Differentiating between Affine and Perspective-Based Models for the Geometry of Visual Space Based on Judgments of the Interior Angles of Squares

Vision (Basel). 2018 Jun 2;2(2):22. doi: 10.3390/vision2020022.


This paper attempts to differentiate between two models of visual space. One model suggests that visual space is a simple affine transformation of physical space. The other proposes that it is a transformation of physical space via the laws of perspective. The present paper reports two experiments in which participants are asked to judge the size of the interior angles of squares at five different distances from the participant. The perspective-based model predicts that the angles within each square on the side nearest to the participant should seem smaller than those on the far side. The simple affine model under our conditions predicts that the perceived size of the angles of each square should remain 90°. Results of both experiments were most consistent with the perspective-based model. The angles of each square on the near side were estimated to be significantly smaller than the angles on the far side for all five squares in both experiments. In addition, the sum of the estimated size of the four angles of each square declined with increasing distance from the participant to the square and was less than 360° for all but the nearest square.

Keywords: affine transformations; angle judgments; perspective transformations; space perception; visual geometry; visual space.