Vision Research 50 (2010) 2411–2420

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Vision Research

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Exploitation of natural geometrical regularities facilitates target detection

Sophie Hall, Petra M.J. Pollux, Kun Guo ⇑School of Psychology, University of Lincoln, Lincoln LN6 7TS, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 April 2010Received in revised form 21 July 2010

Keywords:Natural regularityCo-linearityCo-circularityContrast detectionTop-down process

0042-6989/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.visres.2010.09.011

⇑ Corresponding author. Fax: +44 1522 886026.E-mail address: kguo@lincoln.ac.uk (K. Guo).

We have evolved to operate within a dynamic visual world in which natural visual signals are not randombut have various statistical regularities. Our rich experience of the probability structure of these regular-ities could influence visual computation. Considering that spatiotemporal regularity, co-linearity and co-circularity are common geometrical regularities in natural scenes, we explored how our visual systemexploits these regularities to achieve accurate and efficient representations of the external world. Bymeasuring human contrast detection performance of a briefly presented foveal target embedded indynamic stimulus sequences (comprising six short bars appearing consecutively towards the fovea) imi-tating common regularity structures, we found that both contrast sensitivity and reaction time for targetdetection was facilitated by predictable spatiotemporal stimulus structure. Qualitatively consistent withnatural image analysis that co-linearity is a stronger statistical feature than co-circularity, the facilitationin target detection was more evident for predictable stimulus sequences following a co-linear path than aco-circular path. Control experiments further showed that response bias and uncertainty reduction couldnot fully account for our observation. It seems that our visual system exploits geometrical natural regu-larities to facilitate the interpretation of incoming visual signals, such as constraining interpretation onthe basis of contextual priors.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The function of our visual system has traditionally been viewedas a passive and hierarchical analysis of the immediate retinal in-put. That is, the visual information is amplified and conveyed athigh gain and with fidelity through a hierarchically organised vi-sual cortex by feed-forward connections, with neurons at each suc-cessive stage acting effectively as local filters (e.g. Felleman & VanEssen, 1991; Lennie, 1998; Livingstone & Hubel, 1988). However,recent advances in vision research do not readily bear this view.Considering that visual neurons are embedded in an extensive neu-ral network with feed-forward, lateral and feedback connections,they should have access to a wide variety of spatially and tempo-rally dispersed signals on which to base their computations(Young, 2000). Indeed, numerous studies have demonstrated thatneurons at different cortical stages ‘make sense’ of the informationthat is present inside their classical receptive fields (CRFs) by inte-grating information from larger areas outside their CRFs, hencecontribute to more ‘global’ perception such as contour integration,surface perception and figure-ground segregation (e.g. Albright &Stoner, 2002; Gilbert & Sigman, 2007). More interestingly, neuronsare sensitive to images containing real world probability struc-tures, such that they use context to predict missing information

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and to generate tuned responses that are only weakly dependenton the analysis of local image region corresponding to their CRFs(e.g. Guo, Robertson, Mahmoodi, & Young, 2005; Guo et al., 2007;Rao, Olshausen, & Lewicki, 2002; Sugita, 1999; Vinje & Gallant,2000; Weliky, Fiser, Hunt, & Wagner, 2003). Clearly, the computa-tion of visual neurons is subject to influences of attention, expecta-tion and perceptual tasks. Our internal representation of the visualworld affects brain’s strategy for scene analysis (Gilbert & Sigman,2007).

These compelling results are broadly consistent with a differentview of visual function, inferential process in vision, in which thevisual system interprets incoming retinal signals in the contextof existing knowledge of the visual world (Friston, 2005; Knill &Richards, 1996; Kveraga, Ghuman, & Bar, 2007). Given that wehave evolved to operate within a dynamic visual world wherebynatural visual signals are not random but have many common sta-tistical regularities such as co-linearity (Geisler, 2008), our richexperience and prior knowledge of these natural regularities influ-ences both what we see and the computations that neurons per-form during natural vision (Simoncelli & Olshausen, 2001; Guoet al., 2004, 2007; Knill & Pouget, 2004; Roberts & Thiele, 2008;Schwarzkopf & Kourtzi, 2008). As various visual features do not ap-pear with equal probability in our natural environment, our brainmay represent/compute visual information in the form of probabil-ity distributions, by combining prior knowledge of the statistics ofthe visual world with the likelihood obtained from current sensory

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input. This Bayesian perspective has been successfully imple-mented to deal with dynamic visual processing at the perceptuallevel, such as brightness perception, motion perception, depth per-ception, shape perception, object recognition, visual search andsensorimotor control (e.g. Ascher & Grzywacz, 2000; Ciaramitaro,Cameron, & Glimcher, 2001; Hürlimann, Kiper, & Carandini,2002; Kersten & Yuille, 2003; Najemnik & Geisler, 2005; Weiss,Simoncelli, & Adelson, 2002), suggesting that this prior experi-ence-based inferential process may be a fundamental element ofvisual processing.

