Visual resolution decreases toward the periphery of the visual field, compared to foveal vision. Accordingly, while functional brain imaging research using a visual occlusion paradigm shows that the content of a visual scene can be decoded from brain activity patterns in a non-stimulated, peripheral part of the retinotopic visual cortex (Smith and Muckli, 2010; Muckli et al., 2015; Revina et al., 2018; Morgan et al., 2019), human peripheral vision tends to generalise scene information, as evidenced by behavioural phenomena such as crowding (e.g., Balas et al., 2009), the uniformity illusion (Otten et al., 2017), and a higher prominence of gist processing (Larson and Loschky, 2009). This tendency to generalize and blend information is ecologically relevant, if we consider that one of the roles of peripheral vision is to monitor the environment for relevant changes while we use foveal vision to focus on the current task. For example, in rabbits, the upper peripheral visual field is particularly tuned for dark spots on blue skies signifying predator birds (Levick, 1967; Steele-Russell et al., 2012). As humans, we need to cancel out redundant or predictable information in the periphery to save processing power and not be too easily distracted. On the other hand, we need to be made aware of those changes in the environment that are sufficiently salient or unpredictable to be worth further consideration.

Here, we aimed to study behaviourally the specific perceptual processing supporting these features of peripheral vision. In particular, we were interested in whether these phenomena can be explained by a distinct calibration of bottom-up (i.e., sensory information) and top-down (e.g., Stewart et al., 2020) selection of task relevant visual space in the peripheral vision. We selected numerosity as a perceptual property because it is a low-level feature susceptible to gist processing (Park et al., 2016; Fornaciai et al., 2017), and independent to other primary visual properties like objects, colour, shape, or location (Burr and Ross, 2008). It is also easy to manipulate on a numerical continuum for psychophysics purposes (e.g., Valsecchi et al., 2013).

We designed a task using Maximum Likelihood Conjoint Measurement (MLCM; Ho et al., 2008; Knoblauch and Maloney, 2012; Maloney and Knoblauch, 2020), a signal-detection based scaling paradigm which we used to characterises the separate contribution of perceptual attributes to perceived numerosity in the periphery. We presented arrays of dots of varying numbers in the left and right peripheral visual fields and participants had to indicate whether there were more dots on the left or the right side. The peripheral areas on each side were further divided into a centre and a surrounding region, only one of which was the task-relevant target while the other was a task-irrelevant context. We could then quantify how perceived numerosity in the relevant part of the display (bottom-up information) is biased toward the number of dots presented in the irrelevant part (contextual information).

In the case that we found a perceptual bias toward the task-irrelevant signal, a possible account would be based on the imprecision of the top-down connections that span out to a larger region. The feedforward input is then not matched by the correct top-down predictions. In such a leaking model prediction errors around the boundaries could lead to an over or underestimation around the boundaries. This Predictive Coding account would lead to an integrative process in which bottom-up and top-down signals are combined to a distorted perception based on integration of a prediction error around boundaries (e.g., Rao and Ballard, 1999; Friston, 2005). An alternative outcome would be observing a serial process under which only one source of information can be perceived at a time (e.g., limited perceptual capacity; Yiǧit-Elliott et al., 2011), and including contextual signals increases the ambiguity of the overall stimuli to the extent that the irrelevant cue is sometimes perceived as the target (e.g., Craig, 1976; Berry and Fristedt, 1985). This model of a serial process could be explained in terms of Predictive Coding the way Jakob Hohwy explains binocular rivalry (Hohwy et al., 2008): the target model explains away the stimuli of the target region, but leaves the stimuli in the irrelevant regions unexplained as a consequence the irrelevant region creates so much prediction error that it sometimes forces the internal model into one that is consistent with the irrelevant information. In order to assess these two accounts, we consider the integration and switching models that make different assumptions about mandatory integration for perceiving the target and contextual stimuli. We aimed to clarify whether the perceptual decisions were made as a weighted average of relevant and irrelevant signals, or were made on the basis of a probability either according to the relevant or irrelevant part of the display, on a trial by trial basis.

