Therefore, it is not clear whether the human vision system is choosing a rectangular object or a highly symmetric object in perceiving a rectangular parallelepiped from the picture. Indeed, a rectangular parallelepiped is highly symmetric, and such symmetric structures can explain why we perceive a cube from the Necker cube figure ( Hidaka and Takahashi, 2021). Symmetry is effectively assumed in order to distinguish 3D structures from 2D pictures ( Sawada et al., 2014). In Gestalt psychology, on the other hand, symmetry is also considered to be a factor that the human vision system places high priority on when perceiving 3D objects ( Michaelsen et al., 2013 Michaelsen, 2014).

Even an Ames room, which is a particular type of non-rectangular room, is perceived as rectangular from a particular viewpoint ( Gregory, 1970 Ninio, 2001). This property is also used effectively for machine interpretation of engineering drawings ( Valley et al., 2004). Indeed, a picture of a parallelepiped is almost always interpreted as a rectangular parallelepiped if this interpretation is mathematically possible. It has been observed that the human vision system has a strong preference for rectangular objects ( Perkins, 1971, 1972, 1973). This means that the human vision system does not consider all possibilities, but only a small subset of possible interpretations, determined by certain rules ( Clowes, 1971 Hoffman, 1998 Hertzmann, 2020). However, we usually interpret images of simple objects such as cubes and bricks without any difficulty. Indeed, a single image does not specify the 3D shape of the object uniquely various 3D shapes can create the same 2D projected image ( Marr, 1982 Sugihara, 1986). When we see an image using two eyes, the binocular stereo tells us the distance to the sheet of paper on which the image is printed, but not to the object represented in the image. When we see a projected image of a 3D object, on the other hand, perception of depth is not easy because the image is 2D, with the depth information lost. When we see a 3D object directly, we can use two eyes and consequently the binocular stereo works to perceive the depth. Visual perception of depth is one of the fundamental functions of the human vision system because we need depth information in order to act in 3D environments, such as grasping objects and avoiding obstacles. This observation will help us to understand various 3D optical illusions, including the room-size illusion and the ambiguous object illusion. We found that the preference for rectangularity is stronger than that for symmetry. Thus, a question is raised: which is more basic, the rectangularity preference or the symmetry preference? To answer this question, we carried out experiments using pictures that have at least two interpretations as 3D objects, one of which was rectangular but not symmetric, and the other of which was symmetric but not rectangular. Symmetry is also considered to be a factor that the human vision system places high priority on when perceiving 3D objects. It is known that the human brain has a strong preference for rectangularity in interpreting pictures as 3D shapes. 2Department of Biomedical Sciences, University of Sassari, Sardinia, Italy.1Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan.

2d common picture shapes