Although natural scenes contain a vast array of local structureswith different spatial and temporal complexities, statistical analy-sis has revealed common geometrical regularities of oriented ele-ments presented in natural images. For instance, co-linearity andco-circularity are two repeatedly documented features in the prob-ability densities for the co-occurrence of line segments in visualscenes (Geisler & Perry, 2009; Geisler, Perry, Super, & Gallogly,2001; Ruderman & Bialek, 1994; Sigman, Cecchi, Gilbert, & Magn-asco, 2001). Our abundant environmental experience of such geo-metrical regularities, therefore, could be reflected in visualperformance such as contour grouping and contour detection. In-deed, psychophysical studies have observed that from back-grounds consisting of randomly oriented line segments or Gaborpatches, a few separated lines or Gabor elements can be mostdetectable and grouped together to form coherent perception ofa smooth contour if they are co-presented in a co-linear or co-cir-cular path (e.g. Geisler et al., 2001; Li & Gilbert, 2002; Schwarzkopf& Kourtzi, 2008), possibly through Gestalt notion of ‘good continu-ation’ (Wertheimer, 1958) and roles of local grouping functionsuch as ‘association fields’ (Bonneh & Sagi, 1998; Field, Hayes, &Hess, 1993). The contour detectability heavily depends on stimulusgeometry and is constrained by co-linearity and proximity spatialconfigurations (Bonneh & Sagi, 1998; Hess, Hayes, & Field, 2003).Misalignment in orientation between contour elements and con-tour curvature (orientation jitter) results in a substantial reductionin detectability (Field et al., 1993; Pettet, McKee, & Grzywacz,1998), suggesting that our visual system is probably optimised toprocess contours defined by geometrical regularities.

These studies, however, mainly examined the effect of geomet-rical regularities on contour detection in space or spatial configura-tion (the static condition in which local elements are presentedsimultaneously). Given that we operate within a dynamic visualworld in which local components often vary in space–time or spa-tiotemporal domain, it would be interesting to inspect whether co-linearity and co-circularity arranged in space–time have similarfacilitation effect on target detection as those arranged in space.Furthermore, the common geometrical regularities often have dif-ferent density distributions in natural environment. For instanceco-linearity is a relatively stronger statistical feature than co-circu-larity (Geisler et al., 2001; Sigman et al., 2001), although the exactdifference in density distribution is difficult to quantify because ofcomplexity and variety of natural scenes (i.e. edge co-occurrenceprobability for co-circularity can vary with angular location of edgeelements in a circular arc). It remains unclear to what extent ourexperience of different density distribution of co-linearity andco-circularity in natural scenes can be exploited for dynamic visualcomputation, at least qualitatively.

Spatiotemporal regularity, in which objects around us often oc-cur and move in statistically predictable ways to create a stream ofvisual inputs which are spatially and temporally coherent, is an-other common regularity in natural environment. Our visual sys-tem frequently expects that a particular feature is presented at aparticular location and time because of the spatial and temporalstructure of the current scene, and prior knowledge of the spatio-temporal regularities in the visual world (Guo et al., 2004). A fewrecent studies have revealed that our rich experience of the

probability structure of these spatiotemporal regularity and co-lin-earity can bias our orientation perception (Guo et al., 2004; Roberts& Thiele, 2008). The participants’ orientation judgments of a fovealbar was biased towards the orientation of four collinear bars (pre-dictors) appearing consecutively towards the fovea. The degree ofthis bias was correlated to the spatiotemporal prior probability in-duced by the predictors (i.e. stronger bias for the predictors pre-sented in a highly ordered and predictable sequence, with lessbias for the predictors presented in a randomized order), and couldbe accounted for by a Bayesian inference model associating pre-dictable spatiotemporal stimulus structure with increased priorexpectation of collinear events (Guo et al., 2004). Our electrophys-iological studies further indicated that the neural computation ofthese natural regularities could start at the earliest stage of corticalprocessing (Guo et al., 2007; Pollux & Guo, 2009). Taken together, itseems that the spatiotemporal regularities of the external worldare used to reconstruct the visual scene whereby local visual infor-mation is processed in light of the context within which it occurs.

In this study we aimed to investigate the influence of spatio-temporal regularity and co-linearity and co-circularity arrangedin space–time configuration on target detection, one of our funda-mental visual processes. We also wanted to clarify to what extentthe enhanced visual performance in responding to such stimulusarrangements is accounted for by natural regularity effects (Guoet al., 2004) and other relatively simple effects such as responsebias, uncertainty reduction and flanker facilitation. We systemati-cally manipulated the dynamic stimulus structures to ‘mimic’ thebasic structure of common regularities (spatiotemporal regularity,co-linearity and co-circularity) and measured their impact on hu-man contrast detection performance of a foveal target bar (detec-tion rate and reaction time). If we exploit our prior experience ofnatural geometrical regularities to interpret incoming retinal sig-nals, our contrast detection performance would be facilitated bythe stimulus structure arranged to imitate these basic structureof natural regularities.

2. Methods

Four male and nine female participants (including two authors),aged between 18- and 41-years (24 ± 6, Mean ± SD), participated inthis study. All participants had normal or corrected-to-normal vi-sual acuity. Informed consent was obtained from each participant,and all procedures complied with British Psychological Society‘‘Code of Ethics and Conduct”, and with the World Medical Associ-ation Helsinki Declaration as revised in October 2008.

