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Widening the basin of convergence for the bundle adjustment type of problems in computer vision 10.17863/CAM.22241 Hong, Je Hyeong 000000032797553X Cipolla, Roberto 0000000289992151 Fitzgibbon, Andrew William 000000029839660X Zach, Christopher Bundle adjustment is the process of simultaneously optimizing camera poses and 3D structure given image point tracks. In structure-from-motion, it is typically used as the final refinement step due to the nonlinearity of the problem, meaning that it requires sufficiently good initialization. Contrary to this belief, recent literature showed that useful solutions can be obtained even from arbitrary initialization for fixed-rank matrix factorization problems, including bundle adjustment with affine cameras. This property of wide convergence basin of high quality optima is desirable for any nonlinear optimization algorithm since obtaining good initial values can often be non-trivial. The aim of this thesis is to find the key factor behind the success of these recent matrix factorization algorithms and explore the potential applicability of the findings to bundle adjustment, which is closely related to matrix factorization. The thesis begins by unifying a handful of matrix factorization algorithms and comparing similarities and differences between them. The theoretical analysis shows that the set of successful algorithms actually stems from the same root of the optimization method called variable projection (VarPro). The investigation then extends to address why VarPro outperforms the joint optimization technique, which is widely used in computer vision. This algorithmic comparison of these methods yields a larger unification, leading to a conclusion that VarPro benefits from an unequal trust region assumption between two matrix factors. The thesis then explores ways to incorporate VarPro to bundle adjustment problems using projective and perspective cameras. Unfortunately, the added nonlinearity causes a substantial decrease in the convergence basin of VarPro, and therefore a bootstrapping strategy is proposed to bypass this issue. Experimental results show that it is possible to yield feasible metric reconstructions and pose estimations from arbitrary initialization given relatively clean point tracks, taking one step towards initialization-free structure-from-motion. University of Cambridge 2018-05-19 Thesis Doctoral Doctor of Philosophy (PhD) en Microsoft Toshiba Research Europe https://www.repository.cam.ac.uk/handle/1810/275067 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/9b6714ff-a43e-4b05-b92b-1e26ef074f20/download 87eda9de84448d1f82354d60eee3eb5f https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/cacdacb6-1620-4608-83aa-b3e47ac617f5/download 94aaa5cc8576db3f462da4faaa2c1b5f https://www.rioxx.net/licenses/all-rights-reserved/ computer vision bundle adjustment nonlinear optimization variable projection joint optimization structure-from-motion matrix factorization pseudo object space error varpro wiberg nonlinear least squares 3d reconstruction