On the problem of shape formation: New effects related to the Oppel-Kundt and the Helmholtz’s square illusions

According to the Oppel–Kundt illusion, an empty (unfilled) space looks wider than a space filled by some objects (Oppel, 1854–1855). This illusion is related to the Helmholtz’s square illusion, where a square appears wider when it is filled with vertical lines and higher when filled with horizontal lines (Helmholtz, 1866). Recently, Pinna (2010) demonstrated the rectangle illusion, according to which, given a large square shape made up of small black squares, the grouping of the small squares influences the shape perception of both small and large squares. The rectangle illusion is opposite to what expected on the basis of Oppel–Kundt and Helmholtz’s square illusions. Aim of this work is to solve the antinomy between the two sets of illusions and to demonstrate a common explanation based on the interaction between different sources of directional organization. This was accomplished by introducing some new phenomena and through phenomenological experiments. According to our results, the Oppel–Kundt and the Helmholtz’s square illusions show at least two synergistic sources of directional organization: the direction of the grouping of the lines due to their similarity of the luminance contrast and the direction of the grouping of the lines due to the good continuation.