Three-Dimensional Interpretation of Quadrilaterals

Abstract

The three-dimensional interpretation of two-dimensional images was studied by using quadrilateral patterns, and some relationships between their structure, depth, and shape interpretations were analyzed under various viewing conditions. We defined rectangular and nonrectangular viewing conditions as follows: the viewing condition in which the quadrilateral, including parallel sides, could be a projection from a rectangle and the viewing condition in which it could not be so. For 9 subjects, 10 measurements were made in each experiment. Analysis showed that a pair of parallel sides of a quadrilateral were viewed as parallel to the viewer's forehead when the sides were horizontal in the image plane and were seen as slanting in depth if they were slanted in the image plane. The quadrilateral composed of parallel and nonparallel sides was perceived as rectangular when viewed with foveal vision even though under the nonrectangular viewing condition, if that viewing condition was not so different from the rectangular viewing condition. The quadrilateral did not appear to be rectangular when viewed in peripheral vision even though the rectangular viewing condition was used.