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 ||Y - UV(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 L1, minimizing ||Y - UV(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 L1 bundle adjustment, the first algorithm for that problem. 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 L1 projective bundle adjustment, solving for camera matrices, points, and projective depths. 

Bio:  Dennis Strelow is an engineer on Google’s computer vision research team.  He is interested in structure-from-motion, vision-aided navigation, sensor fusion, and image classification.  His recent work includes Wiberg optimization, image feature hashing for improved image classification, and fast local descriptors for large-scale image and video classification.  Previously, he worked at Quantapoint and Honeywell, and received his B.S., M.S., and Ph.D. degrees from the University of Wisconsin, University of Illinois, and Carnegie Mellon, respectively.