---
title: "Three-Dimensional Interpretation of Quadrilaterals"
authors:
  - "Gang Xu"
  - "Saburo Tsuji"
doi: ""
url: "https://ijcai.org/proceedings/1989/256"
pdf: "https://ijcai.org/proceedings/1989/0256.pdf"
venue: "Proceedings of the Eleventh International Joint Conference on Artificial Intelligence"
year: 1989
pages: "1610-1615"
track: "Vision and Robotics"
keywords:
---

# Three-Dimensional Interpretation of Quadrilaterals

Gang Xu, Saburo Tsuji

*Proceedings of the Eleventh International Joint Conference on Artificial Intelligence*, pages 1610-1615.

## 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 image 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.