With the method of constant stimuli, visual stimuli were pre-sented through a ViSaGe Graphics system (Cambridge ResearchSystems, UK) and displayed on a non-interlaced gamma-correctedcolour monitor (100 Hz frame rate, 40 cd/m2 background lumi-nance, 1024 � 768 pixels resolution, Mitsubishi Diamond Pro2070SB). At a viewing distance of 57 cm the monitor subtended avisual angle of 40 � 30�. The visual stimuli comprised six shortbars (1� length, 0.1� width) appearing successively towards the fo-vea (predictor–target sequence, see Fig. 1A for examples). The firstfive ‘predictor’ bars with 15% contrast were presented in theperipheral visual field. The sixth ‘target’ bar was presented 1� be-low a small red fixation point (FP, 0.2� diameter, 10 cd/m2) in vary-ing contrast (0%, 0.25%, 0.5%, 0.75%, 1%, 1.25%, 1.5%, 1.75%, 2%, 2.5%,15%). Each bar was presented for 200 ms. Typically there was nospatial and temporal gap (or spacing) between adjacent bars. Thebars were flashed in turn, in a position immediately adjacent(end-to-end) and in a time immediately preceding the next barat successive positions. The trajectory of this dynamic predictor–target sequence was following either co-linear or co-circular path,and the orientation of individual predictor bar and its presentation

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Fig. 1. (A) Demonstration of four predictor–target sequences used in this experiment. Stimulus configurations are for demonstration purposes only and are not to scale. (B)and (C) Averaged detection rate and reaction time to target with varying contrasts and embedded in predictable, random location, random orientation and target alonesequences. Reaction time was calculated for those target contrasts inducing 50% or higher detection rate. Error bar represents standard error of mean.

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order were manipulated independently in different predictor–tar-get sequences (the detailed manipulation of stimulus structurewas introduced in individual experiments later in Section 3).Regardless of experimental manipulation of the predictor–targetsequences, the horizontal target bar (1� length, 0.1� width) wasidentical and always presented 1� below the FP.

During the experiments the participants sat in a quiet, darkenedroom, and viewed the display binocularly with the support of achinrest. The trial was started by a 350 Hz warning tone lasting150 ms followed by a delay of 1000 ms. A predictor–target se-quence drawn randomly from different predictor–target conditionswith varying target contrast was then presented. For instance, inthe predictable predictor–target sequence, the five predictors andthe target (with varying contrast) were presented on the screen ina highly predictable spatial and temporal order (predictor 1 ? pre-dictor 2 ? predictor 3 ? predictor 4 ? predictor 5 ? target). Theparticipants were instructed to maintain fixation of the FP through-out the trial, and to indicate, by pressing the ‘enter’ key on a com-puter keyboard as quick as possible, when they were reasonablyconfident that the target had been presented below the FP withinthis predictor–target sequence (target present/absent detection).No feedback was given. The trial interval was set to 1500 ms. A min-imum of 20 trials were presented for each target contrast, for eachpredictor–target sequence. During the experiments the observerswere encouraged to have a short break if it was necessary. Beforethe formal test, the participants were given a training session (nor-mally 20 trials) to familiarise with the task.

The participants’ detection performance (percentage of targetdetection judgment and reaction time) was measured as a functionof target contrast. Catch trials (0% and 15% target contrast) wereused to correct for guessing target detection. Across the partici-pants and predictor–target sequences, the mean hit rate for the

presence of 15% target contrast was 99.2% ± 2.1, and the mean falsealarm rate for the presence of 0% target contrast was 6.3% ± 6.8. Thedetection rate for target presence with a tested contrast was thencalculated as (observed hit rate � false alarm rate)/(1 � false alarmrate) � 100 (Norton, Corliss, & Bailey, 2002). In order to have a rea-sonable sample size for statistical analysis, the reaction time wascalculated only for those target contrasts inducing 50% or higherdetection rate.

3. Results and discussion

We first examined to what degree spatiotemporal regularityfacilitates our target detection. The stimulus structure was manip-ulated in four sequences, decreasing in spatiotemporal regularity(Fig. 1A): (1) Predictable sequence: five collinear predictors ap-peared successively towards the fovea in highly predictable spatialand temporal sequence, followed by the target; (2) Random locationsequence: predictors were illuminated in random spatial and tem-poral sequence, followed by the target; (3) Random orientation se-quence: predictors with random orientation (0–180� in steps of22.5�) appeared successively towards the fovea, followed by thetarget; (4) Target alone sequence: no predictors were presented,only the target. If the visual system is sensitive to the spatiotempo-ral regularity, the target detection rate and reaction time should befacilitated by increased predictability of the target.

Ten volunteers participated in this experiment. Their contrastdetection performance for the target was systematically manipu-lated by the predictability of predictor–target sequence. Four(stimulus sequences) � 11 (contrast levels) repeated measuresanalysis of variance (ANOVA) with detection rate or reaction timeas the dependent variable revealed that compared to target alone

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sequence, predictable sequence significantly increased targetdetection rate (F(3, 396) = 13.56, p < 0.01; Fig. 1B) and shortenedreaction time (F(3, 161) = 13.69, p < 0.01; Fig. 1C). The enhance-ment in contrast detection performance was most evident whenthe target contrast was varied between 0.75% and 2.5% (Tukey’sleast significance post hoc test, p < 0.05). Breaking this spatiotem-poral regularity inherent in the predictable sequence by randomis-ing illumination order (random location sequence) or predictororientation (random orientation sequence) had indistinguishableeffect to reduce target detection rate (F(1, 198) = 0.34, p > 0.05)and to increase reaction time (F(1, 81) = 4.09, p > 0.05). The targetdetection performance (detection rate and reaction time) was bet-ter than that measured in target alone sequence, but worse than inpredictable sequence. It seems that our visual system does take thespatiotemporal regularity of the stimulus structure into accountwhen interpreting incoming visual signals. This is reflected in theincreased detection performance in response to the target embed-ded in the predictable sequences.

