-dimensional figure itself or the binary array defined by the presence of spikes, that is, with ones where Equation 2 is satisfied and zeros elsewhere. The 1N × N symbol denotes an N × N matrix containing just ones. Because excitatory receptive fields have size one, excitatory signals are point-by-point (retinotopic) copies of F itself, multiplied by the corresponding weight. The inhibitory part, whose associate receptive field has the same size as F, produces a spatially constant term—hence, the 1N × N matrix—which is proportional to the normalized sum of all the F coefficients times the inhibitory weight. Alternatively, we used a receptive field with size of 64 × 64. In our design, the employed weights are ωexc = 1, ωinh = 0 for the stimulus input to neural Layer 1 and ωexc = 2000 (1000), ωinh = −1800 (−500) for the signals from neural Layer 1 to neural Layer 2 in the blind spot (color dove) experiment.

RESULTS

Neurons in the first layer receiving the continuous input from the surface stimulus responded with a transient burst of six action potentials after the onset of a surface stimulus. Subsequently, the corresponding, that is, at the same retinotopic location, Layer 2 neurons responded with a similar spike burst (Figure 2). Thus, the global inhibition that all Layer 2 neurons received did not annul the excitatory drive of the feed-forward connections from Layer 1 neurons.

Figure 2. 

Neural responses to surface stimulus. (A) Model output and firing rates of neurons located at the blind spot region and at the surrounding region. The light-dark squares represent the matrix of neurons of the model. The white center square in Layer 1 represents the blind spot, and the dotted white lines in Layer 2 delineate this region. The gray circles depict neurons and the arrows originating from them point to the corresponding spike responses. (B) The spike times of all the neurons from a center column of the model matrices (gray vertical lines). Each small dot represents a spike. Time is from stimulus onset. (C) Amplification of the first two spikes of the central neuron shown in panel A.

Figure 2. 

Neural responses to surface stimulus. (A) Model output and firing rates of neurons located at the blind spot region and at the surrounding region. The light-dark squares represent the matrix of neurons of the model. The white center square in Layer 1 represents the blind spot, and the dotted white lines in Layer 2 delineate this region. The gray circles depict neurons and the arrows originating from them point to the corresponding spike responses. (B) The spike times of all the neurons from a center column of the model matrices (gray vertical lines). Each small dot represents a spike. Time is from stimulus onset. (C) Amplification of the first two spikes of the central neuron shown in panel A.

Surface Filling-in of the Blind Spot

For those Layer 2 neurons located at the center (representing the blind spot region), the global inhibition was the sole input since no neuronal cells were present at the center of the first layer. Without the excitatory drive, the global inhibition resulted in a strong and rapid hyperpolarization of the membrane potential of the center neurons. At the end of the hyperpolarizing period, these neurons produced rebound spikes (Figure 2A and B). The onset latency of rebound spikes is variable (Tremere, Pinaud, Irwin, & Allen, 2008; Margolis & Detwiler, 2007). Rebound responses can be as fast as 5 msec or take several seconds to occur after the end of hyperpolarization period. Our data show that a rebound spike occurred immediately after each inhibitory pulse from the first neural layer (see Figure 2C). Similar biphasic spikes are observed frequently in the visual cortex (Gold, Girardin, Martin, & Koch, 2009). Therefore, the onset of the rebound burst was similar (almost identical) to the excitatory-driven burst from the surrounding neurons in the second layer. To calculate the effectiveness of the surface filling-in, we divided the number of spikes in the rebound response by the number of spikes evoked by the surrounding Layer 2 neurons. The results show that the strength of the rebound responses was identical to the response strength of the other Layer 2 cells. When the surface stimulus contrast was decreased, this ratio remained unit although the spike rate decreased (Figure 3). Stimulus contrast below 0.4 did not evoke spikes in Layer 1 cells. This signifies that the magnitude of surface filling-in of the blind spot is as robust as the response to the surrounding surface.

Figure 3. 

The strength of filling-in as a function of stimulus contrast. Ratio is the number of rebound spikes of a Layer 2 neuron within the blind spot divided by the number of spikes from a surrounding neuron. Stimulus contrast below 0.4 did not evoke spikes in Layer 1.

Figure 3. 

The strength of filling-in as a function of stimulus contrast. Ratio is the number of rebound spikes of a Layer 2 neuron within the blind spot divided by the number of spikes from a surrounding neuron. Stimulus contrast below 0.4 did not evoke spikes in Layer 1.

Figure 4 summarizes the results of the surface filling-in at Layer 2 of the model. A small stimulus confined to the blind spot region will remain invisible for the Layer 2 cells, like in the visual cortex (Komatsu et al., 2002). However, a surface stimulus excites many (all) Layer 1 neurons. On their turn, these neurons produce retinotopic activation and widespread inhibition in Layer 2 neurons. The balance between excitation and inhibition is so that the magnitude of the local excitatory input is sufficient to overcome the strong global suppressive input. For the neurons located at the blind spot, the global inhibitory signal produces strong hyperpolarization of the membrane potential, which after termination of the inhibitory pulse results in a rebound spike. So a hole in a surface is filled-in immediately by the Layer 2 cells, which is not caused by lateral spreading of visual information but by global inhibition.

