Wiberg matrix factorization breaks a matrix Y into lowrank factors U and V by solving for V in closed form given U , linearizing V (U ) about U , and iteratively minimizing ||Y − U V (U )|| 2 with respect to U only. This approach factors the matrix while effectively removing V from the minimization. Recently Eriksson and van den Hengel extended this approach to L 1 , minimizing ||Y − U V (U )|| 1 . We generalize their approach beyond factorization to minimize an arbitrary function that is nonlinear in each of two sets of variables. We demonstrate the idea with a practical Wiberg algorithm for L 1 bundle adjustment. We also show that one Wiberg minimization can be nested inside another, effectively removing two of three sets of variables from a minimization. We demonstrate this idea with a nested Wiberg algorithm for L 1 projective bundle adjustment, solving for camera matrices, points, and projective depths. We also revisit L 1 factorization, giving a greatly simplified presentation of Wiberg L 1 factorization, and presenting a successive linear programming factorization algorithm. Successive linear programming outperforms L 1 Wiberg for most large inputs, establishing a new state-of-the-art for for those cases.
In a recent companion paper REF , we extended Eriksson and van den Hengel's L 1 -Wiberg factorization to minimize general nonlinear functions of two sets of variables, analogous to the L 2 and maximum likelihood general Wiberg we present here.
General and nested Wiberg minimization
2012 IEEE Conference on Computer Vision and Pattern Recognition
2012 IEEE Conference on Computer Vision and Pattern Recognition
Mathematics Computer Science