Slant-tilt: the visual encoding of surface orientation

Abstract

A specific form for the internal representation of local surface orientation is proposed, which is similar to Gibson's (1950) "amount and direction of slant". Slant amount is usually quantified by the angle sigma between the surface normal and the line of sight (0 degrees less than or equal to sigma less than or equal to 90 degrees). Slant direction corresponds to the direction of the gradient of distance from the viewer to the surface, and may be defined by the image direction tau to which the surface normal would project (0 degrees less than or equal to tau less than or equal to 360 degrees). Since the direction of slant is specified by the tilt of the projected surface normal, it is referred to as surface tilt (Stevens, 1979; Marr, 1982). The two degrees of freedom of orientation are therefore quantified by slant, an angle measured perpendicular to the image plane, and tilt, an angle measured in the image plane. The slant-tilt form provides several computational advantages relative to some other proposals and is consistent with various psychological phenomena. Slant might be encoded by various means, e.g. by the cosine of the angle, by the tangent, or linearly by the angle itself. Experimental results are reported that suggest that slant is encoded by an internal parameter that varies linearly with slant angle, with resolution of roughly one part in 100. Thus we propose that surface orientation is encoded in human vision by two quantities, one varying linearly with slant angle, the other varying linearly with tilt angle.