Surface tilt (the direction of slant): A neglected psychophysical variable

Surface slant (the angle between the line of sight and the surface normal) is an important psychophysical variable. However, slant angle captures only one of the two degrees of freedom of surface orientation, the other being thedirection of slant. Slant direction, measured in the image plane, coincides with the direction of the gradient of distance from viewer to surface and, equivalently, with the direction the surface normal would point if projected onto the image plane. Since slant direction may be quantified by the tilt of the projected normal (which ranges over 360 deg in the frontal plane), it is referred to here assurface tilt. (Note that slant angle is measured perpendicular to the image plane, whereas tilt angle is measured in the image plane.) Compared with slant angle’s popularity as a psychophysical variable, the attention paid to surface tilt seems undeservedly scant. Experiments that demonstrate a technique for measuring apparent surface tilt are reported. The experimental stimuli were oblique crosses and parallelograms, which suggest oriented planes in 3-D. The apparent tilt of the plane might be probed by orienting a needle in 3-D so as to appear normal, projecting the normal onto the image plane, and measuring its direction (e.g., relative to the horizontal). It is shown to be preferable, however, to merely rotate a line segment in 2-D, superimposed on the display, until it appears normal to the perceived surface. The apparent surface tilt recorded in these experiments corresponded closely to that predicted by assuming the 3-D configurations consist of equal-length lines and perpendicular intersections.