Inverse perspective projection of a line segment pair

Takeshi Shakunaga

Research output: Contribution to journalArticlepeer-review


This paper discusses how a line segment and segment pair in a 3‐dimensional space are constrained by an image obtained by their perspective projection. Also, it introduces the concept of polarity in the interpretation of a line‐segment image obtained under perspective projection and gives a definition of a spherical PAT curve. In addition, the relationship is explained between a PAT constraint [5], which is of an angle formed by two line segments on a plane, and the spherical PAT curve [7], which is a constraint of two line segments at an arbitrary position in a 3‐dimensional space (an extended idea of the former). Although the spherical PAT curve an be obtained formally by projecting a plane PAT curve onto a sphere, and this is justified for a semisphere, the meaning of this on the opposite semisphere has not been clarified with a justification. This paper justifies the sphere PAT curve by discussing the polarity of the segment interpretation, and explains its accurate meaning. This paper also describes the characteristics of a spherical PAT curve. The idea will have many applications to image understanding. Copyright © 1994 Wiley Periodicals, Inc., A Wiley Company

Original languageEnglish
Pages (from-to)22-32
Number of pages11
JournalSystems and Computers in Japan
Issue number4
Publication statusPublished - 1994


  • line segment pair
  • PAT constraint
  • Perspective projection
  • single image

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Hardware and Architecture
  • Computational Theory and Mathematics


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