Figure 4. 

Explanation of the observed filling-in process. A small sensory stimulus that falls within the blind spot region will not evoke a neural response. A large stimulus (surface) will activate surrounding cells, which will produce rebound spiking in neurons whose receptive fields are located within the blind spot. Open and filled circles denote inactive and active neurons, respectively.

Figure 4. 

Explanation of the observed filling-in process. A small sensory stimulus that falls within the blind spot region will not evoke a neural response. A large stimulus (surface) will activate surrounding cells, which will produce rebound spiking in neurons whose receptive fields are located within the blind spot. Open and filled circles denote inactive and active neurons, respectively.

Filling-in of an Empty Object: Color Dove Illusion

Instant filling-in not only occurs at the blind spot or occluded regions where no visual events are recorded but also regions that correspond to the normal visual field can be filled-in. For example, in the color dove illusion, an empty object (dove) will fill-in when the surrounding background (sky) flashes. Directly at the end of the flash, the “empty bird” becomes filled-in with a color similar to the previous color of the sky, albeit intensity of the filled-in color is less than the one of the surrounding color. Thus, the background color produces an afterimage on an “empty” shape where physically no color was presented. This illusion holds for moving as well as for static images and bears similarities to the Twinkle after image. The color dove effect is different to the common afterimage effect, which produces the perception of the complementary color at the same retinal location.

We tested our model for the color dove filling-in effect (Figure 5A; see Methods). Note that now the center location in Layer 1 representing the empty object location contains neurons. To mimic the surrounding background flash, 30 msec after starting the model, the values of the pixels at the background were set to 1 for 20 msec and then back to 0. Neurons at the background region in Layers 1 and 2 responded to this flashing by a single burst of spikes (Figure 5B). The center neurons of the second layer received strong suppression from the activated background cells in Layer 1. Each time Layer 1 neurons fired a spike, the membrane potential of the neurons located at the object location in Layer 2 became hyperpolarized, however, which was not sufficiently strong to produce a rebound spike. Only when the inhibitory signal was removed by switching off the background stimulus the center Layer 2 cells at the empty object location rebounded to more depolarized levels producing a spike burst (Figure 5B). We used different flash durations (30–1000 msec) to test the model behavior. For all durations always a rebound burst was observed, which was always equally strong (six spikes) and only occurred immediately after the removal of the background stimulus. Furthermore, the number of spikes in the burst was lower than the number of spikes in the bursts of the surrounding cells (Figure 6A). This result mimics the perceived afterimage of the object in the color dove illusion where the perceived contrast is lower for filling-in regions compared with the surrounding region (see Meng, Ferneyhough, & Tong, 2007). Finally, we tested the robustness of the model by decreasing the background contrast and object size. The findings show that for low background contrasts and for small object sizes, a rebound burst always occurred after the termination of the background flash (Figure 6B). Background contrast below 0.1 did not evoke spikes in Layer 1 cells.

Figure 5. 

Filling-in of an empty object. (A) Illustration of the afterimage effect in the color dove illusion. An empty object and background is presented. After flashing the background, the object gets filled-in by the same color as the color of the flashed background. (B) Responses of the model. The gray circles depict neurons and the arrows originating from them point to the corresponding spike responses. The flashed background produces spike activity in the first and second layer. After termination of the background, color neurons at the object location produce a spike burst. Squares indicate the layer matrices of the model. Horizontal black bar in the bottom panel indicates onset and duration of background flash. Time is from stimulus onset.

Figure 5. 

Filling-in of an empty object. (A) Illustration of the afterimage effect in the color dove illusion. An empty object and background is presented. After flashing the background, the object gets filled-in by the same color as the color of the flashed background. (B) Responses of the model. The gray circles depict neurons and the arrows originating from them point to the corresponding spike responses. The flashed background produces spike activity in the first and second layer. After termination of the background, color neurons at the object location produce a spike burst. Squares indicate the layer matrices of the model. Horizontal black bar in the bottom panel indicates onset and duration of background flash. Time is from stimulus onset.

Figure 6. 

The strength of filling-in as a function of background contrast (A) and object size (B). Ratio is the number of rebound spikes of a Layer 2 neuron within the empty object divided by the number of spikes from a neuron on the background. Stimulus contrast below 0.1 did not evoke spikes in Layer 1.

Figure 6. 

The strength of filling-in as a function of background contrast (A) and object size (B). Ratio is the number of rebound spikes of a Layer 2 neuron within the empty object divided by the number of spikes from a neuron on the background. Stimulus contrast below 0.1 did not evoke spikes in Layer 1.