Does this facilitation of spatiotemporal regularity vary as afunction of natural image statistics? Co-linearity and co-circularityare common probability densities for the co-occurrence of line seg-ments in natural scenes. Although it is difficult to quantify theirdensity distribution because of complexity and variety in naturalscenes, statistical analysis of a representative collection of naturalimages has revealed that co-linearity is a relatively stronger statis-tical feature than co-circularity (Geisler et al., 2001; Sigman et al.,2001). We hypothesised that these regularities and their differentprobability densities could be exploited for efficient coding in vi-sual system and reflected in our behavioural performance, at leastqualitatively. To examine this possibility, the dynamic structure ofpredictor–target sequence was manipulated in three conditions to

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Fig. 2. (A) Non-scaled demonstration of three predictor–target sequences used in thistemporal gap (or spacing) between adjacent bars. The bars were flashed in turn, in a ponext bar at successive positions. (B) and (C) Averaged detection rate and reaction time to tsequences. Error bar represents standard error of mean.

reflect different strengths of natural image statistics (Fig. 2A): (1)Co-linear sequence: predictors and target appeared successively to-wards the fovea in predictable spatial and temporal sequence, fol-lowing a co-linear path; (2) Co-circular sequence: predictors andtarget appeared successively towards the fovea in predictable spa-tial and temporal sequence, following a co-circular path; (3) Tar-get alone sequence: only the target bar was presented. Wemeasured participants’ contrast detection performance for the tar-get embedded in different predictor–target sequences. If our visualsystem is aware of different strengths of these statistical features,then the target detection performance would be facilitated themost for the target presented in the co-linear context.

Three (stimulus sequences) � 11 (contrast levels) ANOVA ofexperimental data collected from ten participants confirmed thatdifferent predictor–target sequences resembling different strengthof natural image regularities had significant impact on both targetdetection rate (F(2, 297) = 25.35, p < 0.01; Fig. 2B) and reactiontime (F(2, 133) = 26.90, p < 0.01; Fig. 2C). Specifically when the tar-get contrast was varied between 0.5% and 1.5%, the detection ratewas significantly enhanced when the target was embedded inco-linear sequence, which was 32% and 71% higher than that inco-circular and target alone sequence, respectively (Tukey’s leastsignificance post hoc test, p < 0.01). The reaction time was alsomanipulated in the same trend with the shortest reaction timefor co-linear sequence and the longest for target alone sequence(post hoc test, p < 0.01). Furthermore, when the detection ratebecame indistinguishable between co-linear and co-circular se-quences for the target with higher contrasts (>2% contrast), aquicker reaction time was still recorded in co-linear sequence thanthat in co-circular sequence (post hoc test, p < 0.05, Fig. 2C). Over-all, this experiment clearly demonstrated that our target detection

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experiment. For both co-linear and co-circular sequence, there was no spatial andsition immediately adjacent (end-to-end) and in a time immediately preceding thearget with varying contrasts and embedded in co-linear, co-circular and target alone

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Fig. 3. Detectability (d’) for the target with varying contrasts and embedded in different predictor–target sequences: predictable, random location, random orientation andtarget alone sequences in Fig. 3A; co-linear, co-circular and target alone sequences in Fig. 3B. Error bar represents standard error of mean.

S. Hall et al. / Vision Research 50 (2010) 2411–2420 2415

performance was modulated by dynamic stimulus structures imi-tating different geometrical regularities. Compared with co-circu-larity, co-linear predictor–target sequence produced greaterfacilitation on target detection in low contrast.

It could be argued that the enhanced contrast detection perfor-mance for the target embedded in the predictable co-linearsequence may be accounted for by two relatively simple mecha-nisms, response bias and uncertainly reduction. We adopted atemporal two-interval forced-choice paradigm to control for theparticipants’ response bias. Each trial consisted of two temporalintervals separated by 1 s. Both intervals contained the same pre-dictor sequence, but only one of them contained the target. Theparticipants were instructed to maintain fixation on the FPthroughout the trial, and to indicate (guess if necessary), by press-ing one of two keys in a computer keyboard, in which interval thetarget was presented. The structure of the predictor–target se-quence was manipulated in the same way as those shown inFig. 1A and 2A. A minimum of 50 trials were presented for each tar-get contrast (0.5–15%) in each predictor–target sequence. Usingthe method of signal detection theory (Norton et al., 2002), thedetectability (d0) for the target presence in different predictor–tar-get sequences (predictable, random location, random orientationand target alone sequences in one experiment; co-linear, co-circu-lar and target alone sequences in another experiment) was calcu-lated and averaged from three participants, who had participatedin the previous comparison experiments. We chose not to use thiscalculation from the start as it does not allow measurement ofreaction times.

