Invariants of six points and projective reconstruction from threeuncalibrated images
Long Quan
LIFIA-CNRS-INRIAG, Grenoble;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Jan 1995
Volume: 17,
Issue: 1
On page(s): 34-46
ISSN: 0162-8828
References Cited: 33
CODEN: ITPIDJ
INSPEC Accession Number: 4871851
Digital Object Identifier: 10.1109/34.368154
Current Version Published: 2002-08-06
Abstract
There are three projective invariants of a set of six points in
general position in space. It is well known that these invariants cannot
be recovered from one image, however an invariant relationship does
exist between space invariants and image invariants. This invariant
relationship is first derived for a single image. Then this invariant
relationship is used to derive the space invariants, when multiple
images are available. This paper establishes that the minimum number of
images for computing these invariants is three, and the computation of
invariants of six points from three images can have as many as three
solutions. Algorithms are presented for computing these invariants in
closed form. The accuracy and stability with respect to image noise,
selection of the triplets of images and distance between viewing
positions are studied both through real and simulated images.
Applications of these invariants are also presented. Both the results of
Faugeras (1992) and Hartley et al. (1992) for projective reconstruction
and Sturm's method (1869) for epipolar geometry determination from two
uncalibrated images with at least seven points are extended to the case
of three uncalibrated images with only six points
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