Unfilled Flicker Illusion

To conclude, we tested our model for the unfilled flicker illusion (Macknik, 2006; Macknik & Martinez-Conde, 2004; Macknik, Martinez-Conde, & Haglund, 2000). In this illusion, the perception of the surface of a wide stimulus is weak or disrupted when it is briefly presented while edge detection is normal. For longer presentation times, both the edges and the surface are clearly detected. This surface filling-in is different than the previous stimuli we used in that neurons located at the surface region of the stimulus receive visual signals via the excitatory receptive field connections. In contrast, neurons in the blind spot and color dove illusion do not receive direct receptive field stimulation of the surface. In the unfilled flicker illusion experiment, we adopted the same weights of the connections as for the blind spot experiment and applied a 3 × 3 kernel for the excitatory connections to the detect borders. We then presented to the model a squared stimulus of 32 × 32 or 16 × 16 pixels, with a pixel value of 1, for 10 or 50 msec, respectively. The results show that for short stimulus presentation (10 msec), neurons located at the edge of the stimulus had the highest spike frequency (Figure 7). For the large squared figure, neurons at the center of the stimulus had the same response strength as the ones located at the background (Figure 7B), whereas for the small figure, center neurons had stronger responses than background neurons (Figure 7A). When the stimulus is presented for longer time (50 msec), neurons at the edge and at the surface of the stimulus showed a higher response rate compared with the response rate of the neurons at the background (Figure 7).

Figure 7. 

Filling-in of an unfilled flicker illusion for a small (A) and large (B) input figure. The arrows point to spike frequency (thick gray and black lines) of all neurons from a center row (dark gray horizontal line) of Layer 2 of the model matrix, depicted by the lower gray squares. The dotted white lines represent the small and large figure locations.

Figure 7. 

Filling-in of an unfilled flicker illusion for a small (A) and large (B) input figure. The arrows point to spike frequency (thick gray and black lines) of all neurons from a center row (dark gray horizontal line) of Layer 2 of the model matrix, depicted by the lower gray squares. The dotted white lines represent the small and large figure locations.

DISCUSSION

Perceptual filling-in is a phenomenon where visual information is perceived although information is not physically present. Filling-in occurs in normal and blind parts of the visual field. Some filling-in illusions take seconds to happen, whereas others are rather instantaneous. Adaptation is believed to be the main cause for slow surface filling-in of normal regions. The neural mechanisms for the immediate filling-in, like at the blind spot, are unclear. In this study, we show that the behavior of rebound spiking by global suppression mimics the immediate surface filling-in illusions observed at the blind spot and the after image of an empty object as in the color dove illusion. Also our model replicates the perceptual effects observed in the unfilled flicker illusion.

Filling-in at Early Visual Stages by Rebound Activity

The surface responses in the second layer of our model are explained by the relative differences between excitatory and inhibitory inputs. Layer 1 neurons activated by the relatively large background region provoked a strong suppression of Layer 2 neurons. Such surround or global suppression is present at the first stages of sensory processing, like in the retina and LGN (Solomon et al., 2006; Solomon, White, & Martin, 2002; Ruksenas, Fjeld, & Heggelund, 2000). For the neurons located at the center (representing the location of the blind spot), the global inhibitory signal was the sole input resulting in a strong and rapid hyperpolarization of the membrane potential. After termination of the inhibitory input, the strong hyperpolarization caused rebound spiking of these cells. This implies the existence of a biphasic spike with first a large positive peak followed by a negative peak, which has been observed in the visual cortex (Gold et al., 2009). Such inhibition-induced spiking is possible in neurons having slow h-currents or T-currents (Bessaïh, Leresche, & Lambert, 2008; Lüthi & McCormick, 1998) and occurs in rebound to fast GABAa-mediated inhibitory events (Baufreton & Bevan, 2008; Destexhe & Sejnowski, 2002; Grenier, Timofeev, & Steriade, 1998).

Rebound activity is found in the retina and is a characteristic feature of Off ganglion cells (Margolis & Detwiler, 2007). Retinal cells may evoke rebound burst in the thalamic relay cells (Destexhe & Sejnowski, 2002). Rebound bursts in the thalamocortical cells occur before rebound depolarization in cortical cells (Grenier et al., 1998), suggesting that rebound excitation in cortical neurons is inherited from thalamocortical cells. This notion is supported by absence of rebound activity in isolated cortical swabs (Grenier et al., 1998). In V1, rebound activity is also observed. Here responses leading to rebound activity are feature selective having similar orientation selectivity as the visual response (Huang, Levine, & Paradiso, 2008; Huang & Paradiso, 2008). In our model, feed-forward excitation and surround inhibition are also feature specific.

Conform with an early account for filling-in is the observation of interocular rivalry at the blind spot (Tong & Engel, 2001) and with reports showing that surface filling-in occurs in the absence of attention and takes place before sensory signals arrive at cortical level (Crossland & Bex, 2008; Meng et al., 2007; Tailby, Solomon, Peirce, & Metha, 2007; Meng, Remus, & Tong, 2005; He & Davis, 2001; Hardage & Tyler, 1995). Besides our data, support for early filling-in by rebound activity comes from studies on the aftereffect in the Twinkle illusion. It is hypothesized that the Twinkle illusion is a postinhibitory rebound effect of unstimulated cells after removal of inhibition from the surround stimulation (Crossland & Bex, 2008; Hardage & Tyler, 1995). It has been suggested that the locus of the Twinkle aftereffect is within monocular magnocellular ganglion cells in the retina and/or cells in LGN with small receptive fields (Crossland & Bex, 2008). Hence, in accordance with the proposal of a precortical filling-in process (Crossland & Bex, 2008; He & Davis, 2001; Hardage & Tyler, 1995), our data advocate that surface filling-in occurs at early stages of visual processing.

