Relation between the Wundt–Hering Illusion, the Tilt Illusion, and Estimation of Length of Inclined Line Projections

In psychophysical studies, we compared the Wundt–Hering illusion (or fan’s illusion) with distortions in perception of the orientation of lines and in estimation of lengths of the inclined lines projections. Four experiments were carried out: the curvature of the lines crossing the divergent lines (fan) was determined; the curvature of the mentally drawn lines through points located on the fan was evaluated; the tilt illusion that appeared due to contact of the inclined line with the test one was studied; and the length of the projections of the inclined lines was estimated. It was shown that the curvature of the lines is evaluated identically for the continuous lines and for the lines interpolated through the points of intersection with the fan. The length of projections of the inclined lined is overestimated by some observers and underestimated by others. A test line seems to be inclined to an additional line for small difference in orientations, but it seems tilted in the opposite direction with increasing differences. The hypotheses of the genesis of the Wundt–Hering illusion and the tilt illusion, as well as the connection between the obtained distortions of visual perception are discussed.