Understanding the geometrical properties of an Ames room and controlling it systematically and quantitatively

Journal of Mathematical Psychology. 2024. Vol. 123. Article 102885.

Myrov V., Gorina E., Vodorezova K., Dvoeglazova M., Koshmanova E., Gorbunova E. S., Sawada T.

Within an Ames room, the perceived size of objects, such as people, changes dynamically when the objects move about within the room. The shape of the Ames room is not actually rectangular but it is perceived to be rectangular. Unfortunately, the geometrical properties of the Ames room have often been misunderstood, and rooms that have different shapes are also referred to as “Ames rooms” in many articles. In this study, the geometrical properties of the original Ames rooms constructed by Adelbert Ames, Jr. were analyzed and the generalization of the Ames room was discussed. We found that these original Ames rooms are 3D-to-3D perspective transformations of rectangular illusory rooms. Based on this analysis, we also developed a computational model that can construct a generalized Ames room that has a hexahedral shape with some free parameters that quantitatively control (i) the size and aspect-ratio of a rectangular illusory room, (ii) the amount of distortion of the Ames room from a rectangular room, and (iii) the viewpoint of an observer. This model was implemented as a computational program so that an Ames room can be constructed in a VR space. Note that the transformations of the Ames rooms can be applied to an arbitrary 3D scene and that they can be regarded as members of a subset of 3D-to-3D perspective transformations. Any perspective transformation in this subset distorts the 3D scene in such a way that the retinal image of the distorted scene, when seen from a specific viewpoint, is identical to the retinal image of the initial scene, when seen from a specific viewpoint. These generalizations allow us to control the conditions of an Ames room systematically with more flexibility when we study this illusion.

Keywords: projective geometry, visual illusion, Ames room, group invariants, model-based invariants, accidental view, Perspective transformation, Projective transformation

Publication based on the results of: Psychological mechanisms for completing cognitive tasks in human-digital interaction (2024)