New Rank Deficiency Condition for Multiple View Geometry of Line Features

Ma, Yi; Huang, Kun; Košecká, Jana

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https://hdl.handle.net/2142/103771 Copy

Description

Title

New Rank Deficiency Condition for Multiple View Geometry of Line Features

Author(s)

• Ma, Yi
• Huang, Kun
• Košecká, Jana

Issue Date

2001-05

Keyword(s)

• Multilinear constraints
• Rank deficiency condition
• Feature matching
• Image transfer
• Motion recovery

Abstract

In this paper, a new rank deficiency condition for multiple images of a line is presented. It is shown that a set of m image lines correspond to a unique 3-D line if and only if an associated (m-1 x 4 matrix Hl is of maximum rank 1. This condition is shown to be equivalent to all multilinear constraints among image lines, but it tremendously simplifies previously known derivations. Since rank deficiency is a purely linear algebraic condition, it gives rise to a set of natural linear algorithms for line matching, line transfer to a new view and motion estimation from images of multiple lines. These linear algorithms use all available data simultaneously without specifying a particular choice of image triplets. Hence apart from the initialization, the algorithms allow us to bypass trifocal tensors used for similar purposes. The theory and algorithms for the line case are developed in exact parallel to that for the point case. Geometric interpretation of the Hl matrix and the duality between point and line are also clearly revealed through this approach.

Publisher

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign

Series/Report Name or Number

Coordinated Science Laboratory Report no. UILU-ENG-01-2209, DC-201

Type of Resource

text

Language

en

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http://hdl.handle.net/2142/103771

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