General and nested Wiberg minimization: L2 and maximum likelihood
Venue
European Conference on Computer Vision, Springer (2012)
Publication Year
2012
Authors
Dennis Strelow
BibTeX
Abstract
Wiberg matrix factorization breaks a matrix Y into low-rank factors U and V by
solving for V in closed form given U, linearizing V (U) about U, and iteratively
minimizing jjY UV (U)jj2 with respect to U only. This approach factors the matrix
while eectively removing V from the minimization. We generalize the Wiberg approach
beyond factorization to minimize an arbitrary function that is nonlinear in each of
two sets of variables. In this paper we focus on the case of L2 minimization and
maximum likelihood estimation (MLE), presenting an L2 Wiberg bundle adjustment
algorithm and a Wiberg MLE algorithm for Poisson matrix factorization. We also show
that one Wiberg minimization can be nested inside another, eectively removing two
of three sets of variables from a minimization. We demonstrate this idea with a
nested Wiberg algorithm for L2 projective bundle adjustment, solving for camera
matrices, points, and projective depths.
