Both parallelism and orthogonality are used to perceive 3D slant of rectangles from 2D images

A 2D perspective image of a slanted rectangular object is sufficient for a strong 3D percept. Two computational assumptions that could be used to interpret 3D from images of rectangles are as follows: (1) converging lines in an image are parallel in the world, and (2) skewed angles in an image are orthogonal in the world. For an accurate perspective image of a slanted rectangle, either constraint implies the same 3D interpretation. However, if an image is rescaled, the 3D interpretations based on parallelism and orthogonality generally conflict. We tested the roles of parallelism and orthogonality by measuring perceived depth within scaled perspective images. Stimuli were monocular images of squares, slanted about a horizontal axis, with an elliptical hole. Subjects judged the length-to-width ratio of the holes, which provided a measure of perceived depth along the object. The rotational alignment of squares within their surface plane was varied from 0 degrees (trapezoidal projected contours) to 20 degrees (skewed projected contours). In consistent-cue conditions, images were accurate projections of either a 10 degree- or 20 degree-wide square, with slants of 75 degrees and 62 degrees, respectively. In cue-conflict conditions, images were generated either by magnifying a 10 degrees image to have a projected size of 20 degrees or by minifying a 20 degree image to have a projected size of 10 degrees. For the aligned squares, which do not produce a conflicting skew cue, we found that subjects' judgments depended primarily on projected size and not on the size used to generate the prescaled images. This is consistent with reliance on the convergence cue, corresponding to a parallelism assumption. As squares were rotated away from alignment, producing skewed projected contours, judgments were increasingly determined by the original image size. This is consistent with use of the skew cue, corresponding to an orthogonality assumption. Our results demonstrate that both parallelism and orthogonality constraints are used to perceive depth from linear perspective.