Directional organization and shape formation: new illusions and Helmholtz's Square

According to Helmholtz's Square illusion, a square appears wider when it is filled with vertical lines and higher when filled with horizontal lines (Helmholtz von, 1866). Recently, Pinna (2010a) demonstrated that the grouping of small squares on the basis of the similarity principle influences also perception of their shape and of the whole emerging shapes. The direction imparted by grouping is the main attribute that influences the shape by polarizing it in the same direction both globally and locally. The rectangle illusion is opposite to what expected on the basis of Helmholtz's Square illusion. 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 proving the role played by the directional shape organization in shape formation. According to our results, Helmholtz's square illusion shows 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.