The perception of 3-D rotation from translating sine-wave lines: the reverse of the barber-pole illusion

An ambiguous moving pattern which gives rise to the reverse of the barber-pole illusion is reported. When vertical sine-wave lines translate, vertically and endlessly, on a two-dimensional (2-D) plane, one can perceive rotating three-dimensional (3-D) helixes without the impression of translation. With a single sine-wave line, 3-D rotation was seen for about half the exposure period. With three sine-wave lines shifted in phase by 120 degrees, this illusion easily arose when one fixated a point near the endpoints of the lines, which moved horizontally and sinusoidally along the imaginary upper edge of the screen. When 3-D rotation was seen, the sine-wave lines which were intersecting on a 2-D display were perceptually decomposed into pairs of lines separated in depth. On fixating a point at the center of the figure, vertical translation was mainly seen. Foveal viewing of the horizontal sine movement of the endpoints of the lines produces the impression of 3-D rotation and the impression appears to provide some specific information towards solving the aperture problem and towards reconstructing the whole figure as such.