Efficient Cues for Discriminating Skewed Curved-Line Segments

Visual discrimination of circular arcs differing in curvature reaches hyperacute levels of performance. What spatial attributes of curved contours provide the necessary visual cue? Statistical-efficiency theory has previously been applied to data on the discrimination of symmetric curved-line segments undergoing expansions and contractions perpendicular to their chords. The results have suggested that relative invariants with respect to these transformations are the best cues, since they accounted for the most variance in the data (a relative invariant is an attribute such that the ratio of its values is constant under transformation). Expansions and contractions are examples of affine transformations, which in general provide a good approximation to the effects of viewpoint change. If some attribute of a curved line is a relative invariant with respect to affine transformations, is it then a good cue? An experiment was performed in which observers discriminated curved-line segments that had been affine transformed by progressive amounts of shear along their chords as well as expansions and contractions along and perpendicular to their chords. Shear can be interpreted as a relative affine invariant, and, since shear destroys symmetry by skewing the curve, it should provide a good cue. In fact, although expansions and contractions proved to be good cues, shear did not. Candidate cues that were not relative affine invariants (eg Euclidean curvature, turning angle) were also poor cues. It appears that being a relative affine invariant is a necessary but not sufficient condition for a cue to be efficient in the discrimination of curved-line segments.