‘Reversed’ Illusion with Three-Dimensional Müller-Lyer Shapes

The purpose of this study was to determine whether the Müller-Lyer illusion is produced by a mechanism which uses information defined in the retinal coordinates, or by a mechanism taking into account the three-dimensional (3-D) shape of the illusion figure. The classical Müller-Lyer figure could not be used to address this question since it is two-dimensional. Three-dimensional Müller-Lyer figures were created to see if the illusion they produce is correlated with the shape of the projected retinal image, or with the shape of these figures defined in a 3-D coordinate frame. In the experiments retinal image shape was juxtaposed against the 3-D shape of the illusion displays. For some displays the direction in which the fins pointed, relative to the shafts, in the 3-D frame was the ‘opposite’ of the direction in which they pointed in the retinal images. For such displays, the illusion predicted on the basis of the 3-D structure was the opposite of that predicted on the basis of retinal image shapes. For another 3-D display the fins were oriented such that each projected a single straight line in the retinal image, thus the typical retinal image (< >, > <) was replaced by straight lines (‖, ‖). For all the displays the observed illusion was consistent with how the fins were oriented relative to the shaft in the 3-D coordinate frame, ie with the 3-D shape of the illusion displays. The retinal image shape appeared to play little, if any, role. One conclusion that emerges is that the specific retinal image shape projected by the classical line-drawn pattern is neither necessary nor sufficient for producing the illusion. The present findings are inconsistent with two well known theories of the Müller-Lyer illusion: inappropriate constancy scaling and selective filtering.

Apparent Height of a Stereokinetic Cone is Decreased by Departure from Circularity

Subjects made judgements of the comparative height of the stereokinetic cones seen for pairs of rotating figures with varying eccentricity and ellipticity. For any given eccentricity, ellipticity of the figure reduced the apparent height, with narrow ellipses seeming to be shallower. The effect is attributed to an interaction in constancy scaling.

Triangles and Squares Look Smaller Than They are: Some New Illusions of Extent

Some new illusions of extent are described, and they are discussed in relation to the Müller-Lyer illusion and the constancy-scaling hypothesis. It is concluded that they support a minimal version of this hypothesis in which certain configurations of lines cause changes in local scale in certain directions, independently of whether or not these configurations are incorporated in larger patterns in a way which supports and receives a depth interpretation.

Position in the Visual Field and Spatial Expansion

Measurements of the tilt illusion by parallelism matches have taken as their baseline data estimates of parallelism between two lines. This is because Carpenter and Blakemore and others found in this situation that parallel lines appeared to diverge at their upper ends. It was hypothesised that this effect was due to inappropriate constancy scaling—the parallel lines being interpreted as being located in a receding plane—and that consequently it was inappropriate to take this effect into account in assessing the degree of the tilt illusion. To test the theory, a horizontal line was compared with other horizontal and vertical lines lower down in the visual field. A tendency to underestimate the length of lines lower down in the visual field was found but this varied inversely with distance from the standard. The findings were accounted for on the assumption that the occurrence of inappropriate constancy scaling depended upon prior organization by contiguity which determined whether the two lines were taken as a group or not.

Subjective Towers: Depth Relationships in Multilevel Subjective Contours

The perceived depth associated with subjective contours was studied with a three-level subjective contour configuration. An analysis of subjects' size judgments showed significant size-constancy scaling consistent with the prediction that subjects would perceive the various subjective surfaces as superimposed upon one another in depth. Direct depth estimations, however, showed only weak depth effects, easily reversed by conflicting depth cues, and observed with real, as well as subjective contours. The discrepant results point to the possibility of different functional depth cues for the two tasks. The order of tasks, indicative of priming, further suggested that depth processing may be secondary to pattern recognition rather than being causal in the formation of subjective contours.

Inappropriate Constancy Scaling Theory and the Mueller-Lyer Illusion

Gregory's Inappropriate Constancy Scaling explanation for visual illusion was investigated. If perceptual experience with real-life edges and angles, near and far, leads to constancy scaling which is inappropriately applied to the Mueller-Lyer configuration, then configurations which are based upon angles of regard in between the two extreme field patterns would produce illusory effects between the two conventional Mueller-Lyer effects. A model representing one edge of a cubic figure, i.e., one vertical and four horizontal lines, was constructed of wooden dowel rods and photographed at predetermined angles. Transparencies based on the photographed images were then used to determine the PSE at each of these angles. Generally, we interpret our results as supportive of the theory, since PSEs increase as a function of angular change from 0° to 180°. The linear trend is complicated by an unexpected cubic trend, but an explanation is proposed.