The spatiotemporal structure of the predictor–target sequenceshad a similar effect on the d0 (Fig. 3A and 3B) and detection rate(Fig. 1B and 2B). Decreasing predictability of the spatiotemporalregularity by changing predictable sequence to random location,random orientation and target alone sequences systematically re-duced d’ for target detection (F(3, 107) = 11.67, p < 0.01; Fig. 3A),in the similar trend as it did to reduce detection rate (Fig. 1B). Fur-thermore, when the stimulus structure was manipulated to resem-ble increased probability densities in natural scenes (fromtarget alone to co-circular and then to co-linear sequence), the d0

for the target embedded in these sequences was enhanced accord-ingly (F(2, 54) = 20.66, p < 0.01; Fig. 3B), similar to the measure-ment of detection rate shown in Fig 2B. Given this observation, itis unlikely that the enhanced contrast detection performance forthe target embedded in predictable sequence can be explainedsimply by a response bias.

Some recent psychophysical studies have suggested that theimprovement in contrast detection and discrimination perfor-

mance in some stimulus arrangements, such as collinear facilita-tion in which the presence of collinear flankers improves thedetection of a low-contrast central Gabor patch, is largely due toa significant reduction in spatial and/or temporal uncertaintyabout target presentation (e.g. Pelli, 1985; Petrov, Verghese, &McKee, 2006). This uncertainty reduction process could increasetarget detectability by focusing attentional allocation and reducingsystem noise in decision making (Gould, Wolfgang, & Smith, 2007).In our experiment, the presentation of the last predictor in the pre-dictable predictor–target sequence provided clear local cues aboutlocation and timing of the target appearance. It is possible, there-fore, that the increased detection performance for the targetembedded in the predictable sequence could be accounted for byrelatively local mechanism of uncertainty reduction in target pre-sentation. To address this possibility, we manipulated the uncer-tainty of the target presentation in four conditions (Fig. 4A): (1)Target alone sequence: no predictors were presented, only the tar-get was presented during time window of 1000–1200 ms; (2) Pre-dictable sequence: five collinear predictors appeared successivelytowards the fovea in predictable spatial and temporal sequence,followed by the target; (3) Reduction in spatial uncertainty sequence(spatial certainty): similar as target alone sequence, but a faintthin-line oval (0.03� width, 5% contrast) surrounding the targetlocation was present through out the trial; (4) Reduction in spatialand temporal uncertainty sequence (temporal certainty): similar astarget alone sequence, but a faint thin-line oval surrounding thetarget location was present 200 ms before the target onset.

The contrast detection performance for the target embedded inthese sequences was collected from five participants, a 4 (stimulusconditions) � 11 (contrast levels) ANOVA with detection rate andreaction time as the dependent variables was performed. As ob-served before (Fig. 1B), compared to the target alone sequence, pre-dictable sequence significantly facilitated participants’ targetcontrast detection performance by increasing detection rate(F(3, 176) = 11.79, p < 0.01; Fig. 4B) and decreasing reaction time(F(3, 65) = 13.30, p < 0.01; Fig. 4C). Reducing spatial and/or tempo-ral uncertainty about the target presentation, on the other hand,had negligible enhancement effect on contrast detection perfor-mance. Specifically, extra spatial and temporal cues to focus partic-ipants’ attention to the target location had a tendency to slightlyincrease target detection rate and to shorten reaction time in com-parison with target alone sequence, but this enhancement had notreached the significant level (detection rate: F(2, 142) = 1.42,p = 0.25; reaction time: F(2, 38) = 0.66, p = 0.53). Clearly the en-hanced contrast detection performance for the target embeddedin the predictable sequence cannot be fully attributed to local

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Fig. 4. (A) Demonstration of four stimulus conditions used in this control experiment. (B) and (C) Averaged detection rate and reaction time to target with varying contrastsand embedded in different stimulus conditions. Error bar represents standard error of mean.

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uncertainty reduction process in target presentation. Instead, thepredictable sequence could provide global predictive cues to facil-itate the interpretation of the target presentation, and to enhancetarget detectability by increasing its signal-to-noise ratio.

Although similar stimulus arrangement is often used in otheruncertainty reduction studies (Gould et al., 2007; Petrov et al.,2006), the surrounding faint thin-line oval in Fig. 4A could havemasking effect on the co-presented target (Enns & Di Lollo,1997). Furthermore compared to the oval contour, the last predic-tor in the predictable sequence not only could provide more pre-cise spatiotemporal cues about the target presentation, but alsocould have localised flanker interaction effect on the target detec-tion (Chen & Tyler, 2002). To further examine the overall contribu-tion of local mechanisms to the spatiotemporal regularity effect,we manipulated the predictor–target sequence in three conditions(Fig. 5A): (1) Target alone sequence: no predictors were presented,only the target was presented during time window of 1000–1200 ms; (2) Predictable sequence: five collinear predictors ap-peared successively towards the fovea in predictable spatial andtemporal sequence, followed by the target; (3) Control sequence:one predictor was flashed five times in the spatial location of thefifth and final predictor, followed by the target. The predictableand control sequence would provide the same spatiotemporalproximity information prior to the target presentation. If the localcomputation could account for the spatiotemporal regularity ef-fect, then participants should show identical target detection per-formance for the predictable and control sequences.

