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.
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).
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.
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.
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.
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.
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 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.
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.
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).
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.
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.
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).