Simultaneous brightness induction is defined as a change in the brightness (perceived luminance) of a test stimulus with a change of surround luminance. A gray disk, for example, appears brighter if it is embedded in a dark surround than if it is embedded in a light surround. If the surround luminance is temporally modulated from dark to light and back to dark again, the disk appears to flicker roughly out of phase with the surround modulation—from light to dark and back to light. There is substantial evidence that brightness induction is nonuniform both spatially and temporally (McCourt,
1982; Foley and McCourt,
1985; De Valois, Webster, De Valois, & Lingelbach,
1986; Kingdom & Moulden,
1988; Paradiso & Nakayama,
1991; Rossi & Paradiso,
1996; Blakeslee & McCourt,
1997,
1999,
2004; Pereverzeva & Murray,
2008; see also Paradiso & Hahn,
1996 for temporal nonuniformity in luminance change perception). The specific characteristics of the spatial and temporal nonuniformities can potentially provide important constraints on the types of mechanisms underlying brightness induction.
In the spatial domain, in the case of induction from static surrounds, there is a decrease in induction strength with an increase of distance from the inducing field, consistent with the predictions of most spatial filtering models (Blakeslee & McCourt,
2004; Blakeslee, Pasieka, & McCourt,
2005; Robinson & de Sa,
2008; Blakeslee & McCourt,
2013). For induction from surrounds modulated in luminance at the fixed temporal frequency, there is less induction at the center of the test disk than at the disk–surround border (Pereverzeva & Murray,
2008; see also Cornelissen, Wade, Vladusich, Dougherty, & Wandell,
2006). These findings were recently confirmed by Blakeslee and McCourt (
2013), who used quadrature-phase motion cancellation paradigm to find a decrease in induction with an increase of the distance from the inducing edge. However, it is possible that the spatial nonuniformities that have been observed in these experiments, particularly in case of disk–surround induction, are the result of the stimulus occupying different retinal positions. It is known that flicker sensitivity varies across the retina (Tyler & Torres,
1972; McKee & Taylor,
1984). It is therefore possible that any perceptual spatial nonuniformities observed using a flickering stimulus were due to retinal position rather than actual distance from the border with the inducing surround. This issue is addressed in the current study by having subjects monitor different spatial positions of the test disk either by direct fixation or through covert spatial attention.
In the temporal domain, there is a temporal delay in brightness induction modulation (De Valois et al.,
1986; Paradiso & Nakayama,
1991; Rossi & Paradiso,
1996; Davey, Maddess, & Srinivasan,
1998; see also Zaidi, Yoshimi, Flanigan, & Canova,
1992). For example, Rossi and Paradiso (
1996) demonstrated a small phase offset between the inducer (surround) and the induced brightness variation in the test. A temporal delay in brightness induction would be indicative of filling-in, the process in which a neural “brightness” signal takes a certain amount of time to spread from the edges to the center of the cortical area being filled-in. In other words, filling-in would have a certain propagation velocity (for simplicity, we assume that the velocity is constant), defined as the distance being covered divided by the time it takes to cover it.
Brightness induction has also been shown to decrease with increasing temporal frequency of the surround modulation (De Valois et al.,
1986; Rossi & Paradiso,
1996; Davey et al.,
1998; see also Zaidi, Yoshimi, Flanigan, & Canova,
1992). The cutoff induction frequency, which usually occurs at about 2–3 Hz, is presumably the frequency at which a filling-in process is slower than the luminance change at the border. This is because the decrease in brightness induction will occur when the filling-in process is slower than the luminance change (frequency) at the border. Brightness induction would then depend on both the velocity of filling-in and the distance the brightness signal has to travel from the border, so a general decrease in cutoff temporal frequency is expected, and observed, with an increase in stimulus size (Rossi & Paradiso,
1996; Davey et al.,
1998; but see also Robinson & de Sa,
2008).
Based on this reasoning and temporal cutoff induction frequency estimates from previous studies (De Valois et al.,
1986; Rossi & Paradiso,
1996), such a filling-in mechanism should be relatively slow. For instance, reanalyzing Rossi and Paradiso's (
1996) spatio-temporal data, Davey et al. (
1998) determined a 95% confidence interval for filling-in velocity at 4°/s–19°/s. Paradoxically, however, all attempts to identify brightness filling-in mechanisms have resulted in much higher velocity estimates, which cannot possibly account for the empirical loss of brightness induction at relatively low temporal frequencies of approximately 2–3 Hz. For example, using masking and briefly presented stimuli, Paradiso and Nakayama (
1991) showed that brightness induction has a temporal delay of 110°/s–150°/s. Later, Rossi and Paradiso (
1996) used perceived phase shifts in induction from temporally modulated in luminance square wave gratings to arrive at a filling-in velocity estimate of 140°/s–180°/s. Several recent studies showed that a filling-in process can be even faster (Robinson & de Sa,
2008) or nearly instantaneous (Blakeslee & McCourt,
2008).
We had several goals in the present study. First, it became clear from our earlier experiments that brightness induction from temporally modulated surrounds is spatially nonuniform, generally tapering down as the distance from the border increases, and so, especially in larger test fields, the results would be dependent on both spatial setup and subject instructions. We wanted to obtain spatio-temporal brightness induction estimates free of these possible artifacts. As we were intrigued by large discrepancies in filling-in velocity estimates from different studies (Paradiso & Nakayama,
1991; Rossi & Paradiso,
1996; Robinson & De Sa,
2008) and even bigger inconsistencies in temporal frequency cutoff and velocities measured directly by other methods (Rossi & Paradiso,
1996; Blakeslee & McCourt,
2008), we felt that a new design may be a key to the problem (Experiment 2). On that note, we also wanted to confirm that the spatial nonuniformities we observed in our earlier studies (Pereverzeva & Murray,
2008) are related to the distance from the edge rather than just the retinal position (Experiment 1). Finally and most importantly, we used a novel paradigm to directly assess the velocity of filling-in (Experiment 3) and compare this assessment to the spatio-temporal sensitivity estimates of Experiment 2. This method was based on our observation that at certain temporal frequencies of surround luminance modulation an illusory “dartboard” pattern appears in the static disk (
Figure 1). This pattern consists of regular light and dark concentric rings within the disk. We hypothesized that this percept was caused by the spread of induction “waves” propagating from the border of the disk towards the center. In this case, propagation velocity can be directly estimated from the distance between the rings in the pattern, providing a spatio-temporal measure of the filling-in process.