Wide distribution of external local sign in the normal population

Jan J. Koenderink 0 1 Andrea J. van Doorn 0 1 James T. Todd 0 1 0 J. T. Todd The Ohio State University , Columbus, OH, USA 1 J. J. Koenderink (&) A. J. van Doorn Physics and Astronomy, Buys Ballot Laboratory, Universiteit Utrecht , Princetonplein 5, 3584CC Utrecht, The Netherlands The extent of the apparent visual Weld was determined for a group of 78 nave visual observers. We Wnd that there exists a minority (less than 10%) that is essentially veridical, but that the majority of the population experiences an apparent visual Weld of only about 90, thus much narrower than the dioptrics of the eye would suggest (a little over 180). This is in good accordance with available (albeit mainly anecdotal) evidence, though formal data have been lacking thus far. The Wnding is discussed in the context of metrical calibration of the topological structure of the visual Weld, an aspect of local sign. - In haptics the orientation of rods is referred to the hand orientation of the (blindfolded) observer, rather than his/her physical surroundings (Kappers, 2004; Kappers & Koenderink, 2004). This leads to huge errors in the judgement of parallelity for rods that are located far apart in the left-right dimension on a horizontal table top in front of the observer requiring rotations in the shoulder joint. Anecdotal evidence suggests that spatial surface attitude is likewise referenced to the visual direction (which changes due to rotations about the center of the eye-ball) rather than the straight ahead direction. Thus one expects a hemisphere with the eye at its center to appear as a frontoparallel plane, whereas frontoparallel planes should appear as convex towards the observer (see Fig. 1). That this might indeed be the case is suggested by intuitive (non-perspective) drawings of scenes of panoramic extent from various periods and cultures (Barre & Flocon, 1968; Dubery & Willats, 1983; Gombrich, 1960; Pirenne, 1970). Early authors (Pirenne, 1970) describe the visual Weld as a cone with (full) top-angle of 90. It is not clear whether the phenomenal or the anatomical extent is intended though there is no doubt that these authors were aware of the fact that human observers visually experience about a halfspace in front of them. Later authors are more speciWc. For instance, Helmholtz (1892), after discussing the dioptrics of the eye and the nature of eye movements, remarks: ... the Weld of view (G. Sehfeld) of each eye, which in the geometrical sense measures from right to left about 180, appears much narrower. For the most left and right lying objects that one can still see and whose straight connection is a line through our eye, still appear to us as lying in front of us, as if their visual directions made an obtuse or rather right angle with each other. If one looks at the sky, such that no terrestrial objects of known position or size intrude in the visual Weld, then the bright Weld one has in front of oneself has about the diameter of a right angle from right to left, perhaps even less from top to bottom. It is as if you looked into the external world with your head at a certain depth (Helmholtz, 1892, p. 698, our translation). A similar remark was made much earlier by Keppler in his Paralipomena as he saw (Lindberg, 1976) Fig. 1 Two limiting cases. When the visual rays diverge (as they actually do in external space) a surface normal to all rays is a hemisphere centered at the vantage point (Wgure at left). In case the divergence of the visual rays is not recognized (Wgure at right) the surface normal to all (apparent) visual rays is a frontoparallel plane ... both the sun an my shadow as though they were not opposite but both were situated toward the front. from which he concludes ... you fall only a little short of being able to see your own ears. Thus Keppler knew very well that the physical Weld of view is a hemisphere but he perceived it all as situated toward the front, just as Helmholtz did. As of to date there appears to exist no formal investigation of this issue. We describe an experiment in which many (78) nave, monocular observers reported on the phenomenal shape of a hemispherical surface centered on their vantage point. Design of the experiment The experiment is conceptually simple though there are many possible pitfalls. The essential idea is to have a large number of nave, monocular observers report on the phenomenal shape of a hemispherical surface about their vantage point. A large number of observers is desirable because there might conceivably exist variations in the normal population, but has the disadvantage that the experiment should be simple to do, non-ambiguous and take only little time. One needs to control for misunderstandings of the task, problems with unambiguously and uniformly reporting of even clear-cut phenomenal experiences and interference from a variety of unwanted cues and predispositions. The experimental paradigm and setup have been designed with these factors in mind. Some trade-oVs had to be accepted, these are described here. It is a requirement that the observers are unaware of the actual structure of the scene in front of them and have no possibilities to Wnd out about it except by way of the ostensible cues. The design aims to oVer compelling cues that any local surface element is perpendicular to the (local) line of sight. A texture cue (Gibson, 1950; Grding, 1992) via a random spatial distribution of identical circular discs was chosen. With the texture elements being uniformly, though randomly distributed over a spherical surface concentric with the vantage point, this is an almost ideal choice. The uniform distribution yields zero texture density gradient (thus global local frontoparallelity), there is no anisotropy (thus again global local frontoparallelity) and the individual texture elements strongly indicate local frontoparallelity. A large number of black polka dots were pasted on the inside of a translucent hemisphere to form a panoramic pattern. The distribution was uniform, though overlaps of the polka dots were avoided. The hemisphere had a diameter of 120 cm, the polka dots subtended visual angles of about 1.5, their average separation was ca. 6. The hemisphere was illuminated from behind, thus the polka dots appeared a uniform black against a uniformly white background. The open cross section of the hemisphere was covered by a large wall with a peep hole at the center of the hemisphere (see Fig. 2). The observers were confronted with a peep hole at eyeheight in an otherwise featureless wall. The peep hole was 4 cm diameter forcing monocular viewing. Since the anatomy of many human faces makes it hard to place the eye at the nominal vantage pointthe nose being in the waythe wall near the peephole was made slightly pliable. We estimate that the observers manage to put their eye at the intended location give or take about 2 cm in any direction whereas their Weld of view was the maximum possible. They were encour (...truncated)