Lateral interactions: size does matterqRussell L. Woods*, Alex K. Nugent, Eli PeliThe Schepens Eye Research Institute, Harvard Medical School, 20 Staniford Street, Boston, MA 02114, USAReceived 27 March 2001; received in revised form 31 October 2001AbstractUsually a high-contrast, co-local mask increases contrast threshold (inhibition). Interestingly, a laterally displaced mask (flanker)can facilitate contrast detection (Vision Research 33 (1993) 993; 34 (1994) 73). When spatial scaling of these flanker effects wasimplied, stimulus bandwidth was confounded with spatial frequency (k1). Under conditions where at lower spatial frequencies, thesize (standard deviation, r) of the Gabor patch was smaller (r < k) than higher spatial frequencies (r ¼ k), the effect appeared scaleinvariant. We replicated the original results for all conditions. However, when Gabor size was fixed (r ¼ k), facilitation changedwith spatial frequency (range 2–13 cycles/deg). When Gabor size was varied (r ¼ 0:5–2k), usually the combination of larger patchsizes and lower spatial frequencies caused inhibition. We were unable to find any conditions that demonstrated spatial scaling. Thesize, both k and r, of both stimulus and flankers, influenced contrast threshold. Also, facilitation reduced as contrast of the flankerswas reduced to detection threshold. Some facilitation was apparent with sub-threshold flankers. These results need to be reconciledwith current models of lateral interactions. Ó 2002 Elsevier Science Ltd. All rights reserved.Keywords: Lateral interactions; Contrast sensitivity; Stimulus bandwidth; Contrast1. IntroductionObject detection can be affected by spatial context,other objects facilitating or inhibiting detection. Incre-ment thresholds can be considered as the minimumdetectable change in the characteristics of one sub-threshold target superimposed on a second target withmatching spatial characteristics. Both sub-threshold andsupra-threshold masks can influence contrast detection(Kulikowski & King-Smith, 1973; Legge, 1979; Tolhurst& Barfield, 1978). The second target is called a maskbecause of its effect at high contrast. At high maskcontrasts typically there is inhibition, but as mask con-trast decreases detection may be facilitated (thresholdlower than with no mask) (Legge, 1979; Tolhurst &Barfield, 1978). More generally, spatial masking is theimpact of one target on the detection of another, wherethe two targets may or may not have matching spatialcharacteristics. For example, a large, co-centric mask(e.g. a pedestal) may alter contrast threshold, with masksize one of the important parameters (Legge, 1978;Westheimer, 1965, 1967; Yu & Levi, 1997a,b). Usingsuch increment-threshold paradigms, the spatial fre-quency tuning (Legge, 1978; Tolhurst & Barfield, 1978;Wilson, McFarlane, & Phillips, 1983; Yu & Levi, 1998)and orientation tuning (Phillips & Wilson, 1984; Yu &Levi, 1998) of the mechanisms detecting sine-wavegratings have been investigated. Most masking condi-tions inhibit (worsen) contrast detection. Contextual ef-fects of masks on contrast detection may be mediated byshort-range cortical connections (Das & Gilbert, 1999).Interestingly, an appropriate flanker––a mask that islaterally displaced from the target (i.e. no longer co-centric)––may facilitate (improve) contrast detection(Morgan & Dresp, 1995; Polat & Sagi, 1993, 1994a;Wehrhahn & Dresp, 1998; Yu & Levi, 1997d). Polat andSagi (1993, 1994a) reported that the detection thresholdof a Gabor patch was lower when the patch was flankedby high contrast Gabor patches. Maximum facilitation(approximately half the non-flanked threshold) wasnoted when the flankers were laterally displaced fromthe target patch by a distance equal to two to threewavelengths (k). Larger displacements (up to 8k or12k) produced measurable facilitation, while shortVision Research 42 (2002) 733–745www.elsevier.com/locate/visresqAspects of this study were presented at the Association forResearch in Vision and Ophthalmology Annual Meeting, FortLauderdale––Woods, R. L., Nugent, A. K., & Peli, E. (2000).Bandwidth affects visual lateral interactions. Investigative Ophthalmol-ogy and Visual Science, 41(4), S803.*Corresponding author. Tel.: +1-617-912-2589; fax: +1-617-912-0169/0111.E-mail address: [email protected] (R.L. Woods).0042-6989/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved.PII: S 0 042- 6 9 8 9 ( 0 1 ) 0 03 1 3 - 3displacements (e.g. 0k or 1k) produced inhibition (shortdisplacements are similar to co-centric masking, as theflankers and stimulus overlap). These effects were re-ported to be spatial frequency independent (which im-plies spatial scaling) (Polat & Sagi, 1993). Spatial scalingis important as it implies a general principle of uniformoperation of the visual system across all scales. Similarfacilitation by laterally displaced objects (flankers) havebeen noted for other spatially localised (but less wellspatial frequency defined) objects (Morgan & Dresp,1995; Westheimer, 1965; Yu & Levi, 1997d). Flankereffects have been ascribed to long-range connections inthe visual cortex (Das & Gilbert, 1995; Gilbert, Das, Ito,Kapadia, & Westheimer, 1996; Kapadia, Ito, Gilbert, &Westheimer, 1995; Polat, Mizobe, Pettet, Kasamatsu, &Norcia, 1998; Polat & Norcia, 1996; Yu & Levi, 1997b).Careful examination of Polat and Sagi’s experimentalconditions shows that stimulus spatial frequency andbandwidth were confounded in their demonstrations ofthe spatial scaling of the facilitation effects (Polat &Sagi, 1993). For example, proportionally the Gaussianenvelope used for the high spatial frequency objects andflankers was larger (standard deviation, r ¼ k) than forthe lower spatial frequency objects and flankers (r ¼0:5k), thereby altering the bandwidth of both stimulusand flanker. Previously mask size has been shown toalter contrast detection (Legge, 1978; Yu & Levi, 1997c).As the bandwidth of Polat and Sagi’s stimuli may haveinteracted with the change in spatial frequency, weexamined size effects by systematically altering spatialfrequency (k1) and bandwidth (r). Spatial scaling ofthese effects has implications for visual processing at lowspatial frequencies. Low spatial frequencies are impor-tant to people with visual impairment through foveal (ormacular) vision reduction, as high spatial frequenciesare not detected and many use eccentric retinal locationsto view. Low