Correspondence of Our Model to the Visual System

The first layer of our model may correspond to the ganglion cell layer of the retina because these cells transform continuous input into spikes. For the filling-in of empty objects, the second layer may also correspond to the retina where certain types of ganglion cells receive, besides local excitation, global inhibition from spiking amacrine cells or from recurrent interactions via gap junctions (Trong & Rieke, 2008). Alternatively, the second layer may represent the LGN that receives powerful synaptic excitatory contacts from a few retinal ganglion cells (Sincich, Adams, Economides, & Horton, 2007). The same retinal ganglion cells also provide inhibitory postsynaptic currents (Blitz & Regehr, 2005). The surround suppression in the LGN may be inherited from the retina because it is equal (Alitto & Usrey, 2008) or slightly different (Ruksenas et al., 2000) to that in the retina. In addition, LGN interneurons may contribute to surround inhibition (Norton & Godwin, 1992). The influence of inhibition in the LGN comes from a larger retinal region than that from excitation and takes place at the very beginning of a stimulus response (Alitto & Usrey, 2008; Blitz & Regehr, 2005). Surround suppression of LGN neurons appears to be orientation sensitive (Solomon et al., 2002; Sillito, Cudeiro, & Murphy, 1993), like in our model. This observation may suggest a role of corticothalamic feedback in LGN surround suppression (Sillito, Cudeiro, & Jones, 2006), although other studies suggest no involvement of the visual cortex in LGN surround suppression (Alitto & Usrey, 2008; Nolt, Kumbhani, & Palmer, 2007; Sceniak, Chatterjee, & Callaway, 2006; Bonin, Mante, & Carandini, 2005; Webb, Tinsley, Vincent, & Derrington, 2005).

The second layer of our model may also correspond to the primary visual cortex. In this case, LGN present a relay of retinal information. The thalamocortical connections are highly convergent maintaining the retinotopic mapping in the visual cortex where they synchronously activate Layer 4 spiny cells. Furthermore, thalamocortical synapses specifically and strongly excite the fast spiking network (Gibson, Beierlein, & Connors, 1999). Fast spiking neurons form an inhibitory network connected through electric synapses and mediate strong thalamocortical inhibition (Sun, Huguenard, & Prince, 2006; Swadlow, 2003). Surround suppression can suppress large regions (Sun et al., 2006; Ozeki et al., 2004; Bair, Cavanaugh, & Movshon, 2003; Hirsch et al., 2003; Swadlow, 2003) and can arrive even earlier to the target neuron than excitatory signals (Bair et al., 2003). Surround suppression in V1 is comparable to that observed in the LGN (Ozeki et al., 2004; Solomon et al., 2002). Likely feed-forward inhibition plays a role because surround inhibition (Jones, Grieve, Wang, & Sillito, 2001), like filling-in (Ramachandran & Gregory, 1991), is feature specific. Feedback connections to V1, which match the full spatial range of surround interactions, also contribute to surround suppression (Angelucci & Bressloff, 2006).

Biological Substrates of Fast Global Inhibition

Surround inhibition is carried by lateral inhibitory connections and are modulated by feed-forward and feedback input. If lateral connections are the neural substrate of rebound spiking, the widespread inhibitory signal should arrive fast because the response times of neurons at the blind spot in V1 to the presence of a stimulus are similar as the ones of the surrounding cells (Komatsu et al., 2000). Such a fast filling-in may argue for a feed-forward control of surround inhibition. Feedback input from extrastriate cortex, which is conjectured to be important for surface segregation (Lamme, Rodriguez-Rodriguez, & Spekreijse, 1999), can act also fast and influences the earliest feed-forward-induced responses (Hupe et al., 2001). Moreover, corticogeniculate feedback projections may already integrate visual signals around the blind spot region (Yokoi & Komatsu, 2009). Furthermore, fast suppressive signals, which sometimes arrive earlier than excitatory ones, could be explained by the difference in synaptic distribution; inhibitory cells synapse near the soma, whereas excitatory contacts are made at more distal locations. In our model, we modeled global inhibition by adding a negative weight to the feed-forward connections and not by introducing local inhibitory cells at Layer 2. In this way, the combination in time of excitatory and strong inhibitory inputs mimics the synchronous activation and the strong and global inhibition described in the early visual system. Further studies should reveal how surface filling-in by rebound activity occurs by including inhibitory cells and lateral circuits. For instance, is rebound filling-in achieved by local acting inhibitory cells that receive widespread feedback projections or by local feed-forward inhibition that is transmitted laterally within an area?

