Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion

Iglesias, José Pedro Lopes,1994Chalmers University of Technology,Chalmers tekniska högskola (författare)

Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when applying more general singular value penalties, such as weighted nuclear norm priors, direct optimization over the elements of the matrix is typically used. Due to non-differentiability of the resulting objective function, first order sub-gradient or splitting methods are predominantly used. While these offer rapid iterations it is well known that they become inefficient near the minimum due to zig-zagging and in practice one is therefore often forced to settle for an approximate solution. In this paper we show that more accurate results can in many cases be achieved with 2nd order methods. Our main result shows how to construct bilinear formulations, for a general class of regularizers including weighted nuclear norm penalties, that are provably equivalent to the original problems. With these formulations the regularizing function becomes twice differentiable and 2nd order methods can be applied. We show experimentally, on a number of structure from motion problems, that our approach outperforms state-of-the-art methods.

Olsson, CarlChalmers University of Technology,Lund University,Lunds universitet,Mathematical Imaging Group,Forskargrupper vid Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Lund University Research Groups,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH,Chalmers tekniska högskola(Swepub:cth)caols (författare)
Valtonen Örnhag, MarcusLund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)ma4173va (författare)
Vedaldi, Andrea (redaktör/utgivare)
Bischof, Horst (redaktör/utgivare)
Brox, Thomas (redaktör/utgivare)
Frahm, Jan-Michael (redaktör/utgivare)
Chalmers University of TechnologyChalmers tekniska högskola (creator_code:org_t)

Ingår i:Computer Vision – ECCV 2020 - 16th European Conference, 2020, ProceedingsCham : Springer International Publishing12372 LNCS, s. 21-370302-97431611-33499783030585822

Av författaren/redakt...: Iglesias, José P ...; Olsson, Carl; Valtonen Örnhag, ...; Vedaldi, Andrea; Bischof, Horst; Brox, Thomas; visa fler...; Frahm, Jan-Micha ...; visa färre...

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