scholarly journals Invariants of six points and projective reconstruction from three uncalibrated images

1995 ◽  
Vol 17 (1) ◽  
pp. 34-46 ◽  
Author(s):  
Long Quan
Keyword(s):  
Projective Reconstruction ◽  
Uncalibrated Images

Projective reconstruction from line-correspondences in multiple uncalibrated images

2006 ◽  
Vol 39 (5) ◽  
pp. 889-896 ◽  
Author(s):  
A.W.K. Tang ◽  
T.P. Ng ◽  
Y.S. Hung ◽  
C.H. Leung
Keyword(s):  
Projective Reconstruction ◽  
Uncalibrated Images

scholarly journals A Linear Method to Derive 3D Projective Invariants from 4 Uncalibrated Images

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
YuanBin Wang ◽  
XingWei Wang ◽  
Bin Zhang ◽  
Ying Wang
Keyword(s):  
Linear Method ◽  
Projective Reconstruction ◽  
Reconstruction Problem ◽  
Linear Transformations ◽  
Explicit Formulas ◽  
Projective Invariants ◽  
Projective Invariant ◽  
Uncalibrated Images ◽  
Bilinear Equations ◽  
2D Images

A well-known method proposed by Quan to compute projective invariants of 3D points uses six points in three 2D images. The method is nonlinear and complicated. It usually produces three possible solutions. It is noted previously that the problem can be solved directly and linearly using six points in five images. This paper presents a method to compute projective invariants of 3D points from four uncalibrated images directly. For a set of six 3D points in general position, we choose four of them as the reference basis and represent the other two points under this basis. It is known that the cross ratios of the coefficients of these representations are projective invariant. After a series of linear transformations, a system of four bilinear equations in the three unknown projective invariants is derived. Systems of nonlinear multivariable equations are usually hard to solve. We show that this form of equations can be solved linearly and uniquely. This finding is remarkable. It means that the natural configuration of the projective reconstruction problem might be six points and four images. The solutions are given in explicit formulas.

scholarly journals Projective Reconstruction in Algebraic Vision

2019 ◽  
Vol 63 (3) ◽  
pp. 592-609
Author(s):  
Atsushi Ito ◽  
Makoto Miura ◽  
Kazushi Ueda
Keyword(s):  
Projective Space ◽  
Arbitrary Dimension ◽  
Projective Spaces ◽  
Rational Maps ◽  
Projective Reconstruction ◽  
Reconstruction Theorem

AbstractWe discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.

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