Is Filling-in at the Blind Spot Different than Normal Surface Filling-in?

It has been argued that different neural mechanisms for surface filling-in exists (Crossland & Bex, 2008; Komatsu, 2006; Hardage & Tyler, 1995). In the blind spot and color dove illusion, surface filling-in is automatic and fast, whereas normal filling-in depends on retinal stability and may take seconds to occur. In addition, the visual experience is different. In normal filling-in, the disappearance of a stimulus is experienced, whereas at the blind spot and color dove illusion, a sensory percept appears. In fact, filling-in at the blind spot occurs without awareness. Finally, normal filling-in starts from the boundaries of an object and gradually fills in the surface, and it occurs after the initial figure-ground segregation of the scene (De Weerd et al., 1995), whereas for filling-in at the blind spot, this is questionable. Our results show no gradual filling-in of the surface and may indicate that filling-in at the blind spot forms part of figure-ground segregation. Hence, we speculate that the neural mechanisms for surface filling-in at the blind spot to be different than for normal surface filling-in.

Limitations of Our Model

We constructed a simple feed-forward model architecture on the basis of realistic spiking neurons to test the idea that global inhibition may lead to surface filling-in by producing rebound spiking in neurons located at the surface of a stimulus. By omitting recurrent processing, we obviously restrained the model. This means that the model is limited in its capacity, and it was thus not expected that all filling-in phenomena can be replicated by the model, in particular taking into account that normal filling-in effects occur after figure–ground segregation. However, our model is versatile in the sense that our binary input can be extrapolated to any visual feature, like orientation, color, brightness, and direction of motion that is carried by the feed-forward connections.

Other models (Grossberg & Hong, 2006; Macknik, 2006; Macknik & Martinez-Conde, 2004) explain surface filling-in by border detection followed by a gradual filling-in of the surface by lateral interactions. For instance, in the spatio-temporal edge model (Macknik et al., 2000), visual excitation is transmitted laterally in the form of inhibition resulting in edge enhancement. We reproduced edge enhancement in the unfilled flicker illusion that was predicted by the spatio-temporal edge model. Thus, although we did not include lateral interactions, the spatio-temporal edge model is expected to respond in the same way as ours.

Conclusions

Our data show that surround inhibition produces rebound spiking that may serve for surface filling-in in parts of the visual field for which no retinal signal exists, for example, in the blind spot. A functional role of rebound spiking in visual processing is not known, perhaps because in vivo recordings of rebound activity are difficult to realize (Alviña, Walter, Kohn, Ellis-Davies, & Khodakhah, 2008). However, according to our model data, it is attractive to consider rebound spiking as an important contributor to filling-in.

Acknowledgments

This work was supported by the Spanish Ministry of Education and Science (MICINN) (grant nos. SEJ2006-15095 and SAF2009-10367) and the Catalan government (AGAUR) (grant no. 2009-SGR-308).

Reprint requests should be sent to Hans Supèr, Department of Basic Psychology, Faculty of Psychology, UB/ICREA, Pg Vall d'Hebron 171, 08035 Barcelona, Spain, or via e-mail: hans.super@icrea.es, Web: http://www.icrea.es/www.grinvi.org.

