Generalizing Wiberg algorithm for rigid and nonrigid factorizations with missing components and metric constraints

In spite of intensive endeavor over decades, rigid and nonrigid factorizations under metric constraints, possibly in the presence of missing components, remain to be very challenging. In this work, we try to break the hard nut by generalizing to these problems the Wiberg algorithm, one of the most successful solutions for unconstrained bilinear factorization. To properly handle missing components, we advocate a bilinear factorization formulation with an extra mean vector. In spirit of the Wiberg algorithm, we first propose an efficient and initialization-insensitive algorithm for unconstrained factorization, posterior correction of whose solution offers reasonable initialization for metric upgrade. For factorization with metric constraints, we reformulate it into an unconstrained problem through quaternion parametrization, which merges elegantly into our unconstrained factorization algorithm. Extensive experiment results verify that our proposed methods are fast, accurate and robust to high percentage of missing components.