The retinal image is a two-dimensional projection of the three-dimensional world. Information about the third dimension, i.e. the depth of an object or a scene, originates from several cues. One of them is the shading caused by directional light. Here, we demonstrate a compelling visual illusion that is probably caused by a misinterpretation of shading information. A three-dimensional head model was stretched along the axis perpendicular to the symmetry plane by a factor of cos(25)/cos(35) and was compressed along the horizontal axis in the symmetry plane by a factor of sin(25)/sin(35). If this head is rendered in orthographic projection with an orientation of 35° (with respect to the frontal view) using only ambient light, it results in exactly the same image as the projection of the undistorted head projected with 25° orientation. Instead of ambient light we use directional light. Surprisingly, rather than revealing the distortion in depth, directional illumination causes the projected image of the distorted head to appear considerably wider. We quantitatively measured this illusion by determining the point of subjective equivalence (PSE) using a fixed-interval nulling paradigm. From both images (the undistorted and the distorted head) we derived a series of images with constant height but with a width that ranged in nine steps from 93% to 107% of the original width. In a series of 180 trials these images were simultaneously shown together with the reference head (undistorted, 25í orientation, 100% width). Subjects had to indicate which of the heads appeared to be wider. Psychometric functions were fitted to the data and PSEs were determined. The mean PSE across 15 subjects was 3.2%. As revealed by the psychometric function for the undistorted head, identical images that differ in their width by that amount were correctly discriminated at a rate of 90%. We discuss the observed illusion in the context of shape-from-shading models.
This research is funded by the Volkswagen Foundation.