Projected size judgements 1 RUNNING HEAD: P639 Projected size judgements The effect of pictorial depth information on projected size judgements

When full depth cues are available, size judgements are dominated by physical size. However, with reduced depth cues, size judgements are less influenced by physical size and more influenced by projected size. This study reduces depth cues further than previous size judgement studies, by manipulating monocularly presented pictorial depth cues only. Participants were monocularly presented with two shapes against a background of zero (control), one, two or three pictorial depth cues. Each cue was added progressively in the following order: height in the visual field, linear perspective, and texture gradient. Participants made a „same-different‟ judgement regarding the projected size of the two shapes, i.e. ignoring any depth cues. As expected, accuracy increased and response times decreased as the ratio between the projected size of the two shapes increased (range of projected size ratios, 1:1 to 1:5). In addition, with the exception of the larger size ratios (1:4 and 1:5), detection of projected size difference was poorer as depth cues were added. One-cue and two-cue conditions had the most weighting in this performance decrement, with little weighting from the three-cue condition. We conclude that even minimal depth information is difficult to inhibit. This indicates that depth perception requires little focussed attention. Projected size judgements 3 The effect of pictorial depth information on projected size judgements Introduction When depth cues are available, these combine to enable us to perceive the physical size of a static object in depth. This perception of physical size remains constant despite changes in the distance of the object from the observer and the visual angle that it subtends (size constancy; see Sedgwick, 1986). In contrast to physical size, the projected size of an object is established by the visual angle that it subtends on the retina. When making judgements of size, the relative influence of physical size and projected size is dependent on the amount of depth information available, i.e. when depth is perceived, we expect an object which is further away to have a smaller projected size, but the same physical size, than when it is closer in depth (Epstein, 1973). Depth can be determined using the binocular cues of vergence and retinal disparity and by monocular information, available through accommodation, motion parallax and pictorial cues. We know that, in adults, when asked to make size judgements, such judgements are dominated by physical size, over projected size, even in the absence of binocular cues, accommodation and motion parallax, i.e. when only pictorial cues are available (Yonas & Hagen, 1973; Ulharik, Pringle, Jordan & Misceo, 1980). However, little is known about the effect of reducing the number of pictorial cues, on the perception of size. In this study we aim to determine the point at which depth cues begin to influence size judgements, i.e. how much depth information is required for the perception of size to be influenced by physical size information. Yonas and Hagen (1973) investigated depth perception by manipulating accommodation (3D vs. 2D presentation) and motion parallax (present vs. absent) depth cues in a size judgement task. Two real triangles of different physical size were Projected size judgements 4 monocularly presented, positioned in a real textured alley and participants were asked which of the triangles was larger. The visual angle (projected size) subtended by the large triangle was either equal to that subtended by the small triangle, or was 70% or 80% of the projected size of the smaller triangle. Adult participants used the available cues, and gave judgements according to physical size. Threeand 7-year-olds responded to physical size when the projected size of the two triangles was equal. However, when the projected and physical size differences were incongruent, children required at least 3D depth information in order to respond according to physical size, and on the hardest trials (70% projected size difference), 3-year-olds also required the additional depth cue of motion parallax. These results indicate that, with development, perception of physical size is possible with progressively fewer depth cues and for adults, pictorial cues alone are sufficient for physical size to dominate. The present study further investigates this dominance by using zero to three pictorial cues. Ulharik et al. (1980) demonstrated that pictorial depth cues impact size judgements even when participants are asked to respond according to projected size. Participants viewed a 2D photograph of a shape placed in a textured 3D alley under binocular viewing conditions. Participants were explicitly asked to judge the physical size (referred to as „objective size‟) or „projected size‟ of a shape, in units, relative to a standard sized shape. Whilst physical size judgements were generally accurate, projected size judgements were distorted by depth information; projected size responses were almost halfway between that predicted by physical and by projected size. This demonstrates that depth cues cannot be completely inhibited for projected size judgements and suggests that at least some depth information is processed automatically. However, as numerous pictorial cues remained present, we do not know the extent of this distorting effect. In the present study, we ask whether Projected size judgements 5 distortion remains with reduced pictorial cues, and if the strength of the bias is influenced by the type or number of depth cues available. The influence of depth cues has also been demonstrated in studies of visual search. Visual search performance is affected by depth information such as 3D orientation (Enns & Rensink, 1991), direction of light in a scene (Aks & Enns, 1992) and texture gradient (Aks & Enns, 1996). It therefore