Rank Conditions of the Multiple View Matrix in Multiple View Geometry

Ma, Yi; Huang, Kun; Vidal, René; Košecká, Jana; Sastry, Shankar

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https://hdl.handle.net/2142/99583 Copy

Description

Title

Rank Conditions of the Multiple View Matrix in Multiple View Geometry

Author(s)

• Ma, Yi
• Huang, Kun
• Vidal, René
• Košecká, Jana
• Sastry, Shankar

Issue Date

2001-06

Keyword(s)

• Multiple view matrix
• Multilinear constraints
• Rank deficiency condition
• Feature matching
• Motion and structure recovery

Abstract

This technical report is a comprehensive collection of four self-contained technical papers which I have jointly written with my PhD student Kun Huang (UIUC ECE), PhD student Rene Vidal (UCB EECS), professor Jana Košecká (GMU CS) and professor Shankar Sastry (UCB EECS). It consists of a coherent treatment of multiple view geometry from a linear algebraic viewpoint. In particular, a newly introduced concept of multiple view matrix and its associated rank deficiency condition have been extensively studied for the purpose of 2-D to 3-D reconstruction. The proposed framework provides a brand new approach to multiple view geometry, which is independent of previous approaches based on projective geometry, tensor analysis or algebraic geometry, and which has, nonetheless, demonstrated significant theoretical and algorithmic advantages. The technical report adopts a homogeneous terminology - which makes it slightly different from each original paper. Each chapter corresponds to an original paper and it is still kept rather self-contained in this report. Although we are still in the process of grasping the full implication of the developed theory and algorithms and carrying out more experiments on real images, the report is contrived for the purpose of communicating among researchers who share the same interest in multiple view geometry and would like to try to extend the theory and apply to other applications.

Publisher

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign

Series/Report Name or Number

Coordinated Science Laboratory Report no. UILU-ENG-01-2215, DC-202

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/99583

Sponsor(s)/Grant Number(s)

• U.S. Army Research Office / DAAD19-00-1-0466
• National Science Foundation KDI initiative / SBC-MIT-5710000330
• ONR / N00014-00-1-0621
• GMU CS department startup fund
• UIUC ECE department startup fund

Owning Collections