Globally optimal estimates for geometric reconstruction problems
- 1 January 2005
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 2 (15505499) , 978-985 Vol. 2
- https://doi.org/10.1109/iccv.2005.109
Abstract
We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or nonoptimality - or a combination of both - we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve nonconvex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimumKeywords
This publication has 16 references indexed in Scilit:
- Globally convergent autocalibration using interval analysisPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2004
- Convex OptimizationPublished by Cambridge University Press (CUP) ,2004
- Exact two-image structure from motionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Optimal structure from motion: local ambiguities and global estimatesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Estimating the fundamental matrix via constrained least-squares: a convex approachPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Global Optimization with Polynomials and the Problem of MomentsSIAM Journal on Optimization, 2001
- Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric conesOptimization Methods and Software, 1999
- On the optimization criteria used in two-view motion analysisPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1998
- Shape ambiguities in structure from motionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1997
- Shape and motion from image streams under orthography: a factorization methodInternational Journal of Computer Vision, 1992