The contrast detection performance for the target embedded inthese sequences was collected from five participants. A 3 (stimu-lus conditions) � 11 (contrast levels) ANOVA with detection rateand reaction time as the dependent variables revealed thatcompared to the target alone sequence, the predictable sequencesignificantly increased target detection rate (F(2, 165) = 40.4,

p < 0.01; Fig. 5B) and shortened reaction time (F(2, 105) = 59.6,p < 0.01; Fig. 5C). The control sequence, on the other hand, hadless enhancement effect on the target detection performance.The improvement in detection rate was only evident for relativelyhigher target contrast (P0.75%) (Tukey’s least significance posthoc test, p < 0.05). The reaction time measured in the control se-quence was also approximately 20 ms longer than those mea-sured in the predictable sequence (p < 0.05). Taken together, itis unlikely that the local computation (i.e. localised predictivecues and flanker interaction) is the sole underling process of dy-namic geometrical regularities.

If the more ‘global’ process is involved in the computation ofspatiotemporal regularity, then increasing the number of predic-tors would provide more regularity cues from a large part of the vi-sual field and consequently enhance the facilitation effect on targetdetection. Using predictable predictor–target sequence in co-lineartrajectory but systematically varying the number of predictors (1, 5or 9), we recorded five participants’ contrast detection perfor-mance for targets embedded in these sequences and target alonesequence, and performed a 3 (predict number levels) � 11 (con-trast levels) ANOVA with detection rate and reaction time as thedependent variables. In comparison with target alone sequence,predictable predictor–target sequence significantly enhanced par-ticipants’ contrast detection rate (F(3, 176) = 26.6, p < 0.001;Fig. 6A) and shortened reaction time (F(3, 82) = 10.6, p < 0.001;Fig. 6B). Furthermore, the amount of facilitation for target detec-tion rate was increased with increasing number of predictors inthe predictable sequences (F(2, 132) = 6.4, p = 0.002) which wasmore evident for low-contrast targets. For instance, the detectionrate for 0.5% contrast target presented after 9 predictors was signif-icantly higher than the same target presented after 1 or 5 predic-tors. This suggests that the computation of spatiotemporalregularity is not restricted by local visual inputs, the relevant visual

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Fig. 5. (A) Non-scaled demonstration of three stimulus conditions used in this experiment. (B) and (C) Averaged detection rate and reaction time to target with varyingcontrasts and embedded in different stimulus conditions. Error bar represents standard error of mean.

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Fig. 6. Target detection rate (A) and reaction time (B) as the function of target contrast. The target was embedded in predictable predictor–target sequence with varyingnumber of predictors. Error bars represent the standard error of mean.

S. Hall et al. / Vision Research 50 (2010) 2411–2420 2417

cues from peripheral visual field could be integrated together tofacilitate the foveal process of spatiotemporal regularity.

4. General discussion

It has been argued that the development of visual processingand perception is shaped by our visual experience with naturalsurroundings (Schwarzkopf & Kourtzi, 2008; Simoncelli & Olshau-sen, 2001; Sugita, 2004) and we are likely to exploit strong statis-tical regularities within natural vision (Elder & Goldberg, 2002;Geisler et al., 2001; Ruderman & Bialek, 1994; Sigman et al.,2001) to achieve accurate and efficient representations of the

external world. Our perceptual computations may be ‘Bayes’ opti-mal’ by combining prior knowledge of the statistics of the naturalworld with the likelihood obtained from current sensory input (e.g.Bar, 2007; Friston, 2005; Knill & Pouget, 2004; Knill & Richards,1996; Rao, Olshausen, & Lewicki, 2002). Using prior distributionsconsistent with real-world measurements of optical flow, statisti-cal co-variations in spectral stimuli, edge co-occurrence and statis-tical shape regularities, this Bayesian perspective has beensuccessfully implemented to interpret our motion perception,colour perception, contour detection and object perception (e.g.Geisler et al., 2001; Kersten & Yuille, 2003; Long, Yang, & Purves,2006; Weiss et al., 2002; Zhaoping & Jingling, 2008).

2418 S. Hall et al. / Vision Research 50 (2010) 2411–2420

Using a predictable predictor–target sequence following co-lin-ear path, our previous study has observed that our orientationjudgement for the target bar was biased towards the orientationof the co-linear predictors, the degree of this bias was correlatedto the spatiotemporal prior probability induced by the orientatedpredictors and could be accounted for by a Bayesian inferencemodel which associated predictable spatiotemporal stimulusstructure with increased prior expectation of co-linear events(Guo et al., 2004). In this study, we extended this finding to targetdetection. We systematically demonstrated that our detection oflow-contrast targets depended heavily on the contextual priors,and that the behavioural performance (target detection rate andreaction time) was facilitated by dynamic stimulus structuresresembling the basic structure of natural geometrical regularities,such as spatiotemporal regularity, co-linearity and co-circularity.Breaking these statistical regularities by manipulations such asrandomising illumination order (disrupting spatiotemporal regu-larity) or predictor orientation (disrupting co-linearity) led to re-duced target detection rate and increased reaction time (Fig. 1).Interestingly, the degree of facilitation was broadly consistent withthe probability distributions of different natural regularities. Spe-cifically, greater facilitation was achieved by stimulus sequencewith predictable spatiotemporal regularity in co-linear path thanin co-circular path (Fig. 2). Given the complexity and variety of nat-ure scenes, a direct and quantitative comparison between scenestatistics (such as quantifying density distribution of co-linearityand co-circularity) and our psychophysical observation is beyondthe scope of this paper. A more direct comparison, therefore, wouldbe necessary in future work to establish to what degree our targetdetection performance measured with different stimulus struc-tures are reflecting different density distributions of geometricalregularities in natural scenes .