Quantifying contextual effects also allowed us to study how the combination of perceptual cues is modulated by both higher-level top-down and bottom-up factors. Firstly, as a bottom-up factor, we varied the duration of presentation intervals to assess how contextual influence is related to the amount of acquired information. Summary representation of visual features in the periphery can be processed within a brief temporal window as short as 50 ms (Chong and Treisman, 2003), and here we aimed to investigate how perceived numbers in the periphery is affected by the strength of bottom-up signals with temporal intervals up to 1 s. Secondly, as a top-down factor, we modulated the area of display participants were attending to. We compared a condition in which the task-relevant targets were the centre areas and the irrelevant context were the surround areas (i.e., contextual filling-in from surround to centre), to a condition in which the task relevant targets were the surround areas and the irrelevant context were the centre areas (i.e., contextual expansion from centre to surround). By varying the spatial arrangement of task-relevant regions, we examine whether the perceptual mechanism of spatial interaction is comparable for filling-in or expanding the context information.

We investigated the processing of numerical magnitude in peripheral visual displays, in which we found that the perceived numerosity of the target area is biased toward the number of dots presented in irrelevant neighbouring areas. Specifically, our results suggested that numerical magnitudes in the periphery were sampled following either a “weighted integration” or a probability switching’ process between the target and irrelevant areas. In other words, contextual cues presented in the surroundings were used for inferences about the numerosity in the centre; whereas contextual cues presented in the centre competed on a trial-by-trial basis to the perceived numerosity in the targeted surround. Thus, we argue that top-down factors, such as directing attention toward different areas in the peripheral visual field, have an impact on how predictions are incorporated into perceptual decisions about numerosity in peripheral vision.

We generally observed that numerosity perception in peripheral displays required a sufficient sampling time. Results from both centre and surround tasks showed that peripheral displays presented for 100 ms seemed highly ambiguous, and consistent with random responses of simulated observers. For presentation intervals longer than 100 ms, our results suggested an involuntary perceptual bias between task relevant and irrelevant parts of a display, supported by the significant advantage of the MLCM additive model (where the model’s decisions were based on both relevant and irrelevant areas), compared to the independence model (where the model considered only the relevant area). Interestingly, results showed that the perceptual contribution of target and irrelevant areas remained consistent across all intervals above 100 ms in the centre task, while the contribution of irrelevant central information while judging the surrounding region decreased progressively with longer intervals. By comparing the results of centre and surround task to the simulated observers, we identified an integration process for the centre task and a switching process for the surround task.

Specifically, perceived numerosity of a target region with irrelevant surrounding influences is best described as “contextual leaking in” effect, i.e., perceived numerosity of the central area is a perceptual combination with a weight of 0.8 attributed to the number of dots physically presented in centre, and 0.2 to the number of dots physically presented in its surround. In other words, it is as if the integration window fits with some insufficient precision on the centre areas, and 20% of the information from the surrounding spills into the decision in a way that the two channels cannot be separated with sufficient spatial precision. These weight values are stable across timing conditions above 100 ms, suggesting a common mechanism of integration for stimuli presented briefly and for longer durations. This low-level spatial integration involves incorporating a small amount of sensory signal from the surround area, and corresponds to an integration process described in the cue combination literature whereby independent noisy sources of information are combined into a weighted average, boosting the precision of perceptual estimates (e.g., Ernst and Banks, 2002; Ernst and Bülthoff, 2004; Hillis et al., 2004; Acerbi et al., 2014). Sensory integration, in fact, has been the only interpretation for additive MLCM models so far.

In contrast, perceptual decisions about surrounding areas with irrelevant central influences are described as an expansion contextual prior. In this case, participants’ responses are most consistent with a perceptual switching process, i.e., participants responded inaccurately according to the central region in some instances, while the surround targets are perceived accurately in the remaining majority of trials. Contrary to the weighted combination of perceptual inputs described above, this switching process does not require spatial integration of signals from relevant and irrelevant areas. Our results showed that participants made incorrect switches 30% of the time with 400 ms intervals, but the proportion was reduced to 20% of the trials for 700 and 1,000 ms intervals. To put this more parsimoniously, perhaps two separate streams of information are processed for the surround task, and the perceptual decision is reached by a lateral inhibition process between the two channels. Unlike an integration process, the switching process was therefore sensitive to changes in interval lengths, although with a floor effect. One may argue that a perceptual switching process is evidence for sequential processing with limited resources (e.g., Landy et al., 2007; Whiteley and Sahani, 2008; Scharff et al., 2011; Yiǧit-Elliott et al., 2011). This account implies that participants only had time to process one of the two parts of the display due to capacity limitations (e.g., difficulty of the surround task), where participants mistakenly prioritised assessing the number of dots in centre, instead of surround, for a small proportion of the trials. This account is partially supported by our empirical data where we showed a decreased tendency to make incorrect switches when participants were provided longer temporal intervals with the display. However, the fact that we still observed the switching behaviour at the longest interval makes this explanation less plausible unless we consider the possibility of another, incompressible, source of error such as motor or attentional mistakes.