REFERENCES

REFERENCES
Adrian
,
E. D.
, &
Matthews
,
R.
(
1927
).
The action of light on the eye: Part I. The discharge of impulses in the optic nerve and its relation to the electric changes in the retina.
Journal of Physiology
,
63
,
378
414
.
Alitto
,
H. J.
, &
Usrey
,
W. M.
(
2008
).
Origin and dynamics of extraclassical suppression in the lateral geniculate nucleus of the macaque monkey.
Neuron
,
57
,
135
146
.
Alviña
,
K.
,
Walter
,
J. T.
,
Kohn
,
A.
,
Ellis-Davies
,
G.
, &
Khodakhah
,
K.
(
2008
).
Questioning the role of rebound firing in the cerebellum.
Nature Neuroscience
,
11
,
1256
1258
.
Angelucci
,
A.
, &
Bressloff
,
P. C.
(
2006
).
Contribution of feedforward, lateral and feedback connections to the classical receptive field center and extra-classical receptive field surround of primate V1 neurons.
Progress in Brain Research
,
154
,
93
120
.
Bair
,
W.
,
Cavanaugh
,
J. R.
, &
Movshon
,
J. A.
(
2003
).
Time course and time–distance relationships for surround suppression in macaque V1 neurons.
Journal of Neuroscience
,
23
,
7690
7701
.
Baufreton
,
J.
, &
Bevan
,
M. D.
(
2008
).
D2-like dopamine receptor-mediated modulation of activity-dependent plasticity at GABAergic synapses in the subthalamic nucleus.
Journal of Physiology
,
586
,
2121
2142
.
Bessaïh
,
T.
,
Leresche
,
N.
, &
Lambert
,
R. C.
(
2008
).
T current potentiation increases the occurrence and temporal fidelity of synaptically evoked burst firing in sensory thalamic neurons.
Proceedings of the National Academy of Sciences, U.S.A.
,
105
,
11376
11381
.
Blitz
,
D. M.
, &
Regehr
,
W. G.
(
2005
).
Timing and specificity of feed-forward inhibition within the LGN.
Neuron
,
45
,
917
928
.
Bonin
,
V.
,
Mante
,
V.
, &
Carandini
,
M.
(
2005
).
The suppressive field of neurons in lateral geniculate nucleus.
Journal of Neuroscience
,
25
,
10844
10856
.
Bright
,
D. P.
,
Aller
,
M. I.
, &
Brickley
,
S. G.
(
2007
).
Synaptic release generates a tonic relay neurons.
Journal of Neuroscience
,
27
,
2560
2569
.
Buzsaki
,
G.
(
2006
).
Rhythms of the brain.
Oxford
:
Oxford University Press
.
Crossland
,
M. D.
, &
Bex
,
P. J.
(
2008
).
The Twinkle aftereffect is pre-cortical and is independent of filling-in.
Journal of Vision
,
8
,
1
10
.
De Weerd
,
P.
,
Gattass
,
R.
,
Desimone
,
R.
, &
Ungerleider
,
L. G.
(
1995
).
Responses of cells in monkey visual cortex during perceptual filling-in of an artificial scotoma.
Nature
,
377
,
731
734
.
Destexhe
,
A.
, &
Sejnowski
,
T. J.
(
2002
).
The initiation of bursts in thalamic neurons and the cortical control of thalamic sensitivity.
Philosophical Transactions of the Royal Society of London, Series B, Biological Sciences
,
357
,
1649
1657
.
Ekstrom
,
L. B.
,
Roelfsema
,
P. R.
,
Arsenault
,
J. T.
,
Bonmassar
,
G.
, &
Vanduffel
,
W.
(
2008
).
Bottom–up dependent gating of frontal signals in early visual cortex.
Science
,
321
,
414
417
.
Fiorani
,
M.
,
Rosa
,
M. G. P.
,
Gattas
,
R.
, &
Rocha-Miranda
,
C. E.
(
1992
).
Dynamic surrounds of receptive fields in primate striate cortex: A physiological basis for perceptual completion?
Proceedings of the National Academy of Sciences, U.S.A.
,
89
,
8547
8551
.
Gibson
,
J. R.
,
Beierlein
,
M.
, &
Connors
,
B. W.
(
1999
).
Two networks of electrically coupled inhibitory neurons in neocortex.
Nature
,
402
,
75
79
.
Gold
,
C.
,
Girardin
,
C. C.
,
Martin
,
K. A. C.
, &
Koch
,
C.
(
2009
).
High-amplitude positive spikes recorded extracellularly in cat visual cortex.
Journal of Neurophysiology
,
102
,
3340
3351
.
Grenier
,
F.
,
Timofeev
,
I.
, &
Steriade
,
M.
(
1998
).
Leading role of thalamic over cortical neurons during postinhibitory rebound excitation.
Proceedings of the National Academy of Sciences, U.S.A.
,
95
,
13929
13934
.
Grossberg
,
S.
, &
Hong
,
S.
(
2006
).
A neural model of surface perception: Lightness, anchoring, and filling-in.
Spatial Vision
,
19
,
263
321
.
Hardage
,
L.
, &
Tyler
,
C.
(
1995
).
Induced Twinkle aftereffect as a probe of dynamic visual processing mechanism.
Vision Research
,
35
,
757
766
.
He
,
S.
, &
Davis
,
W. L.
(
2001
).
Filling-in at the natural blind spot contributes to binocular rivalry.
Vision Research
,
41
,
835
840
.
Hirsch
,
J. A.
,
Martinez
,
L. M.
,
Pillai
,
C.
,
Alonso
,
J. M.
,
Wang
