Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Critical Configurations for Projective Reconstruction from Multiple Views
International Journal of Computer Vision
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Verifying Global Minima for L2 Minimization Problems in Multiple View Geometry
International Journal of Computer Vision
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Solutions to non-linear least squares problems play an essential role in structure and motion problems in computer vision. The predominant approach for solving these problems is a Newton like scheme which uses the hessian of the function to iteratively find a local solution. Although fast, this strategy inevitably leeds to issues with poor local minima and missed global minima. In this paper rather than trying to develop an algorithm that is guaranteed to always work, we show that it is often possible to verify that a local solution is in fact also global. We present a simple test that verifies optimality of a solution using only a few linear programs. We show on both synthetic and real data that for the vast majority of cases we are able to verify optimality. Further more we show even if the above test fails it is still often possible to verify that the local solution is global with high probability.