Seminarium: Christopher Zach, Toshiba Research, Cambridge
Convex relaxation and variable projection methods for 3D reconstruction
In the first part of my talk I will give an introduction to the label assignment problem and how it can be used to perform joint volumetric 3D reconstruction and semantic segmentation. The underlying formulation is based on a unification of convex models for label assignment that were introduced for discrete and for continuous image domains. In the second part of my presentation I will describe how the basin of convergence in bundle adjustment can be drastically enlarged in order to obtain a faithful 3D reconstruction even from random initial camera parameters and 3D points. The key insight is that the bundle adjustment objective can be well approximated by a matrix factorization-like optimization problem, which can be very effectively solved by the variable projection method. We recently gained an understanding, why the variable projection method is required and why more straightforward optimization methods frequently tend to fail on this type of problems.