Inverse perspective projection of a line segment pair

✍ Scribed by Takeshi Shakunaga

• Book ID: 104591627
• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 946 KB
• Volume: 25
• Category: Article
• ISSN: 0882-1666
• DOI: 10.1002/scj.4690250403

✦ Synopsis

Abstract

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.