Algorithms for the recognition of 2D images of m points and n lines in 3D

✍ Scribed by R. Gleeson; F. Grosshans; M. Hirsch; R.M. Williams

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 165 KB
• Volume: 21
• Category: Article
• ISSN: 0262-8856
• DOI: 10.1016/s0262-8856(03)00029-5

✦ Synopsis

Let a be an ordered collection consisting of m points and n lines, m þ n $ 6; in three-dimensional space. Let b be an ordered collection consisting of m points and n lines, m þ n $ 6; in two-dimensional space. Using a and b; we construct a matrix Mða; bÞ and, then, give two algorithms for determining whether b is an image of a taken with a pinhole camera. These algorithms apply to any configuration, degenerate or not, consisting of points and lines. The first algorithm depends on the calculation of the nullspace of Mða; bÞ and gives necessary and sufficient conditions for b to be an image of a; if the data can be read exactly. The second algorithm depends only on the rank of Mða; bÞ and can be used if errors arise in reading the data; this algorithm also gives equations which any image of a must satisfy. In the special case m þ n ¼ 6; there is a single equation Jða; bÞ ¼ 0 which must hold if b is an image of a: We show that Jða; bÞ is simply the determinant of Mða; bÞ: We conclude with a discussion of some computational aspects of the theory.