Visual Slant in the Circle

Vis. Res.

Vol.7,

pp. 341-343.

Pergamon Press 1967. Printed in Great Britain.

RESEARCH

NOTE

Visual Slant in the Circle ROBERT B. FREEMAN,JR Department of Psychology, Pennsylvania State University, University Park, Pennsylvania (Received 10 August 1966)

IN THEclassical investigations

by THOULE~S(1931) of “phenomenal regression to the ‘real’ object,” observers matched ellipses of various major-minor axis-ratios to the apparent image of a stimulus circle presented at selected slants with reference to the plane normal to the visual axis. Thouless, and other more recent investigators, using similar methods, found that observers tended to select a matching ellipse whose objective axis ratio approached that of the slanted circle. This kind of result, conventionally referred to as “shape constancy”, is an indication of the fact that the matched shape depends not only on the projective shape of the test object, but also on other visual cues to shape and slant. fn spite of the reliability of the shape constancy phenomenon, little is known about the visual cues which are responsible for the constancy effect when circles and ellipses are used for stimulus objects. On the other hand, recent studies (CLARK, SMITHand RABE, 1955; SMITH, 1964; FREEMAN,1966a; 1966b) have shown that linear retinal perspective is effective as a stimulus for visual slant when rectilinear stimulus objects are used. Since retinal perspective is a function of both shape (CLARK er al., 1955) and size (FREEMAN,1966a, 1966b) as well as slant of such stimuli, the fact that visual slant is similarly influenced supports the assumption that perspective is a determiner of visual slant. The purpose of the experiment reported here was to evaluate potential non-linear perspective cues in textureless circular stimulus-objects exposed at a slant to the visual axis of the observer. It was shown by THOULESS(1931) that the retinal image produced by a slanted circle is not symmetrical about the axis of rotation. However, as the circle is increased in slant, it can also be shown that the locus of the maximum visual-angle width of the projected image is displaced toward the side of the circle nearest the observer, with the result that the elliptical image of the slanted circle remains symmetrical about its own major visual-angle axis, regardless of the size of the circle. Discriminable cues to direction of slant should therefore be absent regardless of size and slant of the stimulus circle. The apparatus used was a minor modification of the one described and illustrated in an earlier report (FREEMAN,1966a), and was designed to generate a projective image of a self-luminous disk of predetermined size and variable slant while eliminating all other potential cues to slant, such as surface-texture gradients, “edges”, binocular disparity, motion parallax, and contextual stimuli. The parameter of the experiment was aperture diameter, which ranged in 4.5~cm intervals from 3 cm to 30 cm, exposed at a distance of 135 cm from the observer’s eye. Each observer, tested in three I-hr sessions, responded to each of 18 slants 50 times, using the constant-stimulus method. Three observers were tested on each of the 7 circles. The frequency of “+” responses was recorded for each stimulus slant, yielding a frequency distribution of such responses as a function of stimulus slant (FREEMAN,1966b). 341

342

ROBERTB. FREEMAN,JR,

The mean number of “+I’ responses for each stimulus slant for the three observers tested on a single stimulus is shown in Fig. 1, together with the mean (M) and probable error (PE) of the fitted normal ogive. None of the 21 observers produced an individual

%,NI

FIG. 1. Freqwncy distributioll of

Ot

STIMULUS

CIRCLE (OSSRECSI

“ +” rcsponw stimulus slant.

merul

and fitted ogives as a function of

PE which was leas than the theoretical and experimental limit of 90”. Three of the 7 averaged PE’s, and 6 of the 21 individual PE’s were negative. An analysis of variance showed no significant effect of circle size on threshold slant (1;=0*417; df=6, 14). Since the cireuiar stimuli used in this experiment were presented at slants throughout virtually the entire possible range of settings, from -85” to +85”, with no measurable di~m~a~ty, it can be assumed that the “lopsided” image of a slanted cir& is ine&ctive as a monocular cue for visual slant. Yet, in an earlier investigation (FREBMAN, 1966b), threshold slant was found to be very small for rectangular stimuli, some of which were ~o~id~b~y smrdkr than some of the circles used in the present experiment. It must be assumed that the discriminabiiity of slant of nctangIes is dependent on retinal perspective, or the visual angle di&ence betweun its nearer arad farther edges, whose lengths are ~~~~ ble because of the abrupt change in direction of their contours at the corners of the &je&. On the other hand, when small rectaq@ are used, retinal perspective is below threshold, with the results that the slant of rectangles, like that of circles, is indiscriminable. These two f&iings, taken together, provide further evidence that the mrrjorminor axis ratio is ineffective as a primary cue for direction of slant when other stimulus cues are lacking.

RESEARCH NOTE

343

~Ck~o~le~ge~ent-T~e research reported in this paper was supported by the National Institutes of Health Grant MH 08856, U.S. Public Health Service. The assistance of STEPHENLUDWIG and MARTHA HARSANYI is gratefully acknowledged.

REFERENCES W. C., SMITH, A. H. and RABE,AUSMA(1955). Retinal gradient of outline as a stimulus for slam. Can. J. Psycho/. 9, 247-253. FREEMAN, R. B., Jr. (1966a). Effect of size on visual slant. J. exp. Psychol. 71,96-103. FREEMAN, R. B., Jr. (1966b). Absolute threshold for visual slant: The effect of stimulus size and retina1 perspective. J. exp. Psychol. 71, 170-176. SMITH,A. H. (1964). Judgment of slant with constant outline convergence and variable surface texture gradient. Percept. Mot. Skills 18, 869475. THOULESS, R. H. (1931). Phenomenal regression to the ‘real’ object-1 and II. Br. J. Psychol. 21, 339-359; CLARK,

22, I-30.