,
Q.
, &
Sommer
,
F. T.
(
2003
).
Functionally distinct inhibitory neurons at the first stage of visual cortical processing.
Nature Neuroscience
,
6
,
1300
1308
.
Huang
,
X.
,
Levine
,
S.
, &
Paradiso
,
M. A.
(
2008
).
Rebounding V1 activity and a new visual aftereffect.
Journal of Vision
,
8
,
1
10
.
Huang
,
X.
, &
Paradiso
,
M. A.
(
2008
).
V1 response timing and surface filling-in.
Journal of Neurophysiology
,
100
,
39
47
.
Hupe
,
J.-M.
,
James
,
A. C.
,
Girard
,
P.
,
Lomber
,
S. G.
,
Payne
,
B. R.
, &
Bullier
,
J.
(
2001
).
Feedback connections act on the early part of the responses in monkey visual cortex.
Journal of Neurophysiology
,
85
,
134
145
.
Izhikevich
,
E. M.
(
2003
).
Simple model of spiking neurons.
IEEE Transactions on Neural Networks
,
14
,
1569
1572
.
Jones
,
H. E.
,
Grieve
,
K. L.
,
Wang
,
W.
, &
Sillito
,
A. M.
(
2001
).
Surround suppression in primate V1.
Journal of Neurophysiology
,
86
,
2011
2028
.
Komatsu
,
H.
(
2006
).
The neural mechanisms of perceptual filling-in.
Nature Reviews Neuroscience
,
7
,
220
231
.
Komatsu
,
H.
,
Kinoshita
,
M.
, &
Murakami
,
I.
(
2000
).
Neural response in the retinotopic representation of the blind spot in the macaque V1 to stimuli for perceptual filling-in.
Journal of Neuroscience
,
20
,
9310
9319
.
Komatsu
,
H.
,
Kinoshita
,
M.
, &
Murakami
,
I.
(
2002
).
Neural responses in the primary visual cortex of the monkey during perceptual filling-in at the blind spot.
Neuroscience Research
,
44
,
231
236
.
Lamme
,
V. A. F.
,
Rodriguez-Rodriguez
,
V.
, &
Spekreijse
,
H.
(
1999
).
Separate processing dynamics for texture elements, boundaries and surfaces in primary visual cortex of the macaque monkey.
Cerebral Cortex
,
9
,
406
413
.
Lüthi
,
A.
, &
McCormick
,
D. A.
(
1998
).
H-current: Properties of a neuronal and network pacemaker.
Neuron
,
21
,
9
12
.
MacEvoy
,
S. P.
,
Kim
,
W.
, &
Paradiso
,
M. A.
(
1998
).
Integration of surface information in primary visual cortex.
Nature Neuroscience
,
1
,
616
620
.
Macknik
,
S. L.
(
2006
).
Visual masking approaches to visual awareness.
Progress in Brain Research
,
155
,
177
215
.
Macknik
,
S. L.
, &
Livingstone
,
M. S.
(
1998
).
Neuronal correlates of visibility and invisibility in the primate visual system.
Nature Neuroscience
,
2
,
144
149
.
Macknik
,
S. L.
, &
Martinez-Conde
,
S.
(
2004
).
The spatial and temporal effects of lateral inhibitory networks and their relevance to the visibility of spatiotemporal edges.
Neurocomputing
,
58–60
,
775
782
.
Macknik
,
S. L.
,
Martinez-Conde
,
S.
, &
Haglund
,
M. M.
(
2000
).
The role of spatiotemporal edges in visibility and visual masking.
Proceedings of the National Academy of Sciences, U.S.A.
,
97
,
7556
7560
.
Margolis
,
D. J.
, &
Detwiler
,
P. B.
(
2007
).
Different mechanisms generate maintained activity in ON and OFF retinal ganglion cells.
Journal of Neuroscience
,
27
,
5994
6005
.
Mastronarde
,
D. N.
(
1987
).
Two classes of single-input X-cells in cat lateral geniculate nucleus: II. Retinal inputs and the generation of receptive-field properties.
Journal of Neurophysiology
,
57
,
381
413
.
Matsumoto
,
M.
, &
Komatsu
,
H.
(
2005
).
Neural responses in the macaque V1 to bar stimuli with various lengths presented on the blind spot.
Journal of Neurophysiology
,
93
,
2374
2387
.
Meng
,
M.
,
Ferneyhough
,
E.
, &
Tong
,
F.
(
2007
).
Dynamics of perceptual filling-in of visual phantoms revealed by binocular rivalry.
Journal of Vision
,
7
,
1
15
.
Meng
,
M.
,
Remus
,
D. A.
, &
Tong
,
F.
(
2005
).
Filling-in of visual phantoms in the human brain.
Nature Neuroscience
,
8
,
1248
1254
.
Mitra
,
P.
, &
Miller
,
R. F.
(
2007a
).
Mechanisms underlying rebound activation in retinal ganglion cells.
Visual Neuroscience
,
24
,
709
731
.
Mitra
,
P.
, &
Miller
,
R. F.
(
2007b
).
Normal and rebound impulse firing in retinal ganglion cells.
Visual Neuroscience
,
24
,
79
90
.
Moliadze
,
V.
,
Zhao
,
Y.
,
Eysel
,
U.
, &
Funke
,
K.
(
2003
).
Effect of transcranial magnetic stimulation on single-unit activity in the cat primary visual cortex.
Journal of Physiology
,
553
,
665
679
.
Nolt
,
M. J.
,
Kumbhani
,
R. D.
, &
Palmer
,
L. A.
(
2007
).
Suppression at high spatial frequencies in the lateral geniculate nucleus of the cat.
