Model for a three-dimensional optical illusion

A homogeneous coordinate system is used to describe the transformation from a real three-dimensional stimulus to an illusory three-dimensional perceptual object. The model comprises a series of transformations of which one acts as an illusion operator. The illusion operator is specified by a single parameter whose value determines whether the real or the illusory object is perceived. An experiment to test one prediction derived from the model was performed. The results confirm the prediction.     

The solitaire illusion: An illusion of numerosity

A new illusion in which the apparent number of elements of two kinds is determined by their spatial arrangement is described. The illusion is such that one large cluster appears to contain more elements than several small clusters, clustering being determined by Gestalt principles. The illusion was found both in adults and in children of 8 years.     

An illusion of eccentricity

The illusion investigated here is that two concentric arcs, drawn in different (though possibly overlapping) circular sectors and having the same angular extent, appear to be eccentric. Three possible explanations of the illusion are tested. The first hypothesis is that concentricity judgments are made by elongating the arcs to see if they intersect, the illusion being due to the tendency, when elongating a curve, to follow the end-tangent. The second hypothesis is that concentricity judgments are based on a test of coincidence of centers, the illusion being due to the overestimation of the radius of short arcs. The third hypothesis is that both of these factors contribute in equal measure. These hypotheses make different predictions about the effect (on the magnitude of the illusion) of the following variables: (1) the angular distance between the arcs; (2) the radial distance between the arcs; (3) the degree of curvature of the arcs; and (4) the angular extent of the arcs. The observed values of the illusion angle (obtained by the method of limits) in relation to these variables did not uniformly support any of the hypotheses. A more complex model that is consistent with the observed results is therefore proposed.     

An illusion of ingestion

Three experiments were conducted to find out why subjects ingest substantially more liquid than required when asked to match a visually displayed volume. All three experiments replicated the basic illusion phenomenon, and Experiments 1 and 2 indicated that it was attributable to the subjects’ underestimating the volume of liquid in their mouths. Experiment 3 revealed that the illusion was not present with solid substances, but it was evident with liquids when a quite different measurement procedure was employed.     

An illusion of movement complementary to the horizontal-vertical illusion

Blindfolded subjects moved a stylus held in the hand over a standard distance of 4.5 ins. in a given direction. They then attempted to move the same distance in a direction at right angles to the first. Eight combinations of movements were investigated. The results reveal an illusion such that the extent of movements to left or right across the body is underestimated, while the extent of movements towards or away from the body in the mid-line is overestimated. The illusion applies to speed as well as extent of movement. Movement up or down in a vertical plane is equivalent to movement towards or away from the body in a horizontal plane.

The interaction of this illusion with the well-known horizontal-vertical illusion of visual perception explains a failure to find any net illusory effect where lines visually displayed in different orientations were matched for length by unseen movements in similar orientations.

Whether the visual and movement illusions simply co-exist or whether they are functionally related is not yet clear.     

The box alignment illusion: An orientation illusion induced by pictorial depth

In four experiments, observers attempted to align two sets of oblique edges to parallel. The contexts for these alignments included lines in isolation (2-D control), lines embedded in orthogonal drawings of same-oriented and different-oriented boxes (3-D objects), and each of these viewed against backgrounds depicting strong linear perspective (3-D backgrounds). A consistent distortion was observed in the alignments of different-oriented boxes relative to control lines, indicating that the parallel lines in these stimuli appeared to diverge toward the top of the picture. Furthermore, thisbox alignment illusion decreased with interstimulus distance, whereas alignment distortions in control lines and same-oriented boxes increased with distance. Viewing the stimuli against 3-D backgrounds produced a dramatic reversal of the illusion, with control lines now appearing to converge more than the boxes. These results suggest that the illusion reflects basic processes involved in pictorial depth perception.     

Influence of accommodation on the viewing of an optical illusion

This study demonstrates the role of microfluctuations of accommodation in the viewing of the concentric ring illusion. Four experiments were carried out. Experiment I consisted of changing the distance between the illusion and the eyes but retaining visual angle, luminance and pupil size constant. In Experiment II, the accommodation of the eyes is paralysed by a cycloplegic. In Experiment III, the illusion is shown to a monocular aphakic and in Experiment IV, the exposure time is varied between 1/100 and 5 sec. Furthermore, a series of observations compared the concentric ring illusion seen with both eyes simultaneously. The evidence provided by the results of these experiments plus others discussed provide evidence that the concentric ring illusion is caused by the microfluctuations of accommodation.     

An ambiguous-race illusion in children's face memory

Adults show better memory for ambiguous faces of their own race than for ambiguous faces of another race, even when the faces are identical and differentiated only by extraneous cues to racial category. We investigated whether similar context effects operate early in development. Young children raised in predominantly White environments were presented with computer-generated White-Black morphed faces, each paired with either the White or the Black face that contributed to its construction, and were told that the two faces in each pair were siblings. The children's subsequent recognition memory was more accurate for faces that had been paired with White siblings than for faces that had been paired with Black siblings. The same effect did not obtain when the ambiguous faces were paired with White or Black faces that did not contribute to their construction and did not look like siblings. These findings suggest that face memory in children is not driven exclusively by visual information present in faces and instead depends on an interplay of categorical and perceptual information about race and relationships.     

An illusion of reversed direction in hyperopes

If a subject who is sufficiently farsighted removes his corrective, positive, lenses and looks with one eye from a distance of one or a few meters, at a small lighted area such as the (continuously "on") indicator light of an electric toothbrush, razor, or smoke detector, and if a small object such as a pin is then moved slowly from above to below the subject's eyes (in a plane close to the eye), the subject will perceive the object moving normally from above to below until it encroaches on his view of the lighted area. The object will then be seen to encroach first on the bottom of the lighted area, and as the object continues to move down it will be seen to be moving up across the lighted area, exiting the lighted area at the top. Similarly, an object moved in front of the eye from the subject's left to his right will be seen by the subject to traverse the lighted area in the reverse direction, right to left, even though the subject moves the object himself. Also, while the object is in front of the lighted area, it is perceived as an upside down silhouette having surprisingly clear and sharp edges, and it appears to be located on the lighted area rather than close to the eye where it really is.     

The influence of optical aberrations on the magnitude of the Poggendorff illusion

The amount of blurring of the retinal image can be reduced by proper selection of an artificial pupil and a chromatic filter. Reduction of the amount of blurring due to optical aberrations by viewing through a 1-mm artificial pupil and an interference filter in the eye, results in a concomitant reduction in the magnitude of the Poggendorff illusion. The magnitude of the reduction is smaller, however, than would be expected if the illusion was predominantly determined by blur due to optical aberration.     

An investigation of several parameters of the horizontal-vertical illusion

Length of standard line, degrees of lateral separation of H and V stimuli, and which line served as standard or comparison stimulus were systematically varied in a 4 by 3 by 2 factorial design on the horizontal-vertical illusion. When illusion affects were averaged under H- and V-standard conditions, a negative relationship obtained between magnitude of illusion and length of line. With. vertical as standard, the illusion increased as a function of lateral separation of stimuli, but decreased with horizontal as standard. These differential trends for H- and V-standard conditions contributed to the unsystematic relationship between the size of the illusion and progressive displacement of H and V lines. The illusion curves for three lengths of standard line across degrees of lateral separation were similar. The findings are viewed as incompatible with explanations of the H-V illusion involving the so-called “error of the standard.”