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Bundle Adjustment With and Without Damping
Author(s) -
Börlin Niclas,
Grussenmeyer Pierre
Publication year - 2013
Publication title -
the photogrammetric record
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 51
eISSN - 1477-9730
pISSN - 0031-868X
DOI - 10.1111/phor.12037
Subject(s) - control theory (sociology) , levenberg–marquardt algorithm , perturbation (astronomy) , matlab , reactance , gauss , trigonometry , computer science , mathematics , engineering , mathematical analysis , physics , voltage , artificial neural network , control (management) , quantum mechanics , artificial intelligence , operating system , machine learning , electrical engineering
The least squares adjustment (LSA) method is studied as an optimisation problem and shown to be equivalent to the undamped Gauss–Newton (GN) optimisation method. Three problem‐independent damping modifications of the GN method are presented: the line search method of Armijo (GNA); the Levenberg–Marquardt algorithm (LM); and Levenberg–Marquardt with Powell dogleg (LMP). Furthermore, an additional problem‐specific “veto” damping technique, based on the chirality condition, is suggested. In a perturbation study on a terrestrial bundle adjustment problem, the GNA and LMP methods with veto damping can increase the size of the pull‐in region compared to the undamped method; the LM method showed less improvement. The results suggest that damped methods can, in many cases, provide a solution where undamped methods fail and should be available in any LSA software package. Matlab code for the algorithms discussed is available from the authors.