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Improving the Numerical Stability of Structure from Motion by Algebraic Elimination

Summary: Improving the Numerical Stability of Structure from Motion
by Algebraic Elimination
Mireille Boutin a, Ji Zhang b and Daniel G. Aliaga c
a School of ECE, Purdue University, 465 Northwestern Av., West Lafayette, IN, USA;
bSchool of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, USA ;
cDept. of Computer Sc., Purdue University, 250 N. University St., West Lafayette, IN, USA.
Structure from motion (SFM) is the problem of reconstructing the geometry of a scene from a stream of images
on which features have been tracked. In this paper, we consider a projective camera model and assume that
the internal parameters of the camera are known. Our goal is to reconstruct the geometry of the scene up to
a rigid motion (i.e. Euclidean reconstruction.) It has been shown that estimating the pose of the camera from
the images is an ill-conditioned problem, as variations in the camera orientation and camera position cannot
be distinguished. Unfortunately, the camera pose parameters are an intrinsic part of current formulations of
SFM. This leads to numerical instability in the reconstruction of the scene. Using algebraic methods, we obtain
a basis for a new formulation of SFM which does not involve pose estimation and thus eliminates this cause of
Keywords: Structure from motion, Euclidean reconstruction, pose estimation, elimination theory, invariants.
Being able to accurately simulate large and complex 3D environments is a core challenge of today's computer
technology. Indeed for reasons of cost and speed, and to improve the richness of the 3D models, there is a


Source: Aliaga, Daniel G. - Department of Computer Sciences, Purdue University


Collections: Computer Technologies and Information Sciences