An explanation of directional illusion in terms of retinal curvature

Abstract

Problem : In the figure represented in Fig. 3 (Jap. Test p.88), the oblique line does not appear to meet the lower end of the vertical line, although it would meet objectively. The figure is a basic case of the directional illusion. The Poggendorff illusion, the Zöllner illusion and the Hering illusion are each nothing more than a combination of the figures like this.
At Obonai's hand these illusions have received an explanation in purely retinal terms, depending on the curvature of the retina. He has reminded us that the directions of lines which compose an angle on a flat surface cannot correspond with the directions on the curved retina. The directions of lines in the periphery are displaced towards the vertical as well as the horizontal axes, viz., directions of lines in the periphery shrink along their radial dimensions. The directional or angular illusion is thus attributed to the summation or combination of displacements of these line-directions. In the present study the authors offer another experimental finding to verify the validity of the above mentioned hypothesis.
Method and Results : A linear figure represented in Fig. 3 was employed. Observations were made under various conditions as to the fixation pointi The amount of illusion was measured by the method of adjustment.
Experimental results were as follows : The amount of displacement of the line-the so-called directional illusion-at each of the various directions of the oblique line composing the angles of 15°, 30°, 45° and 60° respectively with the vertical line was measured. When the fixation point was placed outside of the oblique line, the displacement of the line was greatest at 15°and it decreased with the increase in the size of angle (positive displacement). However, when the fixation point was changed to the inside of the oblique line, the reversal, of displacement occurred (negative displacement). The amount of this negative displacemenl was small at first, increased with the increase in the size of angle, reaching the maximum at 30°, then decreased gradually as the angle increased, and at 60°, it was changed into the opposite displacement (positive displacement).
When the fixation point was altered from place to place along inside or outside the oblique line at different distances from the lower end of the vertical line (Fig. 5), a conspicuous feature of displacement was observed. When the fixation point was placed outside the oblique line and near the vertical line, the results were similar to those mentioned above, while in the case of fixation at the distant part from the vertical line, the negative displacement was observed. The transition from positive to negative displacement is gradual and continuous. The reversed feature was observed when the fixation point was placed at the other side of the oblique line.
When the diagram was inclined at various degrees on the frontal-parallel plane, a periodical change of the amount of displacement was observed, which agreed precisely with Obonai's early findings.
Considering the anatomical and physiological properties of the eye, the authors conclude that retinal curvature is involved in the above mentioned illusion.