As co-linearity and co-circularity can typically be used to definecontours in natural scenes, it is not surprising that our visual sys-tem is potentially optimised to process these regularities. Previouspsychophysical studies have suggested that human visual systemutilizes a contour grouping or integration process to detect an ex-tended contour defined by discrete contour elements (i.e. orientedline or Gabor elements) embedded in a field of randomly posi-tioned and oriented elements (e.g. Bonneh & Sagi, 1998; Fieldet al., 1993; Hess et al., 2003; Li & Gilbert, 2002). The detection per-formance is subject to the spatial arrangements of those contourelements, such as orientation uniformity, continuity, smoothnessand proximity. For instance, closed or smooth (single-curved) con-tours are generally more detectable than open or jagged (multi-curved) ones (Bonneh & Sagi, 1998; Hess et al., 2003; Kovacs & Ju-lesz, 1993; Pettet et al., 1998), and curved contours take longer todetect than straight ones (e.g. Hess, Beaudot, & Mullen, 2001). Spe-cifically, decreased detection rate and increased processing timeare associated with the increased curvature (Field et al., 1993;Geisler et al., 2001; Hess et al., 2001). Misalignment in orientationbetween contour elements and contour curvature (orientation jit-ter), on the other hand, result in a substantial reduction in the con-tour detection performance (Field et al., 1993; Pettet et al., 1998).By manipulating stimulus structures in space–time configurationrather than just in space domain, our observations in this study ex-tended previous research by indicating that the bias to detect co-linear and co-circular paths can be utilised by the visual systemto enhance contrast detection performance for the target when itis embedded in a dynamic stimulus sequence that follows a co-lin-ear or co-circular path. In agreement with those findings showingthat curved contours are more difficult to group and detect thanstraight ones (e.g. Hess et al., 2001), we also noticed a quicker re-sponse with increased detection rate for low-contrast target in dy-namic stimulus sequences following a co-linear path thanfollowing a co-circular path. This further complements and

expands the classical notion of collinear facilitation (measured byenhanced contrast detection performance, e.g. Polat & Sagi, 1993,1994) to encompass co-circular enhancement, illustrating theimportance of geometric constraint in stimulus structures in con-tour grouping (Geisler & Perry, 2009; Sigman et al., 2001).

In our experiments the individual predictors briefly presentedin a predictable sequence (Fig. 1A) created an apparent motionpath towards the target location. Previous studies have suggestedthat through the integration of local motion signals, participantsshowed an increased perceptual sensitivity (i.e. motion detection,speed discrimination, contrast discrimination) to stimuli presentedin the direction of motion (Fredericksen, Verstraten, & van deGrind, 1994; Verghese & McKee, 2002; Verghese, McKee, & Grzy-wacz, 2000). The similar mechanism could be argued to accountfor our observation of improved target detection performance inthe predictable sequence. As motion cue is an inherent part of spa-tiotemporal regularity, there is no doubt that its direction wouldprovide facilitative cues in target detection. But the contributionof geometric regularity context should not be underestimated.For example, the random orientation sequence in Fig. 1A had iden-tical motion direction as the predictable sequence, but disruptingco-linearity led to a decreased target detection performance. Fur-thermore disrupting temporal regularity by randomising presenta-tion duration of individual predictors in a co-linear predictablesequence also led to a reduced spatiotemporal regularity effect(Fig. 2A in Guo et al., 2004). It seems, therefore, that integrationof local motion cues cannot fully explain our findings in this study.

Earlier studies about contour grouping (e.g. Bonneh & Sagi,1998; Field et al., 1993; Kovacs & Julesz, 1993) and collinear facil-itation (e.g. Polat & Sagi, 1993, 1994) tended to suggest an impor-tant role of ‘local’ grouping process, in which detectionperformance is highly dependent upon spatial or temporalarrangements of neighbouring contour elements. The dynamicstimulus structure used in our experiments, however, could inducea more ‘global’ process for computing spatiotemporal regularityimitated by consecutive bar presentation. Disrupting global regu-larity embedded in co-linear path by randomizing the presentationsequence of individual predictors (random location sequence inFig. 1A) had detrimental effect on participants’ behavioural perfor-mance on target detection (Fig. 1B). Increasing the number of pre-dictors to provide more regularity cues from a large part of visualfield, on the other hand, could further facilitate target detection(Fig. 6) which is complementary to previous research examiningthe effect of number of contour elements on contour grouping(Bonneh & Sagi, 1998; Li & Gilbert, 2002). Also, given that responsebias and uncertainty reduction had limited impact on facilitatingtarget detection (Fig. 3 and 4), a more ‘global’ mechanism (i.e.through long-range lateral interactions and/or feedback from high-er levels) is likely involved in detecting the target embedded in thedynamic stimulus structures resembling the spatiotemporal regu-larity, co-linearity and co-circularity (for further discussion in localvs global process in spatiotemporal regularity, please also see Dis-cussion in Guo et al., 2004).