A potential mechanism that could induce such an attentional error is biased bistable perception of ambiguous stimuli (e.g., Mamassian and Landy, 1998; Meng and Tong, 2004), in which there is a competition for awareness between several mutually exclusive interpretations of the same stimulus. Bistable perception could be influenced by the boundary extension effect, under which our recollection of scenes tends to extend beyond the border of what was actually presented (as reviewed in Hubbard et al., 2010). It shows how overall perception is affected by ambiguity in our displays. While boundary-extension has mostly been studied for natural scenes, line-drawing paradigms also provided evidence for such an effect (Gagnier and Intraub, 2012) and occurs also in the absence of semantic associations (McDunn et al., 2014), which leads to the possibility of similar processing for the current paradigm. If the display boundary is subjectively defined and the definition varies from trial to trial (e.g., condition to saliency of varying density of dots), such ambiguity would affect the perceived numerosity of the display. In particular, if the boundary includes the end of the complete peripheral display (centre plus surround, left or right), extending this “overall boundary” only affects the broader surrounding area. As a result, perceived numerosity in the surround would not be affected by this extension (see Figure 5A). However, if one considers only the boundary of the centre region, applying boundary extension would have the consequence of generalizing it to the surround area, making the observer perceive the same numerosity in centre and surround (Figure 5B), which may be the cause of incorrect switching in our results.

On the whole, we showed that perception of a task-relevant region is biased toward task irrelevant region, in agreement to contextual influences that have previously been found in situations where the resolution of sensory inputs was low and thus signals were combined to strengthen the reliability of perception (e.g., Levi et al., 2002; Kersten and Yuille, 2003), or foveal-to-peripheral extrapolation in which foveal vision is used to estimate the strength of stimulus properties in the periphery where visual resolution is limited (Toscani et al., 2017). However, we established the persistence of contextual influences with numerosity information presented for as long as 1 s, indicating that the accuracy of numerical magnitude judgment is not rectified with more processing time added awareness. We suggest that the influence of spatial context and the perceptual bias of perceived numerosity that we observed depends on a top-down mechanism, in which that signals from the irrelevant areas automatically create a perceptual expectation that participants used to infer about their perceived number of dots, because peripheral vision is more limited in terms of acuity than foveal vision. Furthermore, we found this perceptual bias to be affected by top-down contextual factors: the surround effect while judging a central area is most consistent with spatial integration, while the centre effect when judging a surrounding area is better explained as switching between two information channels which we hypothesise to be linked to ambiguous boundary extension. These findings illustrate the complexity and flexibility of processing in peripheral vision (Stewart et al., 2020), and more broadly, our data are in line with evidence for predictive models of vision where top-down priors are combined with incoming sensory inputs (Rao and Ballard, 1999; Friston, 2002; Edwards et al., 2017; Spratling, 2017; De Lange et al., 2018). Peripheral vision is more limited in terms of visual acuity than foveal vision and might involve lower precision predictions than cortical areas processing foveal representations. Nevertheless, our data suggest that peripheral vision encodes its inputs in a context-dependent manner, even when that context is not necessary for the task. This process could serve to explain away information in the periphery during navigation for example, where we could use contextual clues to filter out predictable features that we do not need to attend to. In the future, studies should observe in what measure our results are generalizable to other features and complex displays, potentially introducing multimodal effects. Investigating the neuronal bases of the current findings will also be necessary toward understanding how the visual system encodes numerical magnitude.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

The studies involving human participants were reviewed and approved by the Ethics Committee of the College of Science and Engineering of the University of Glasgow. The patients/participants provided their written informed consent to participate in this study.

ML, CA, and LM designed the study together. ML and CA acquired, analysed, and modelled the data. All authors wrote and edited the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.