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Title:Rank Conditions of the Multiple View Matrix in Multiple View Geometry
Author(s):Ma, Yi; Huang, Kun; Vidal, René; Košecká, Jana; Sastry, Shankar
Subject(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.
Issue Date:2001-06
Publisher:Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report:Coordinated Science Laboratory Report no. UILU-ENG-01-2215, DC-202
Genre:Technical Report
Description:The report number is incorrectly printed as DC-220 on the cover and in the front matter. This is in fact report DC-202.
Sponsor: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
Date Available in IDEALS:2018-04-03

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