With stimulus structures similar to those used in studying flan-ker facilitation, and with the same target present/absent detectiontask employed in our study, Zhaoping and Jingling (2008) recentlydemonstrated a strong contextual influence on participants’ detec-tion performance of a central target bar. When the flankers wereconfigured to provide strong grouping cues for a straight line (i.e.low-contrast co-linear flankers with short inter-element separa-tion presented on both side of the central target), participants weremore likely to infer the presence of a target bar, even when the tar-get contrast was zero. A Bayesian model suggested that such con-textual spatial configuration would bias observers’ prior belief oftarget presence according to contour grouping rules (Zhaoping &Jingling, 2008). Similarly, in our experiments the predictors in

S. Hall et al. / Vision Research 50 (2010) 2411–2420 2419

dynamic and predictable co-linear or co-circular sequence wouldprovide strong contextual cues for commonly-experienced geo-metrical regularity, induce dynamic contour grouping process(i.e. Gestalt law of ‘good continuation’) and consequently bias par-ticipants’ belief of the target presence. It is reasonable to infer thatour visual system can exploit common geometrical regularities tointerpret incoming visual signals in both space and space–time do-main, such as facilitating visual perception (i.e. contrast detection)by constraining interpretation on the basis of contextual priors.

By measuring the accuracy of detecting a contour path embed-ded in a field of randomly oriented Gabor elements, Schwarzkopfand Kourtzi (2008) found that we can exploit prior knowledge ofimage regularities, acquired through either long-term environ-mental experience (i.e. co-linearity) or short-term perceptuallearning (i.e. Gabor patches oriented orthogonally to the contourpath), to facilitate contour integration and contour detection. Con-sidering that our participants did not receive extensive training be-fore formal testing (620 trials for protocol familiarisation), andshowed similar target detection performance in different testingsessions, they were more likely to exploit long-term rather thanshort-term prior experience of natural regularities to facilitatethe target detection.

What is the neural basis of this prior-knowledge based interpre-tation process? When local stimulus elements are co-presentedsimultaneously, co-linearity can be processed as early as in areaV1 (Li, Piech, & Gilbert, 2006) through contextual interactionsand intrinsic horizontal connections (Li & Gilbert, 2002), whereasco-circularity elicits strong neuronal activities in area V4 (e.g.Dumoulin & Hess, 2007; Gallant, Braun, & Van Essen, 1993). Onthe other hand, the integration of coherent but spatially and/ortemporally separated visual signals is often subject to the influenceof top-down modulation (i.e. expectation and prediction based onprior experience), and has traditionally been ascribed to the neuralprocesses in high-order cortical areas, such as frontal and parietalcortex (Nobre, Correa, & Coull, 2007; Summerfield & Koechlin,2008; Watanabe, 2007). Given that visual neurons are embeddedin an extensive neural network with feed-forward, lateral andfeedback connections which should enable them to have accessto a wide variety of spatially and temporally dispersed signals onwhich to base their computations, it is quite possible that expecta-tion-related information or experience-based prediction is gener-ated in higher-level areas and projected backward to lower-levelareas, such that the immediate sensory input is interpreted at eachcortical stage within the context of a prior expectation (Bar, 2007),a process similar to ‘predictive coding’ proposed in computationalneuroscience (Friston, 2005).

Indeed, growing evidence has demonstrated that even the func-tion of area V1, the earliest cortical stage of visual processing, issubject to the influences of attention, expectation and perceptualtask (Gilbert & Sigman, 2007). The V1 neuronal responses can re-flect statistical characteristics of natural scenes and show higherefficiency of information transmission while coding images con-taining real world probability structures (e.g. Vinje & Gallant,2000; Rao et al., 2002; Guo et al., 2005, 2007). Using similar visualstimuli, our recent extracellular recordings revealed that V1 neuro-nal responses are systematically modulated by the spatiotemporalinformation occurring well outside and prior to stimulation of theirCRFs in accordance with the statistical regularity of the stimulussequence (Guo et al., 2007). Typically when the co-linear predictors(extra-CRF stimuli) and target (CRF stimulus) were arranged as apredictable predictor–target sequence, orientated towards andthrough to the neuron’s CRF, half of the recorded neurons re-sponded to the predictors presented outside their CRFs at the timethere was no visual stimulus presented inside the CRFs. For aroundone-third of the neurons, their orientation tuning curves to the CRFtarget were biased towards the orientation of the predictors. Infor-

mation Theoretic analysis further revealed that V1 neurons wouldtransmit higher amount and more reliable information about thetarget orientation when the target was embedded in the predict-able sequences resembling natural spatiotemporal regularities(Guo et al., 2007).

Recordings from human participants also demonstrated thatearly components (P1/N1) in event-related potentials (ERPs) weremodulated by the spatiotemporal regularity in stimulus sequence(Pollux & Guo, 2009). In comparison with target alone and randomlocation sequences (see Fig. 1A for examples), the P1/N1 peak la-tency in responding to the target presentation was significantlyshortened by the predictable sequence. The shift of P1/N1 latencywas consistent with the change of target-detection time recordedat the same time, implying a direct link between perceptual perfor-mance and neural processing of spatiotemporal regularities as re-vealed by ERP recordings. Taken together, although we cannotdifferentiate the contribution of long-range horizontal connectionsand feedback connections in the coding of spatiotemporal regular-ities, it seems that such computation starts from the early stage ofvisual processing and V1 neurons can directly contribute to theexploitation of common natural regularities to facilitate our visualdetection performance. We are currently examining the detailedcontribution of early visual cortex in the computation of spatio-temporal regularity, co-linearity and co-circularity through com-bined recordings of ERP and TMS.

Acknowledgements

This research was supported by The Leverhulme Trust Grant No.RF/2/RFG/2009/0152 to K.G.

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