Journal of Neurophysiology
,
98
,
1167
1180
.
Norton
,
T. T.
, &
Godwin
,
D. W.
(
1992
).
Inhibitory GABAergic control of visual signals at the lateral geniculate nucleus.
Progress in Brain Research
,
90
,
193
217
.
Ozeki
,
H.
,
Sadakane
,
O.
,
Akasaki
,
T.
,
Naito
,
T.
,
Shimegi
,
S.
, &
Sato
,
H.
(
2004
).
Relationship between excitation and inhibition underlying size tuning and contextual response modulation in the cat primary visual cortex.
Journal of Neuroscience
,
24
,
1428
1438
.
Pessoa
,
L.
,
Thompson
,
E.
, &
Noe
,
A.
(
1998
).
Finding out about filling-in: A guide to perceptual completion for visual science and the philosophy of perception.
Behavioral and Brain Sciences
,
21
,
723
748
.
Ramachandran
,
V. S.
, &
Gregory
,
R. L.
(
1991
).
Perceptual filling in of artificially induced scotomas in human vision.
Nature
,
350
,
699
702
.
Ruksenas
,
O.
,
Fjeld
,
I. T.
, &
Heggelund
,
P.
(
2000
).
Spatial summation and center-surround antagonism in the receptive field of single units in the dorsal lateral geniculate nucleus of cat: Comparison with retinal input.
Visual Neuroscience
,
17
,
855
870
.
Sceniak
,
M. P.
,
Chatterjee
,
S.
, &
Callaway
,
E. M.
(
2006
).
Visual spatial summation in macaque geniculocortical afferents.
Journal of Neurophysiology
,
96
,
3474
3484
.
Sillito
,
A. M.
,
Cudeiro
,
J.
, &
Jones
,
H. E.
(
2006
).
Always returning: Feedback and sensory processing in visual cortex and thalamus.
Trends in Neurosciences
,
29
,
307
316
.
Sillito
,
A. M.
,
Cudeiro
,
J.
, &
Murphy
,
P. C.
(
1993
).
Orientation sensitive elements in the corticofugal influence on centre-surround interactions in the dorsal lateral geniculate nucleus.
Experimental Brain Research
,
93
,
6
16
.
Sincich
,
L. C.
,
Adams
,
D. L.
,
Economides
,
J. R.
, &
Horton
,
J. C.
(
2007
).
Transmission of spike trains at the retinogeniculate synapse.
Journal of Neuroscience
,
27
,
2683
2692
.
Solomon
,
S. G.
,
Lee
,
B. B.
, &
Sun
,
H.
(
2006
).
Suppressive surrounds and contrast gain in magnocellular-pathway retinal ganglion cells of macaque.
Journal of Neuroscience
,
26
,
8715
8726
.
Solomon
,
S. G.
,
White
,
A. J.
, &
Martin
,
P. R.
(
2002
).
Extraclassical receptive field properties of parvocellular, magnocellular, and koniocellular cells in the primate lateral geniculate nucleus.
Journal of Neuroscience
,
22
,
338
349
.
Sun
,
Q. Q.
,
Huguenard
,
J. R.
, &
Prince
,
D. A.
(
2006
).
Barrel cortex microcircuits: Thalamocortical feedforward inhibition in spiny stellate cells is mediated by a small number of fast-spiking interneurons.
Journal of Neuroscience
,
26
,
1219
1230
.
Swadlow
,
H. A.
(
2003
).
Fast-spike interneurons and feedforward inhibition in awake sensory neocortex.
Cerebral Cortex
,
13
,
25
32
.
Swadlow
,
H. A.
, &
Gusev
,
A. G.
(
2001
).
The impact of “bursting” thalamic impulses at a neocortical synapse.
Nature Neuroscience
,
4
,
402
408
.
Tailby
,
C.
,
Solomon
,
S. G.
,
Peirce
,
J. W.
, &
Metha
,
A. B.
(
2007
).
Two expressions of “surround suppression” in V1 that arise independent of cortical mechanisms of suppression.
Visual Neuroscience
,
24
,
99
109
.
Tong
,
F.
, &
Engel
,
S. A.
(
2001
).
Interocular rivalry revealed in the human cortical blind-spot representation.
Nature
,
411
,
195
199
.
Tremere
,
L. A.
,
Pinaud
,
R.
,
Irwin
,
R. P.
, &
Allen
,
C. N.
(
2008
).
Postinhibitory repound spikes are modulated by the history of membrane hyperpolarization in the SCN.
European Journal of Neuroscience
,
28
,
1127
1135
.
Trong
,
P. K.
, &
Rieke
,
F.
(
2008
).
Origin of correlated activity between parasol retinal ganglion cells.
Nature Neuroscience
,
11
,
1343
1351
.
Webb
,
B. S.
,
Tinsley
,
C. J.
,
Vincent
,
C. J.
, &
Derrington
,
A. M.
(
2005
).
Spatial distribution of suppressive signals outside the classical receptive field in lateral geniculate nucleus.
Journal of Neurophysiology
,
94
,
1789
1797
.
Yokoi
,
I.
, &
Komatsu
,
H.
(
2009
).
Cortico-geniculate feedback linking the visual fields surrounding the blind spot in the cat.
Experimental Brain Research
,
202
,
247
251
.
Zhu
,
J. J.
, &
Lo
,
F. S.
(
1996
).
Time course of inhibition induced by a putative saccadic suppression circuit in the dorsal lateral geniculate nucleus of the rabbit.
Brain Research Bulletin
,
41
,
281
291
.