appears that, in adults, depth perception is a relatively low level process, which occurs in the early stages of visual perception. That is, in common with some visual search mechanisms, depth cues are processed pre-attentively (see Treisman, 1986), and so are difficult to inhibit (Uhlarik et al., 1980). Bennett and Warren (2002) investigated the influence of projected and physical size on performance by adapting a standard size transformation task. Standard size transformation tasks (e.g. Bundesen & Larsen, 1975; Howard & Kerst, 1978; Jolicoeur & Besner, 1987) differ from the size judgement tasks described above. A size transformation task is a mental imagery task. Participants are shown two non-uniform objects which differ in size and also, on 50% of trials, differ subtly in form. Participants must determine whether the two objects are the same or different in form, ignoring any differences in size. Successful completion is thought to rely on the participant‟s ability to mentally scale one object to match the size of the other, thus enabling them to make a same-different judgement of form alone; a linear increase in response time is observed with increased size ratio between the two objects. In standard size transformation tasks, objects are presented in the same depth plane, with no background depth information. As such, projected and physical size are equivalent and their relative influence on performance cannot be differentiated. Projected size judgements 6 Bennett and Warren (2002) introduced progressive amounts of depth information in their size transformation study. This enabled them to investigate the relative influence of projected and physical size on participant‟s judgements of form. Displays were viewed monocularly from behind a reduction screen, and depth information decreased across three conditions; a textured corridor with shadow information; a textured corridor with no shadow; and a vertical textured wall (forms could still differ in height in the picture plane). Stimuli were presented at different simulated distances, using five projected and physical size ratios (range, 1:1 to 1:3). Results demonstrated significant linear increases in RT for both physical and projected size ratios in all conditions. The authors suggest that, before mental size scaling and thus form matching proceeds, size is coded by pooling all available size information. For both of the 3D „corridor‟ conditions, the linear increase in RT was comparable across physical and projected size ratios. This suggests that the influence of projected and physical size was roughly equal. This is surprising, given that size judgement studies report physical size dominance in similar conditions. This could relate to additional „projected size‟ information from the flat screen (accommodation, motion parallax), as suggested by Bennett and Warren (2002), or could be related to the difference in task demands (form vs. size judgement). Performance on the 2D condition, however, showed a stronger influence of projected than physical size. Importantly, this indicates that manipulating pictorial depth cues influences the relative influence of physical and projected size on form judgements and that with only very minimal cues, projected size dominates. This is investigated further in the present study by using a size judgement task. To our knowledge, this is the first study to investigate the effect of manipulating pictorial depth cues on same-different judgements of projected size. Projected size judgements 7 In summary, previous studies have shown that, with reduced depth cues, provided there are numerous pictorial depth cues, physical size remains dominant over projected size (Yonas & Hagen, 1973; Uhlarik et al.,1980). However, Bennett & Warren (2002) provide evidence to suggest that projected size might dominate if pictorial cues are also reduced. To investigate this, we asked participants to make size judgements with reduced pictorial cues only. Stimuli were viewed monocularly, in an environment in which objects rested on the ground plane, the ground plane was flat and the horizon was at eye-level. The first cue added was height in the visual field (Wallach & O‟Leary, 1982). For this cue, the angle between eye level (assuming this is at the horizon) and the location of the base of the object (assuming that this is below eye level) determines the distance of the object from the observer: objects that are further away appear higher in the visual scene, and thus subtend a smaller angle. The second depth cue added was linear perspective. Sedgwick (1986) explains that this indicates size and depth in two ways. First, as a direct indication of size (see Wraga, 1999), there is a constant relationship between the height of an object resting on a surface and the vertical distance between eye-level (assuming this is at the horizon) and that surface. From this the ratio between the visual angles subtended from the point of observation between the top and bottom of the object and between the horizon and bottom of the object can be calculated, known as the horizon-ratio relationship (Sedgwick, 1973). The second way in which linear perspective indicates size and depth is also specified by the third depth cue added, texture gradient. For both linear perspective and texture gradient, depth is indicated by the angular separation between the projection of converging horizontal surface lines (edges or texture) which provide a constant scale factor towards the horizon (Gibson, 1950; Sedgwick, 1986). Projected size judgements 8 For each condition, participants were explicitly asked to make same-different size judgements according to projected size only. The influence of physical size was determined by the negative effect on performance, relative to the control condition where no depth cues were available. We aimed to determine when depth cues begin to affect projected size judgements and the relative weighting of each of the depth cues employed.