Three-Dimensional Interpretation of Quadrilaterals

Abstract

Quadrilaterals are figures with which everybody becomes familiar in his/her very early stage of education. By studying these seemingly simple figures we can obtain some insights into the nature of the general problem of interpreting contours. This paper discusses in detail how quadrilaterals are interpreted three-dimensionally, and draws feasible inferences about the general properties of the human system of processing line drawings. First the rectangularity regularity is proposed to be the prime constraint in the visual interpretation of quadrilaterals. The subjective image center and focal length (finite and infinite) are determined together with rectangle orientation. Secondly, interpretation of quadrilaterals as faces of a rectangular polyhedron is examined at both the geometrical level and the perceptual level. Finally the gravity regularity is proposed to derive constraints on the rectangle orientation by analyzing the relation among the camera, the ground and the rectangles supported by the ground.